Quantum Information - Science topic

Is it more strategic for developing countries like Pakistan to first focus on awareness and training in quantum computing to build a knowledgeable workforce, and then invest in quantum computer development once the ecosystem is ready? What are the potential benefits and challenges of this phased approach compared to an immediate focus on quantum computer development?

I'm trying to implement BB84 on a network, however I don't have a source code that is backed by any organization or a peer reviewed paper. Any help would be appreciated.

Thanks!

Hello all,

In CV QKD, in general, there is two noise sources in the system. the shot-noise, which is the fundamental noise of the signal and arises from quantization of the electromagnetic field, and the excess noise, that includes all other noises present in the system and also the noise introduced by the eavesdropper. In CV QKD, in order to determine whether the eavesdropper detected the signal or not, it is important that the detector able to distinguishes the shot noise contribution to the total noise from the excess noise. To do so, it is proposed to utilized shot noise limited homodyne detection. Why?

-What is the different between the shot noise limited homodyne detector and usual homodyne detectors?

-Is it possible to consider a usual homodyne detector as a shot-noise limited one in special conditions? If yes, what is that conditions?

Bests

I've recently seen some references to Dark Energy and Entanglement as possibly being related, but I haven't been able to fully evaluate such claims, though they got me thinking.

My basic question is about the persistence of relationships and correlations created by wavefunction interactions. Reading Penrose's Road to Reality, it struck me that he said something like "much of the wavefunction is concerned with such matters," meaning nonlocal matters.

Entanglement and nonlocal correlations are created or transferred through interactions between quantum systems. When a photon from an entangled pair is absorbed by Bob's detector, is the correlation with Alice's photon then passed on into the wavefunction of Bob's detector? Or is that correlation--whatever it is--completely destroyed, lost to the *entire* system, not just the entangled pair? (If destroyed, then how can entanglement be erased/restored?)

If correlations somehow persist as some form of information, do they accumulate and flow through the vast number of interactions in large local systems, for example, is there a quantity of non-local correlations largely trapped in the core of our sun that slowly leaks out through light and the solar wind?

Conversely, what are the effects of "ancient" correlations that may persist from very early events such as the breaking of the symmetry between the electric and magnetic forces or from the sudden end of the "dark ages" when light began to flow?

Sorry for "big" pile of questions. This is a hard one to boil down to a five word question!

I had a short paper rejected by Phys Rev X (below). Obviously, not easy to publish in PRX.

My question: if there is a fatal flaw, as implied by PRX, then what is that flaw ?

This paper was given short shrift, rejected just after submission. Thus, not even sent for expert review. I have asked for any feedback.

CCUCUUUCCUCUCUU…-type digital signalling, based on collections of collapsed (C) and uncollapsed (U) ensemble-pairs, transmitting 1 bit per ensemble-pair with no state cloning, does not appear to be disallowed by either the No Communication Theorem, or the No Cloning Theorem. https://en.wikipedia.org/wiki/No-communication_theorem

I suspect that the wiki derivation of the No Communication Theorem final equality, depends implicitly on symmetry. Clearly, the derivation is symmetric. If asymmetry is introduced in the entangled wave function, and in weakly rather than maximally entangled Bell states, then I suspect that the final equality does not hold in general.

If so, then DQT is important in principle, despite the practical difficulties, e.g., turning off the laser beam, thermalisation and decoherence.

Digital Quantum Teleportation

Author: W. Batty

Email: WllmBatty@aol.com

Homepage: https://www.linkedin.com/in/william-batty-0889238/

Affiliation: WB Analytical Ltd, **, UK

Date: 28 April 2021

1. Abstract

Conventional quantum teleportation requires a classical Alice->Bob co-channel, for transmission of decode information, hence actual information transfer. This paper proposes digital quantum teleportation, requiring no such co-channel.

In principle, digital QT allows infinite speed information transfer, without attenuation or maximum range. Though always with inevitable measurement speed limitation.

2. Introduction

Quantum teleportation is increasingly well explored and has been demonstrated all the way from semiconductor chip level [1], to earth-to-orbiting-satellite over distances ~1000 km [2].

The usual requirement for a classical Alice->Bob co-channel, for transmission of decode information, hence actual information transfer, means that the effective speed of information transfer is at the speed of light, or below.

However, using digital signalling, that co-channel is not required for actual information transfer.

Thus, no upper speed, or range, limitation.

What is new, is that nobody has proposed previously, any viable-looking method for instantaneous communication across arbitrary distances, up to the scale of the whole Universe, without attenuation.

This is not standard Quantum Teleportation or Quantum Mechanics. The proposed Digital Quantum Teleportation is totally original, in this regard.

Consider N boxed collections, or ensembles, of entangled qubit-pair halves, 1a-1b, 2a-2b, ..., Na-Nb.

It is clear that collapsing fully by measurement, an a-box ensemble, C, or leaving completely uncollapsed an a-box ensemble, U, will be decidable unambiguously by measurement/observation of the respective entangled b-box ensembles.

There appear to exist viable experimental configurations, in which we can distinguish immediately C from U (without requiring a classical co-channel for Alice->Bob relay of decode information), thus allowing digital signaling, CCUCUUUCCUCUCUU... .

Collapsed and uncollapsed ensembles, C and U do generally appear to be unambiguously distinct. For instance, for maximally entangled Bell states, b-box ensembles appear to split 50:50 for C, and |alpha|^2:|beta|^2 for U, or for weakly entangled Bell states, |E|^2:|F|^2 for C, for some general alpha ≠ beta and E, F.

Given achievable experimental configurations realising the above basic requirements, DQT would appear viable. The flip-side argument would appear to be that DQT will be non-achievable, only if no such configuration exists. The achievability of such experimental configurations is described further, below.

The classical co-channel, e.g., laser beam, can be retained, if necessary. All that is required, is that it does not transmit or relay, actual information.

3. Further Discussion

The key step of the proposed DQT method, is to use entangled qubit-pair ensembles. And then either collapse them fully, or not at all.

Consider N qubit-pair ensembles, 1a-1b, 2a-2b, ... Na-Nb, each containing M entangled qubit-pair halves, all prepared in the same way: pure state |psi>, and entangled state |psi-entangled>,

|psi> = A |1> + B |1>'

|psi-entangled> = alpha |1> |1>' + beta |1>' |1>

where generally, alpha ≠ beta, i.e., alpha, beta ≠ 1/sqrt(2) (to phase factor).

The pure state must be further entangled with the already entangled pair state, for QT.

No cryptography involved here. No complicated info-coding or -decoding.

Always collapse everything, all qubit-pairs of an ensemble in any a-box, e.g., all to states |1> or |1>’, by measurement. Then the corresponding b-box goes to all |1>' or |1>, respectively. Nothing unknown at all. States collapse in well-defined proportions, e.g., 50:50 for maximally entangled Bell states.

For an uncollapsed a-box, the corresponding b-box will always be mixed, |alpha|^2:|beta|^2, where generally, alpha ≠ beta. Thus, we can either collapse any a-box, or not collapse that a-box. Collapse any a-box in this fashion, and the corresponding b-box states will be 50:50, |1> and |1>,' for maximally entangled Bell states. Do not collapse any a-box and the corresponding b-box states will be mixed |alpha|^2:|beta|^2, with alpha ≠ beta, generally.

Thus, we can always tell unambiguously, when we have collapsed, or not collapsed, an a-box.

Then digital signalling in terms of collapsed, C, or uncollapsed, U, ensemble box-pairs just looks like: CCUCUUUCCUCUCUU... .

Thus, direct digital information transfer. Instantaneous transmission. Infinite range. Zero attenuation. Though clearly, finite measurement speed.

-- Apart from actual measurement times, in principle, instantaneous actual info-transmission, potentially across the whole Universe.

Thus, actual digital info transfer, without any classical Alice->Bob co-channel.

-- No 'at or less than the speed of light' classical transmission.

-- For the simplest digital transmission, with no encoding/decoding scheme, this gives arbitrary upper speed limit, depending on speed of measurement and distance transmitted.

-- A much simpler method than conventional quantum teleportation. No cryptography. Unless at digital coding CCUCUUUCCUCUCUU... level.

The method depends squarely on the observation that for boxed collections, or ensembles, of entangled qubit-pair halves, 1a-1b, 2a-2b, ..., Na-Nb, it is possible to distinguish unambiguously between b-box collections corresponding respectively to fully collapsed, C, or completely-uncollapsed, U, a-box collections.

Consider N box pairs, 1a-1b, 2a-2b, ... Na-Nb, each containing M entangled qubit-pair halves, all prepared in the same way. Roughly,

|psi > = A |1> + B |1>'

|psi-entangled> = alpha |1> |1>' + beta |1>' |1>

Where generally, alpha ≠ beta, i.e., alpha, beta ≠ 1/sqrt(2) (to phase factor).

Looking at YouTube, MinutePhysics, 'How to Teleport Schrodinger's Cat' [4], the situation looks only slightly more complicated.

The fully entangled state, comprising state to be teleported, plus already entangled qubit pair, is more like:

|psi-fully entangled> = (A |1> + B |1>')_a (alpha |1> |1>' + beta |1>' |1>)_b

Then when the indirect Bell measurement is made and collapsed to one of four Bell states, the fully entangled particle ends up in one of four linear superpositions,

C |1> + D |1>'

and it is those C and D (given in terms of A, B, alpha, beta) that the Alice->Bob decode signal must distinguish.

After entanglement, a-boxes are measured indirectly by Bell measurements, collapsing into one of four states. For the collapsed collection, or ensemble, C, of qubit-pair halves in that a-box, this gives M1, M2, M3 and M4 respective collapsed Bell states, where M1 + M2 + M3 + M4 = M.

In the respective b-box, we then get a linear combination of |1> and |1>' states, dependent on M1, M2, M3 and M4, A, B, alpha, beta. For that b-box ensemble, corresponding proportions of |1> and |1>' states, are then some |C|^2 and |D|^2.

For a b-box corresponding to an uncollapsed a-box, U, the proportions of |1> and |1>' states in the b-box ensemble, will be the original |alpha|^2 and |beta|^2, respectively (independent of any M1, M2, M3, M4).

Thus, again the C and U situations appear unambiguously distinct, so long as the combination of M1, M2, M3, M4, A, B, alpha and beta, for C, does not recombine to give the same |alpha|^2 and |beta|^2 proportions as for U.

Checking, C and U do generally appear to be distinct. For instance, b-box ensembles appear to split 50:50 for C, and |alpha|^2:|beta|^2 for U, for maximally entangled Bell states, or some |E|^2:|F|^2 for C, for weakly entangled Bell states, for general alpha ≠ beta and E, F.

In Special Relativity, the Michelson-Morley experiment only demonstrates that the speed of light in vacuum, c, is the same in all inertial frames.

This does not place any upper speed limit at all on particle or body dynamics.

The Minkowski frame is about Lorentz Transformations, specifically relating coordinates in one frame, (x,t), to those in another, (x’,t’). And SR space is actually R3 x R, not M4.

For non-local QM, I think there is no obvious reason to consider any upper speed limit on particle or body dynamics at all. Nor on DQT.

For a 'most fundamental' quantum theory, the whole structure would be dynamics of free particles, with intermittent particle interconversion. On this basis, i.e., particle dynamics, there would appear to be no reason that SR places any upper speed limit at all on such a 'most fundamental' theory.

Then there is the interesting notion that a particle passing through the speed of light in vacuum, c, might create an 'optic' boom (as a parallel to a sonic boom). Though this is not obvious in the absence of an ether, in contrast to air for the sonic case.

However, for QM non locality and QDT, I would not expect this to be a physical faster-than-light effect. Rather, actual information transfer at effectively faster-than-light speed.

On any potentially related notions like implied time travel possibilities, it appears that irrespective of any detailed physical model at all, if extant 4D (or other) space-time contains time-travel, then time-travel exists, and if it doesn't, then time-travel does not exist.

Thus, for example, Tolman's 'paradox' [5][6]. However, this would assume validity of the Lorentz Transformation for signal propagation which is not classical electromagnetic wave at speed in vacuum, c.

In the context of Digital Quantum Teleportation, there would appear to be no good reasons to rule out any possible ramifications at all. The point would be for a capable team, to try an experiment.

Consider various possibilities for backwards-in-time travel:

(i) extant, self-consistent, 4D (or other) static space-time, with closed time (and perhaps space)-like loops.

(ii) extant, self-consistent, 4D (or other) static space-time, with (perhaps repeated) branching of that space-time at jump-back singularities.

In neither case, can you go back and ‘kill your own grandfather’, preventing your own birth.

(iii) tachyon particle or body backwards-in-time travel, by acceleration of particle or body to greater than the speed of light in vacuum, c, then Tolman’s ‘paradox’ (to the extent that it is consistent).

Speed of light upper limit assumed non-applicable to particle or body, but Lorentz transform assumed with speed, c. Is that a consistent position ?

(iv) Digital Quantum Teleportation, instantaneous, non-local, digital signalling, across arbitrary distances, then Tolman’s ‘paradox’.

Non-local, digital signalling, across arbitrary distances, but Lorentz transform assumed with speed, c. Is that a consistent position ?

Tolman used the following variation of Einstein’s thought experiment [6][7]. Imagine a distance with end points A and B. Let signal be sent from A propagating with velocity, va, towards B. All of this is measured in an inertial frame where the endpoints are at rest. The arrival at B is given by:

Δt = t1-t0 = (B-A)/va.

Here, the event at A is the cause of the event at B. However, in the inertial frame moving with relative velocity v, the time of arrival at B is given according to the Lorentz transformation (c is the speed of light):

Δt’ = t1’-t0’

= (t1 – Bv/c2) / ϒ – (t0 – Av/c2) / ϒ

= (1 – va v/c2) Δt / ϒ,

ϒ = sqrt(1 – v2/c2).

It can then be easily seen that if va > c, then certain values of va, v can make Δt' negative. In other words, the effect arises before the cause in this frame. Einstein (and similarly Tolman) concluded that this result contains in their view no logical contradiction; he said, however, it contradicts the totality of our experience so that the impossibility of va > c seems to be sufficiently proven.[7]

On the working assumption that va > c is already a thing, this says that information can be propagated backwards in time, in some reference frames. Those frames in which va > c, either by particle or body acceleration past the speed of light in vacuum, c, (to become ‘tachyonic’ particles or bodies), or for which non-locality and instantaneous transmission of actual information, occurs at an effective va > c, once finite measurement speed is accounted for, allow actual information transfer backwards in time.

Note, however, the implicit assumptions and contradictions (!). For the particle or body, accelerated past the speed of light to tachyonic, and for the effective faster-than-light, non-local, info-propagation, a Lorentz transformation is being assumed for the Tolman paradox, and based on the standard limiting speed, c. These look inconsistent. It may be that the Lorentz transformation is inapplicable. And no backwards-in-time possibility actually arises.

For sake of argument, assume consistency of the above, in some appropriate forms, to complete the discussions.

Arguably, as soon as any information is sent backwards in time, the space-time continuum splits at the jump-back singularity. This conclusion is based on the butterfly effect for the coupled Earth atmosphere-ocean chaotic weather system. Once backwards-propagated information dissipates as heat in the atmosphere, a hurricane could develop on the other side of the world, which might not have developed otherwise. For speed of sound in air, around ~15+ hours later, assuming some initial exponential growth of small perturbation to make its impact detectable on the other side of the globe. Mostly, new hurricanes will not occur.

The above is a self-consistent picture. The typical contrasting picture, is the usual, also fully self-consistent one, with an assumed single time-line, no space-time splitting [8].

Particle or body acceleration past the speed of light [9], are not precluded by the Michelson-Morley experiment. However, no such speed has ever been achieved experimentally. Digital Quantum Teleportation [9] suggests instantaneous signalling across arbitrary distances with zero attenuation, thus effective, greater than the speed of light, actual info-transfer. This has also not been demonstrated experimentally.

However, if either is achievable, is it possible that backwards-in-time travel of actual information might be possible. If so, the result could be (allowing for the possible formulation inconsistencies flagged above), splitting of the 4D (or other) static space-time continuum.

For safety critical systems, e.g., the Earth, what reasonable assumptions to adopt when contemplating implementing any approach which might imply backwards-in-time travel, e.g., any non-local signalling.

Experiments are required. And if performed, must be performed with due caution.

As a related example, how often are calculations of possible mini-black-hole formation, say, revised against increasing Large Hadron Collider energies ? What reasonable assumptions to weigh against any risk of the Earth being swallowed by a mini-black-hole ? Are LHC safety assumptions re-visited regularly, or could experiments such as those above, be regarded as reckless ?

4. Conclusion

A digital QT scheme has been described, which should allow infinite speed propagation of actual information, without attenuation, over arbitrary distances.

The above would, in principle, allow instantaneous communication across the whole Universe.

An interesting speculation then arises whether the necessary entangled quantum well pairs might already be extant, from the Big Bang. Completely speculatively, consider the possibility that close proximity might be enough to induce quantum entanglement. Consider that entanglement might survive particle interconversion. Finally, consider R^3 x R expansion of Universe space-time, from a well-defined Big Bang centre (not a Universe with no centre, just for simplicity). Then, for the simplest spherical expansion from a point, suitable entangled pairs would lie along radii from current position to centre of Universe, ready to be gathered into relatively displaced ensembles for DQT.

5. Acknowledgement

William Batty would like to acknowledge Philip Gilchrist for helpful discussions.

6. References

[1]: Bennett, Charles H.; Brassard, Gilles; Crépeau, Claude; Jozsa, Richard; Peres, Asher; Wootters, William K. (29 March 1993). `Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels'. Physical Review Letters. 70 (13): 1895–-1899. doi:10.1103/PhysRevLett.70.1895.

[2]: `Satellite-based entanglement distribution over 1200 kilometers'.

Juan Yin1,2, Yuan Cao1,2, Yu-Huai Li1,2, Sheng-Kai Liao1,2, Liang Zhang2,3, Ji-Gang Ren1,2, Wen-Qi Cai1,2, Wei-Yue Liu1,2, Bo Li1,2, Hui Dai1,2, Guang-Bing Li1,2, Qi-Ming Lu1,2, Yun-Hong Gong1,2, Yu Xu1,2, Shuang-Lin Li1,2, Feng-Zhi Li1,2, Ya-Yun Yin1,2, Zi-Qing Jiang3, Ming Li3, Jian-Jun Jia3, Ge Ren4, Dong He4, Yi-Lin Zhou5, Xiao-Xiang Zhang6, Na Wang7, Xiang Chang8, Zhen-Cai Zhu5, Nai-Le Liu1,2, Yu-Ao Chen1,2, Chao-Yang Lu1,2, Rong Shu2,3, Cheng-Zhi Peng1,2,*, Jian-Yu Wang2,3,*, Jian-Wei Pan1,2,*

1Department of Modern Physics and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China.

2Chinese Academy of Sciences (CAS) Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China.

3Key Laboratory of Space Active Opto-Electronic Technology, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China.

4Key Laboratory of Optical Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China.

5Shanghai Engineering Center for Microsatellites, Shanghai 201203, China.

6Key Laboratory of Space Object and Debris Observation, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, China.

7Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi 830011, China.

8Yunnan Observatories, Chinese Academy of Sciences, Kunming 650011, China.

↵*Corresponding author. Email: pcz@ustc.edu.cn (C.-Z.P.); jywang@mail.sitp.ac.cn (J.-Y.W.); pan@ustc.edu.cn (J.-W.P.)

Science 16 Jun 2017:

Vol. 356, Issue 6343, pp. 1140-1144

DOI: 10.1126/science.aan3211

[3]: https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#

[4]: YouTube, MinutePhysics, 'How to Teleport Schrodinger's Cat’

[5]: Tachyonic antitelephone - Wikipedia

[6]: Einstein, Albert (1907). "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen" [On the relativity principle and the conclusions drawn from it] (PDF). Jahrbuch der Radioaktivität und Elektronik. 4: 411–462. Retrieved 2 August 2015.

[7]: R. C. Tolman (1917). "Velocities greater than that of light". The theory of the Relativity of Motion. University of California Press. p. 54. OCLC 13129939.

[8]: Germain 9 et al, Reversible dynamics with closed time-like curves and freedom of choice, Classical and Quantum Gravity (2020). DOI: 10.1088/1361-6382/aba4bc

[9]: https://www.linkedin.com/pulse/bankers-safety-critical-systems-using-maths-models-correctly-batty and related LinkedIn-blogged articles at the same site.

So where is the fatal flaw ? All thoughts and comments welcome.

Is there an equation connecting the wave function and the entropy of the quantum system?

As NV centers are surrounded by electrons, and electron spin is used as qubits but nuclear spin acts as a source of decoherence by creating a varying magnetic field. Now if the NV center is in quantum superposition state due to the decoherence the changes in energy levels will cause dephasing and eventually, the loss of quantum state. To counter this we apply an RF pulse to invert the state of NV center which inverts the effect of the magnetic field on the spin. This is justified by the fact that 'if we have the same time before and after this flip the effect of the field is canceled and quantum state is protected.' But how? And will the noise present in the system affect the protected quantum state? Can't these controlled spin be manipulated in a way so that they can act as qubits and help in carry extra information?

I am looking for Journals that accept and publish papers on Quantum Information and Computing.

I want to know whether these non-equilibrium can transport quantum information in the case of quantum heat engine?

#non-equilibrium_steady_states

#quantum_heat_engine

#quantum_information

In my(very little) understanding of convexity, I am unable to understand how can a set of superchannel(that takes channels in system A to channels in system B) be convex.

We call a function f to be convex if:

f(\sum_{i} a_i x_i ) <= \sum_{i} a_i f(x_i)

[where \sum_{i} a_i = 1]

But in the case of superchannels , f is a superchannel and x_i are appropriate channels. Now, how do we compare channels on either side of the inequality?

There are different simulators aimed at designing quantum circuits. Posing this question is to get familiar with the best ones. Your suggestions are really appreciated.

There is no need of further explanation

As both the SG and DS experiment obey the superposition principle, is it possible that Stern Gerlach experiment with single atom will show the phenomena like that of the ‘which way’ experiment, i.e. the single electron (atom) will be available simultaneously at both spin states?

Quantum information theory (QIT) subsumes several subfields of mathematics. What are these topics? How well qubits fit mathematical physics? Can QIT helps to solve mathematical conjectures?

Please give some hints here or submit a mathematical paper in this special issue of MDPI Mathematics

In Stern-Gerlach system cascade we get electrons of two states (spin up and spin down) even after filtering out any of the one set. We know an intrinsic property is a property that an object or a thing has of itself, independently of other things, including its context. Then how it is legitimate to say that the spin is an intrinsic property of the electron?

In fact, I'm working on a thesis project on Quantum Information and precisely on quantum error correcting codes. I just started not long ago my research on the subject, and specifically how one can go from a classical signal to a quantum signal to describe the algorithms of error correction codes in physical channels.

The original question was wrong thus was completed rewritten.

Context:

Suppose I have a 3 d particle placed in a spherical box of infinite well from [-r,r] in all three directions, it's expectation value of position thus equaled to 0.

Thus its surface area equaled to $4 \pi r^2$

From quantum gravity, (existence) https://arxiv.org/pdf/gr-qc/9403008.pdf and (a fairly good numerical approximation) https://en.wikipedia.org/wiki/Planck_length we knew that space and time were quantized fractions. Suppose the minimum length equal to ds, then the maximum partition of the surface of the spherical ball equal to $N= 4 \pi r^2/ds^2$.

Which meant that, as the increase of r, the number of possible segment that our probe could be placed will increase.

In analogy, suppose I have a particle of spin 1/2. Where we place the particle at the center of the ball and measure its spin. Then the ball with larger r could have more "segment" area for observation.

Question 1

Was these analysis true? If not, why? Further what's its implication?

Question 2

Suppose I created a pair of such spin 1/2 particle entangled together. One placed in a ball of $r_a$ the other placed in a ball or $r_b$. If $r_b>r_a$, then our measurement could be more "precise" about the ball b than ball a.

In an imaginary extreme case where $N=4 \pi r_a^2/ds^2=2 $, measurement for ball a thus could only be up or down.

What's happened to the information here? Were they still consist?

Clarification:

1 in question 2, since it's an infinite well(although it was not possible in real), It did not had to be exact in the "center" of $(0,0,0)$. By the fact that the particle was not at the boundary, and, since it's spherical coordinates, by symmetry, position expectation value was at the center. In fact, it didn't even have to be at the center position. Wave was good. The encoding was based on the probability of $T_{funning}$ was selected such that it equaled to 0 or $<<1$. Thus could be ignored regard to numerical calculation.

2 the imaginary extrem was based on the fact that electron's classical readius was in e-16 and plunk length was in e-32 thus $N=2$ could not happen, but just to demonstrate the idea.

Feel free to ask question about the context.

All the research papers I found so far, are just showing measurement of the squeezing parameter or quantum Fisher Information (QFI). Of course authors mention that, due to large QFI or strong squeezing this setup can be used for metrological purposes beyond standard quantum limit (SQL). I could not find any papers, which actually perform estimation of the unknown phase and show that the precision is beyond SQL. I am curious from the point of view of estimation in the presence of decoherence (which is always present). Theoretical papers indicate that entangled states are basically useless if frequency is estimated (e.q. Ramsey spectroscopy).

Which one is better?

For a higher-dimensional space, I am not sure which encoding scheme is better. Does anyone have suggestions?

The issue whether the wave-function is ontic or not is widely debated. In general people dealing with quantum computing see the wave-function as carying "information". When we perform a classical measurement on an object which is in a superposition of eigenstates of some operator Â, and get some eigenvalue a_j of Â, it is said that we got more exact information.

I saw sometimes such statements, but now when I would like to comment them, I don't find references.

Can somebody indicate me references?

Even though they say information is conserved, can information be biased at the first place?

Example:

Example 1:

Observer A and B saw a 10 *10 matrix. However, due to technique reason(for example, A was very short and B was tall enough) A could only say the last role, yet B was able to see all 10 rolls. Thus even the matrix was the same, A and B had different answers due to observation limits.

Example 2:

Observer A  and B saw a 10 character string 0101010101. However, A use the binary system reading and got 341, B use decimal reading thus got 101010101. Thus even the character string was the same,  A and B got different answers due to interpretation.

Example 3:

Observer A  and B was in a massive gravitational field near a black hole, yet non of them was aware of the situation. B was close to an object and observed it as a cube, A was far away from the field and the object and observed it as an "oval". Thus even the object was the same, A and B got different answers.

e.t.c.

That was, even though the observer agreed on the result/measurement, or agreed on the observation of the outcomes; can the information they preserved being biased towards each other?

I have had a paper published that demonstrates how DNA acts as a quantum logic processor. It is entitled “Model of Biological Quantum Logic in DNA”, and it can be accessed at http://www.mdpi.com/2075-1729/3/3/474

The paper shows how the DNA molecule can act as a quantum logic processor via the demonstrated properties of coherent electron conduction along the pi stacking interactions of the aromatic nucleotide bases and electron spin filtering by interaction of the helicity of the DNA molecule with the spin of coherently conducted electrons, and also by the theoretical property of a logically and thermodynamically reversible enantiomeric symmetry in the deoxyribose moiety that allows nucleotides to act as quantum gates that are coherently concatenated by the above mentioned pi stacking interactions.

A video of a presentation that I made on this topic at the Research Seminar of the University of Tennessee Graduate School of Medicine on March 19, 2013 further illustrates the concepts involved, and it can be accessed at https://www.youtube.com/watch?v=GgPOhhx6hcQ

I would appreciate any comments.

I am interested to find out if there is any method for computing the trace distance between two arbitrary bosonic quantum Gaussian states. It is simple to compute the trace distance between two thermal states because they are both diagonal in the photon-number-state basis. The same is true for coherent states because they are pure, we can then related to fidelity, and there are known expressions for the fidelity between two arbitrary bosonic quantum Gaussian states. (In fact, we can get the trace distance for any two pure quantum Gaussian states by relating to fidelity.) But in general, it seems like a challenging question.

Suppose we know the mathematical description of the states of the two parties A and B. The states are \rho_A and \rho_B respectively and they are mixed states. So the joint state \rho_AB is an entangled state. My question is if we know the mathematical description of \rho_A and \rho_B, how can we formulate \rho_AB? What if the dimension of \rho_A and \rho_B are not the same?

Can anyone please explain how we can evaluate quantum correlation between two feature subset vectors (or two qubit states)?

Some Hermitian Hamiltonians like H = p²  + x ² + x^2m+1

do  not have boundstate behaviour . If this is so ,why we consider all hermitian operators yield real eigenvalues ? The basic formulation of quantum mechanics.

Suggest T-symmetry Hamiltonians having real spectra .

What are the tests/conditions/inequalities which certify the genuine multipartite non-locality? As genuine multipartite entangled state may not violate any Bell inequality.

Dear All

I am running pw.x calculations for Mo2C (orthorhombic) supercell of size 1x1x3 and 2x2x2. The calculations terminating with an error "Primary job terminated normally, but 1 process returned a non-zero exit code.. Per user-direction, the job has been aborted". The energy values goes up and down and the structure is not converging towards low energy value. The cell parameters are according to the .cif files (crystallography.net) and updated according to cell size. 

However the calculation with 1x1x2 Mo2C works fine without any error. By increasing the cell the above mention error arises. I tried with altering the nbnd, degauss, electron maximum steps, but the problem remains same.

mpirun -np 32 ./pw.x -npool 8 < File.input > File.out 

&control

calculation = 'relax'

title = 'Mo2C'

verbosity = 'minimal'

wf_collect = .false

nstep = 2000

prefix = 'BP'

pseudo_dir ='/home/pr1edc00/pr1edc03/PSP/'

/

&SYSTEM

ibrav = 0

nat = 36

ntyp = 2

nbnd = 210

ecutwfc = 50

occupations = 'smearing'

degauss = 0.001

smearing = 'methfessel-paxton'/

&ELECTRONS

electron_maxstep = 300

conv_thr = 1D-5

startingpot = 'atomic'

startingwfc = 'atomic'

diagonalization = 'david'

/

&IONS

ion_dynamics = 'bfgs'

/

&CELL

cell_dynamics = 'bfgs'

cell_dofree = 'z'

/

Atomic species

#

so on

Can anyone assist me to solve this error.

Thank you in advance

Spinning black holes are capable of complex quantum information processes encoded in the X-ray photons emitted by the accretion disk

We have scalar and cross product. Cross product works in 3D only. But why not define a torque in 2D? Or 4D?

Imagine now that we don't know anything about products of vectors. How to multiply? For two vectors a and b it would be the product ab. It is natural to expect distributivity and associativity, but not commutativity (cross product). So, let us decompose our new product (symmetric and antisymmetric part)

ab = (ab + ba)/2 + (ab - ba)/2

It is straightforward to show that antisymmetric part is not a vector (generally squares to negative real number)!

Now we have a simple rule: parallel vectors commute, orthogonal vectors anti-commute. For orthogonal vectors we have Pythagoras theorem without metrics! 

In 3D (Euclidean) we have for orthonormal basis

e_ie_j + e_je_i = 2 d_ij , d_ij is Kronecker delta symbol.

You see, it is Pauli matrix rule, ie, Pauli matrices became 2D matrix representation of orthonormal basis vectors in 3D. 

This is geometric algebra (Grassmann, Clifford, Hestenes, ...).

My question is NOT to discuss geometric (or Clifford) algebras, it is about a general concept of number. How to multiply vectors?

If one accepts new vector product it changes everything! So, what are objections to such a concept (Clifford)? Could somebody suggest another multiplication rule? 

To all researchers in quantum physics and / or systemic constellation: Please have a critical look at this paper referring to the above question.

The paper “Indication that quantum physical mechanisms are applicable to human activities” investigates how the phenomena in systemic constellations can be explained.

See attached PDF!

In most cases, the difference value of Monogamy Inequality is used to measure multipartite entanglement. However, for the quantum systems which violate Monogamy Inequality, how to design a general way to measure multipartite entanglement? It puzzles me very much.

Entangled photon pairs generated via spontaneous parametric down conversion have had many applications such as quantum key distribution(QKD), quantum teleportation, in quantum relay chip, interfacing in quantum memories and generally in quantum information systems. Are there any other possible potential applications of these photons?

How is the reliability of 2 dimensional consecutive k out of n systems?

Consecutive systems, k out of n, reliability, D' Moivre theory, linear consecutive systems.

May some one inform me about using of a two-mode entangled state |a>1|b>2 + |c>1|d>2 , a, b, c , d , being coerent states ?

Using first-order perturbation theory, estimate the correction to the

ground-state energy of a (non-relativistic, spinless) hydrogen atom due to the finite size of the nucleus. Under the assumption that the nucleus is much smaller than the atomic radius, show that the energy change is approximately proportional to the nuclear mean square radius. Evaluate the correction for a uniformly charged spherical nucleus of radius R. Is the level shift due to the finite nuclear size observable? Consider both electronic and muonic (one proton for the nucleus with one muon orbiting instead of one electron) atoms.

In the paper "Violation of local uncertainty relations as a signature for entanglement" by H. F. Hoffmann and S. Takeuchi (http://arxiv.org/pdf/quant-ph/0212090.pdf), sum-type uncertainty relations for finite-dimensional composite systems were proposed which all separable states were shown to abide by. While these relations are absolutely necessary for separability, can we have entangled 2x2 states which do not violate any such local uncertainty relation?

Edited:- Does the total dipole moment of an atom and induced dipole moment between two levels interact together for a transition?

The R script (html notebook) at

shows simulation results for Caroline Thompson's "chaotic spinning ball" model for various values of R, the radius of the circular caps on the sphere.

It is pretty clear from the pictures that there is a continuous convex combination of these curves which exactly matches the cosine curve (the curve predicted by quantum mechanics, for the so-called singlet state).

Questions:

1. can you give a rigorous mathematical proof of my claim?

2. can you find a convenient analytical formula for the resulting mixing distribution?

3. can you compute it numerically to a high degree of accuracy so that the result can be used for high-precision simulation experiments?

Suppose we have a bipartite quantum system which is preapared in some state, say, at t = 0 (preselection) and postselected at a later time, say, t = T. The correlations between two parts of the bipartite system at intermediate times (0> t > T) must depend on the initial and final states according to my understanding. The correlations between parts of the bipartite system with only the initial state is known. Due to time reversal symmetry, similarly correlations can be defined, if only the final state is fixed. But how to define/describe the correlation for a system, which is both pre and postselected?

So this is more a quantum information/computation theory sort of question, but let me try and phrase it the best I can:

An algorithmic computation between two states (ie bitstrings) - any computation - can be performed with a small set of gates, which in QIT, means rotations in Hilbert space. If our set of data is the state of some quantum field, where qubits may be as simple as true-false statements about particle eigenstate existence, or as complex as higher n-ary number states represented by various degeneracies; can we still represent the total algorithmic complexity involved with some small set of "gates" (ie ladder operators) or is quantum field theory not capable of such a feat?

I have developed a simple QC-inspired texture synthesis algorithm, which is fully operative, except for the fact ("small detail") that it assumes the user is able to provide desired values for the involved "input" q-bits. Of course, this is not feasible from a purely QC point of view, as q-bits are (randomly) sampled when observed, and, in this case, it is not feasible to repeat the sampling process until obtaining the desired values (I use around 15-20 q-bits).Any thoughts/links to follow on this problem? Thanks! 

I think that I found an interesting experimental design, related to FTL information transfer. I believe that the experimental design that I propose deserves some thought and is related to the essence of my question. In order to understand the experimental design that I propose, two references are needed (which represent interesting reading on their own).

Reference 1. - John Cramer, Nick Herbert, "An Inquiry into the Possibility of Nonlocal Quantum Communication", (article can be found at arXiv, see attached file).

Reference 2. - M. Zych, F. Costa, I. Pikovski. C. Brukner, "Quantum interferometric visibility as a witness of general relativistic proper time", Nature Communications, 18 Oct. 2011 (see attached file).

In reference 1 Cramer and Herbert consider an experimental design with entangled photons in a path entangled dual interferometer. Their conclusion is that the intrinsic complementarity between two - photon interference and one - photon interference blocks any potential nonlocal signal. Without the coincidence circuits no nonlocal signal can be transmitted from Alice to Bob (in this particular  Alice-Bob EPR setup). In terms of density matrix formalism, nothing that happens at Alice's end has any effect on Bob's density matrix, even when Bob and Alice's photons are maximally entangled (due to unitary evolution - conservation of energy).

In reference 2, the experimental design involves a Mach - Zehnder interferometer in a gravitational field. They consider interference of a "clock" particle with evolving degrees of freedom (for example an electron and the "clock" being the spin precession) that will not only display a phase shift, but also reduce visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space - time. Because of quantum complementarity the visibility of the interference pattern will drop as the which path information becomes available from reading out the proper time of the "clock" going through the interferometer (gravitationally induced decoherence).

The experiment that I propose. Let's consider a path entangled dual interferometer experiment involving entangled particles (electrons, for example), when one MZ - interferometer is in a gravitational field. When we consider the density matrix of the system composed of the entangled particles in the two MZ interferometers, and when we consider the partial trace over system A (Alice's subsystem situated in a gravitational field), then we see that the interference visibility will also be affected for system B (Bob's subsystem). This opens the door for nonlocal signalling since Alice can send binary messages to Bob by moving her MZ - interferometer in and out of the gravitational field, and Bob using statistical analysis, can decode Alice's message based on high or low visibility of his interference pattern (and no coincidence circuits necessary). In this case the evolution of the system represented by the entangled particles going through the dual MZ interferometers in the presence of a gravitational field (for Alice's subsystem) is not unitary (and all FTL information transfer impossibility proofs are based on unitarity).

I see no paradox in the fact that it might be possible to extract information (very quickly) about the result of very long deterministic computations (for example). In a way, the result of a long deterministic computation is already contained in the initial conditions of the deterministic system (the initial state of the computer and initial data), and that is true even if the actual computation takes a very long time (like the age of the universe). I do not look at this design as possibly allowing sending information into the past (with the grandfather paradox that it implies), that is debatable and it probably involves notions like the multiverse (which is more of a philosophical issue than scientific). I look at it as a tool that would give us access to knowledge, information that is invariant of the actual universe that we live in (in the context of the multiverse).

I also have a post about this on stackexchange:

http://physics.stackexchange. com/questions/184379/is- macroscopic-causality-an- issue-in-the-context-of- certain-quantum-experiments

Your comments and feedback will be appreciated.

Is it like in classical Informatics an certain amount of physical bits?

Or more exact: Is any Quantum Memory really existent in physical form and how?

Werner HEISENBERG said that in one particle some properties can be complementary.

What's the difference to entanglement in Quantum Theory?

I have just started reading up on Quantum Communications and I would very much like to work on it some more so any suggestions particular focus areas and related papers is most welcome.

Shor asks if a given formula calculates the capacity of a quantum channel  

And argues that the capacity of a quantum channel is unknown

Any literature about that topic?

I have a fixed channel (CPTP map) and I do not know whether it is inside the class of LOCC. I know explicitly that entanglement of formation, relative entropy of entanglement and negativity decrease monotonically under this CPTP map. I want to know if I consider, say entanglement cost, as a measure of entanglement, will it also be monotonic under this same map?

Let us suppose Alice and Bob share an entangled qubit pair initially prepared in a maximally entangled Bell state. At some moment of time Alice decides to measure her qubit and does so, without informing Bob. Her measurement causes the wave function collapse, but, in general, does not lead to the measurement at the Bob's station. How can Bob understand that his qubit experienced the change? It seems for me that Bob should use kind of a weak measurement, but how realistic this would be. Dear colleagues, how the described situation could be handled experimentally?

I want to know what are the reasons of this interference.

How does quantum mechanics look for this interference? Does the photon interfere with itself or are the waves accompanied with it interfering with each other?

What's the relation of wave particle duality with this experiment?

What are the most acceptable interpretations of this experiment?

I wish to know the set of per-conditions to use entanglement swapping.

There is a paper by mostafazadeh but is there a general proof as such?

Consider three mutually commuting observables from Mermin's square, A_1=σ_x⊗I, A_2=I⊗σ_x, A_3=σ_x⊗σ_x, where σ_x is the Pauli operator and I is the identity operator. We can see that R=(A_1)(A_2)(A_3)=I.

According to the Non-Contextual Realist model v(R)=v(A_1)v(A_2)v(A_3) and is valid for both simultaneous and subsequent measurements. Here v(X) is the outcome of individual measurement of X. As R=I, v(R)=v(I)=+1 only. This implies, v(A_1)=1/(v(A_2)v(A_3)). In any measurement the outcome is random, it can be either +1 or -1.

But in case we measure all the three observables simultaneously, the outcomes of at most two observables can be random because the outcome of other observable is constrained by the previous equation and is therefore definite.

According to this analysis, in the case of subsequent measurements, once we measure two observables the outcome of third one can be known even without measuring it.

But does it really happen?

And please let me know if there are any mistakes in my interpretation.

The flipping of an electron from either down to up or up to down in the magnetic field in a single energy level system, emits a photon of a particular frequency. That frequency depends on the difference in energy of the electron in up and down states, or vice versa. The same electron in a superposition state (i.e. some arbitrary direction w.r.t.field direction) is being used for quantum memory.

Please suggest a (free/paid) software platform with the virtual capabilities for the simulation of concepts in the area of quantum computing and information. Thanks.

Indexed outcome of measurement operators {M_m},m={1,2,3,...} are applied with quantum state |s>.

We get the outcome m={1,2,3,...} with some probability P_m. How do we know which M_m we need to be apply? We can't apply all M_m as we only have a single copy of quantum state |s>.

If we can't do repeated measurements with different measurement operators, then how can we do this? We will make our decisions based on observed probabilities {P_m}, this is one case. In the whole theory I have similar doubts. do we have theory/experimental success to produce the identical quantum states so that we can perform repeated measurements to get the experimental value of probabilities?.

Statement: "design a POVM { E_1,E_2...,E_m+1} such that if outcome E_i occurs, then we are certain that its state was given to us."

my doubt is : what is meaning of "if outcome E_i occurs" as E_I is a POVM element hence it can be "applied" to a state how it can "occur". How do we decide that E_i is occurred?

Quantum discord is said to involve correlations between two quantum systems; but with a clause that it won't necessarily be quantum entanglement correlations. Then mathematically ; whats the criteria of such a condition between two systems? I mean; separability of density matrix was guaranteeing me the fact that two subsystems are not entangled; until i came to the fact of discord. But now if mathematically I have a density matrix that can't be separated; how can i say its entangled when i know the possibility of this new phenomenon? Because no no entanglement implying classical relations is not a full picture. In quantum entanglement; when the states are maximally entangled' we say that we can teleport, so we have a physical application of the phenomenon. what is the case with this quantum discord; can it be extracted and put to use somewhere; or where has it been put to use?

Though 'no cloning theorem' disputed the concept of cloning, it is predicted that cloning will help to signal faster than light.

Recent (November 2013) public debate videos are up on youtube; for description, see: http://www.ece.tamu.edu/~noise/HotPI_2013/HotPI_2013.html

How is quantum entanglement related to heisenberg limit and quantum limit?

Any other information regarding it is also welcome.

I understand from certain papers that this is known for Werner states, but I'm curious if it holds, for example, for classical-quantum states.

Can initialization of two particle states, for example, two isolated spins (say one of the spin's state is set to be the opposite of the other) be considered entanglement without any physical mechanism to connect them? Will manipulation of such spins externally (same manipulation on both, say flipping the state) be considered equal to a physical mechanism that couples two particles?

If we have a maximally entangled pair like (|00> + |11>)/sqrt(2) interacting with an environment, how does entanglement degradation take place? Does it transform into a partially entangled state?

Kraus Operators for Entanglement Degradation.

What is the spin in Quántum Mechanics? Kindly share the majority or all related definitions.

One interesting topic which I'm keen on listening to:

Google and NASA team up together to develop one of the most powerful Quantum processor in the World (A normal computer / processor uses voltage toggling between 5V / 3.3V / 1.8V and 0V to distinguish between a logical '1' and a logical '0'; whereas, a quantum processor / computer uses electron spin quantum number which can be either one of the two values representing 'clockwise spin' or 'counter-clockwise spin' to distinguish between a logical '1' and logical '0'.)

More information and video in the following links:

It has been seen a long ago (http://prl.aps.org/abstract/PRL/v60/i14/p1351_1) that in a pre and post-selected ensemble, the measurement of some observable on the considered system yields exotic average value (weak value) for the observable, in weak measurement limit. Since then weak values are experimentally verified despite a debate over its physical interpretation (these isues partially addressed and solved). Also weak values are used as tools in many disciplines like resolving Hardy's paradox (important to the foundations of quantum mechanics), detecting tiny effects, measuring wavefunction of single photon directly (unlike tomography) and many more. In all these cases, though measurements were weak but the most important fact was the post-selection. Recently it is employed to the parameter estimation in metrology, where it was found that in case of pre and postselection, measurements to determine the parameter of interest leads to the increased Fisher information. The inverse of the Fisher information times the success probability is the lower bound on the variance of the error in the parameter estimation. But due to decreased probabilty of success as a consequence of postselection leads to no further tightening of the lower bound despite the increased Fisher information (http://arxiv.org/abs/1306.2409, http://arxiv.org/abs/1310.5302, ). So, overall, post-selection doesn't help here to estimate the parameter of interest more precisely than that of usual quantum mechanics without post-selection. I ask the following question: Can we know a priory the situations where the additional post-selection will lead to something useful?

I am looking for the general definition, one that does not depend upon whether or not the system is a quantum one. However, please provide context and explanation.

Here is the thought experiment I’ve come up with to celebrate my ignorance.

An electron-positron pair is emitted such that they are entangled on spin.

Case 1: The electron and positron are brought back together and they annihilate while the entanglement is still intact and a pair of gamma rays are emitted. Add everything up.

Case 2: A second entangled electron-positron pair is emitted and travels an energetically identical path to the first pair, except somehow “the entanglement is lost to the environment” in Case 2 before annihilation. Add everything up.

My understanding assumes:

a) The superposition of the two particles is lost to the environment in the second case.

b) But, that the wavefunction doesn’t “collapse” at instant the entanglement is lost.

That said, my knowledge of <brak|ket> notation, wave equations and information theory is too limited to know if there is there a difference in entropy from results of the *isolated* entangled annihilation and *isolated* un-entangled annihilation.

1) Is there something different about the wave-equations of the gamma rays emitted in both cases?

2) Is the information and/or entropy of the *isolated* (electron, positron, gamma-pair) the same in both instances or do I have to account for the information in the wavefunction of the “environment” too?

3) From an information theory standpoint some kind of “half-bit” missing from the second instance that is somehow carried away by the wavefunction of the environment?

You don’t have to answer all of the above questions! I’m really just looking for a nudge in the right direction, since most papers I’ve read are on closing EPR loopholes, not on the information theory perspective on those experiments.

Physical Hamiltonians are a small family of Hamiltonians if compared to all the possible Hamiltonians. In particular physical Hamiltonians consider only local-interactions, while more general non-physical Hamiltonians consider every kind of interaction. In particular in this second case you can describe more general problems. But there is any application of this kind of objects and if yes what?

Bouwmeester et al.(1997) did the "experimental quantum teleportation" in the polarization basis. For this 'Alice' has to perform a complete measurement on the system (particle 1 and 2) in the "Bell operator basis" {Bennet et al. (1993)}. This is done experimentally, by a beam splitter, with two input ports and two detectors for coincidence measurements. All other states either one of the output port and only anti symmetric Psi(-) will give coincidence (25% probability). What is the theoretical reason behind this?

When we look at a hydrogen-atom orbital wave function with non-vanishing

angular momentum, we empirically know that this state causes a magnetic moment. Therefore, it must be coupled with a classical magnetic field.

At the same time however, we know that neither is the wave-function something physical, nor is there an electron before it is measured. There is no measurable charge in this state.

Thus, there can't possibly be anything like a current.

My question is: how can this wave function -that is considered as something purely mathematical by most scientists, - 'create' (or being coupled with) something as physical as a magnetic moment?

(Of course we could assume the opposite - that the wave function might be some sort of 'spread' charge and would contradict other observations.)

How can this be explained?