Quantum Information Theory - Science topic

Quantum Science and Engineering encompass a broad and interdisciplinary field that explores the principles of quantum mechanics and applies them to various technologies and applications. Quantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles. Quantum science and engineering leverage the unique properties of quantum systems to develop new technologies that can outperform classical systems in certain tasks.

The field of quantum science and engineering is rapidly evolving, and research in this area has the potential to revolutionize various industries, from information technology and cryptography to healthcare and materials science. Governments, academic institutions, and private companies worldwide are investing heavily in quantum research and development to unlock the full potential of quantum technologies.

In the Copenhagen interpretation of QM, properties of a system begin to be realistic when the observer makes appropriate measurements and observations. Does it mean that the laws of QM were inconsequential about 2 billion years ago when nobody was there to make observations? This problem does not arise if we take the statistical interpretation. However, then one has to accept that QM does not provide a theory for individual events. But what is the need if the results of individual events are random due to microscopic nature of the systems?

How does one combine the basis of Quantum Physics that the information cannot be destroyed with the GR statement that black holes destroy the info?

Hi, i am sudying some quantum computer science and I am really struggling to find an explanation to the question done above.

Any kind of help would be wonderfull.

Greets.

We have a linear chain of 3 trapped ions system (the interaction are taken XX interaction). We want to apply the external local magnetic field to each of this individual ions. Is it possible experimentally?

Is GR effective geometry from an hypersphere? It would give many benefits.

I read from https://arxiv.org/ftp/quant-ph/papers/0604/0604210.pdf

In quantum physics, and consequently in quantum computation and information science, the Bloch sphere representation for transformations of two state systems has been traditionally used. While this representation is very useful for two state systems, it cannot be generalized to multiple states and when it is generalized, it looses its simple geometrical representation... asymmetric structures appear in N-level systems which do not have rotational invariance 

How? https://arxiv.org/abs/quant-ph/0408014

We show that the maximum radius in each direction, which is due to the construction of the Bloch-vector space, is determined by the minimum eigenvalue of the corresponding observable (orthogonal generator of SU(N)). From this fact, we reveal the dual property of the structure of the Bloch-vector space; if in some direction the space reachs the large sphere (pure state), then in the opposite direction the space can only get to the small sphere, and vice versa.

and from https://pdfs.semanticscholar.org/7ef8/70e87d6589c9fb5046ead0469142c5aa85cf.pdf

...we provided a representation of an arbitrary two-feature pattern x in the terms of a point on the surface of the Bloch sphere S2, i.e. a density operator x. A geometrical extension of this model to the case of n-feature patterns inspired by quantum framework is possible.

What does this mean? This corresponds to the quantization? https://arxiv.org/pdf/chao-dyn/9904002.pdf

...strange attractor shrinks more and more towards the south pole of the Bloch sphere  https://books.google.fi/books?id=llluCQAAQBAJ&pg=PA113&lpg=PA113&dq=bloch+sphere+primes&source=bl&ots=VyRCyaznAT&sig=JBKqetOQ2Rg3TzO0unUSh6Y9ebY&hl=sv&sa=X&ved=0ahUKEwiG4sqpi8LRAhWGNJoKHXiFDJwQ6AEIWjAI#v=onepage&q=bloch%20sphere%20primes&f=false

Finiteness, 'reality' decoherence, density matrix?

http://math.stackexchange.com/questions/1483650/how-to-plot-a-qubit-on-the-bloch-sphere talk about the Bloch sphere, but how to plot states on the sphere due to both states being a complex number, thus resulting in 4 "coordinates".

Mixed (inner) states and uncertainty? A 'collapse' gives a pure state (a Surface), that is an integer? This is what GR requires.

Hope I could make myself understood :)

Regardless of technological limitations, and regardless of the receiver's ability to extract this information. Is there a maximum limit on how much information can be encoded in a photon ?

Thank you for your help

 quantum theory

In my research, I've understood a common belief that the Earth's magnetic field is too weak to have any significant impact on a living thing. However, it would seem that with a little help from Quantum Mechanics it would seem quite possible for a biological entity to reference the magnetic field.

I offer the Quantum Robin, that uses quantum entanglement to offset the balance of chemical reactions occurring in the eye, with the power being provided by the sun. Changes in the Earth's magnetic field enables the chemical reaction to change in such a way that it can be detected by the body, which aids the bird in migration.

From this, I am wondering as to what other body functions are, or could be, affected by low level energies? I would greatly appreciate any insights, articles, news releases, websites, or books that you would be willing to share with me on this fascinating topic!

I'm trying to wrap my head around how this might work.

Let's propose that two electrons are entangled and then separated. Then, one is excited to a new energy level. Does the other reciprocate?

See attached PDF!

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 ?

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

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.

I suppose that in QM the uncertain measurement is founded on using Light and photons. We can't make light "stable" ! A photon is always moving!

Can we find AQP (Artificial Quantum Particles) with definable and steerable Quantum States? 

I suppose actually that Quantum Information Theory is not able to get realised by principal.

After a finite interval of time in Markovian dynamics, system loss all information but there is a revival of entanglement in Non-Markovian process....

we know there are different systems to generate squeezing of light. But I want to know:-

1) which one is the best system and how much squeezing we can get at it's maximum and minimum value?

2) What are the different applications of squeezing of light?

I'm going to provide an example to highlight a possible closeness between memetics and quantum speculations. But first, I should settle what I mean by "macro-entanglement": while quantum entanglements regard groups of particles, macro ones concern macoscopic tangible reality instead. 

Now, a suitable definition of entanglement is: "The effects of the properties/actions of a thing propagate as if it were elsewhere". 

Then, a case of study. 

Let p₀ be a person who takes a picture at the base of an Eiffel Tower imitation. then shares it on social networks commenting "finally in Paris". Let K (kith) be the set of p₁, p₂, ..., p_n his/her acquaintances receiving the photo - notice that the picture shows only the assemblage of beams and the sky, so that the surrounding environment is not recognizable. Well, whether it is the original tower or one of its many copies around the world, it makes no difference: at first (even without a comment), it will affect others as if it were actually the real one! - p₁, p₂, ..., p_n will think about Paris. Why? Simply because the idea of the authentic tower is more rooted than fake's one. 

Here, the entanglement can be ascribed both to the similarity between the features of the fake and the original's (entanglement due to properties, which means "it is such done, so it must be in Paris") and p₀'s [act of] taking a picture (entanglement due to actions, which means "p₀ should have been in Paris in order to take that picture"). Mainly, the peculiarity of this [whole] entanglement is that it makes other individuals to adopt a belief! 

So, which parallelisms can be found between memetics and quirks like entanglements? How can we describe something like these with memetic algorithms? 

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?

Quantum operation including quantum channel is usually described by some operator or super operator performed on the given state, which correspond to a map. A fundamental requirement is that the map should be completely positive. The complete positivity has an obvious physical meaning. The question is whether the positive (not completely positive) map is physically allowed.  If yes, how to realize it?

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

Can it be shaped by a direct coupling to "information fields" in a similar way as geometry shapes the matter and matter influences geometry in General Relativity? Is changing of "quantum geometry" possible? There are problems with "Riemannian geometry" of Hilbert spaces. But, perhaps, we can go for different (nonlinear) models of quantum theory?

What in your opinion can be the role of QKD in the economic growth of a country?

I have just learned about quantum communication. However, it seems a little difficult to understand the state of quantum entanglement. How can we know one quantum's state as soon as the other's state is tested? Furthermore, can we control the state of a quantum? Could someone offer me any help? Thanks!

In a 2005 book - now posted in Research Gate (see the link below) - the authors (led by Dr. Armando Freitas da Rocha) proposed an original model of quantum computing in the brain carried by calcium ions. Ten years later, the concept independently reappears in a convincing new paper (see Abstract below). I thank Chris Nunn for calling my attention to this paper, and congratulate Dr. Freitas da Rocha for his ingenious and visionary work!

Front. Mol. Neurosci., 16 April 2014 | doi: 10.3389/fnmol.2014.00029

Basis for a Neuronal Version of Grover's Quantum Algorithm

Kevin B. Clark1,2*

1Research and Development Service, Veterans Affairs Greater Los Angeles Healthcare System, Los Angeles, CA, USA

2Complex Biological Systems Alliance, North Andover, MA, USA

Abstract

Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church–Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical “subroutines” involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N1/2)) needed to find some “target” solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca2+ response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca2+-induced Ca2+ release and the search (or signaling) velocity of Ca2+ wave propagation. As chemical processes, such as the duration of Ca2+ mobilization, become rate-limiting over interstore distances, Ca2+ waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca2+ diffusion coefficient, D1/2, matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca2+ signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional response regulation choices.

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.

I want to know the answers of the above questions to have a deep idea on mixed state and lose of information.

A short description of Moffat's non-local quantum filed theory is given at http://en.wikipedia.org/wiki/John_Moffat_(physicist) . Yukawa published the following papers: Quantum theory of non-local fields. Part I. Free fields, Phys. Rev. 77, 219 (1950); Part II. Irreducible fields and their interaction, ibid. 80, 1047 (1950). However, I don't find any description that relates these two physicists' studies, which sound to have some similarities. I'm not a particle theorist. So, please write the answer in plain words understandable to laypersons.

Suppose I have a set of multipartite orthogonal product bases, which I want to prove as possessing some quantum non locality. i.e they can't be distinguished perfectly with local operations and classical communications. So one way which I found is to show if they are unextendible product base sets, because that implies that states are nonlocal for measurements. But, is the negation also valid? If the set isn't unextendible product bases, then does it imply that the states don't show any quantum non locality?

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?

No-cloning theorem does not prohibit us for the cloning of orthogonal states. Our recent computer are based on pure states. What kind of hurdles we have in fundamental design of quantum machine? If two states is not in pure state, could it be still orthogonal?

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

I have read in many papers of the application of quantum entanglement in communication field and it is explained in terms of photons.

How can we use the principle of entanglement in energy storage devices?

How the von-Neumann entropy (quantum entropy) and "quantum correlations" related to each other for a system of cold atoms? Is there any other parameter to measure the quantum correlations between the atoms?

Entanglement

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?

Ideal pure classical randomness is deterministic and only appears random as a result of complexity and our ignorance of the system. Whereas a quantum event (eg, flip of a qubit or radioactive decay) is a truly non-deterministic random event.

If we were to subject a long sequence of random numbers to all the statistical tests for randomness, and compare classical vs. quantum ones, we may find for all practical purposes there is no difference.

However, this is NOT the question I am asking.The question is this: pretend you have all the magical powers of a Maxwell-like demon. The laws of quantum mechanics prevent even you, as a demon, from predicting a random sequence from a quantum source. However, you have the power as a demon to observe all the motions of atoms in the block of material inside, say, an electrical resistor. Therefore, with unlimited computing resources you should be able to predict the random sequence of thermal noise that the resistor generates.

The question is: is this really true? Surely, a classical object such as a resistor has quantum events going on inside it. They will indeed decohere very quickly. There even maybe some semi-classical effects such as incoherent relaxation going on inside the resistor. Vacuum fluctuations will cause electrons to change energy levels every now and again; this may affect how the host atom classically bounces around at a given instant. Due to all the classical scattering bouncing around in the lattice, one can imagine short-term classical metastable states that are tipped one way or another by a quantum fluctuation.

These quantum events will all be washed out by the classical thermal noise. However, surely they will nevertheless add an underlying non-deterministic element to the thermal noise? Therefore you, the demon, even in principle should not be able to predict any random signal that comes out of the resistor.

The question is: is this correct? Also is it possible in principle to calculate the magnitude component of the noise that is deterministic vs. non-deterministic? Hence the title of this question: "To what extent is thermal noise a result of the quantum world?"

If it is indeed impossible for you to predict the random behaviour of the resistor, could your demonic powers predict a random signal that is partially correlated with the resistor's signal? If so, we could remove such correlation by XOR-ing the outputs of several independent resistors. Is it possible to calculate how many XOR inputs we would need to guarantee this?

By definition, a reversible process is one that can be undone completely, leaving no trace of it having occurred. Upon reversal "it should be impossible to devise any experiment that could determine whether the process took place" (paraphrasing Planck). This means that every single bit of information that was flipped by such a process going forward, should be flipped back when the process finishes going in reverse. This really means all causal volume traces must be erased including all memories recorded in labbooks, hard drives or brains. Postulating the existence of such a process is therefore an unfalsifiable assumption (since if you succeeded in performing such a process there would be no evidence to show for it and you wouldn't even remember doing it!). This means asserting the existence of truly "reversible" processes is no more than an act of faith. Yet significant portions of physics depend on this belief and we try hard to keep the "micro" laws time-reversible. Since reversible processes are defined as those that can never make their presence known by affecting anything, it means that experimental evidence of CPT violation is inevitable and the microscopic arrow of time is down there, it's just hard to see because of the limitations of current experiments. It follows that the notions of determinism, unitarity of quantum mechanics, symmetries etc. should be understood as approximations the same way as Plato's perfect circle is never realized in any physical system. Keeping these self-contradictory notions at the heart of the mathematical underpinnings of physics as "useful approximations" is confusing physics with engineering. Worse still, our instinct to treat absolute conservation laws as sacrosanct is seriously harmful to furthering our understanding of how it all really works.

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.

Quantum Bayesianism is an emergent view on the foundations of quantum mechanics that is rather interesting (see http://en.wikipedia.org/wiki/Quantum_Bayesianism if you have not heard about it). This is especially the case as it seems (prima facie) to avoid the problems of ontology in quantum mechanics altogether. I am interested to hear people's views on this approach, especially if you know of any hidden ontic assumptions.

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?

A recent publication stated there was a significant divergence in energies of emitted photons of highly charged ions (helium-like titanium) from QED predictions. Since QED is one of the most trusted quantitative theories, this is something.

The paper is available from APS (please see the link). Does somebody have a membership or access to this paper? If yes, please email it to info@quantum-information.org

I'd like to recalculate the measurements with QIT, which predicts such divergences. Is there already another idea why QED differs from these measurements?