Decoherence - Science method

Dear Professor/Researcher,

Book Chapter proposal is invited for the edited book titled “Quantum Machine Learning (QML): Platform, Tools & Applications”.

The main goal of this book is to deliberate upon the various aspects of Quantum Machine Learning in distributed systems, cryptography and security by a galaxy of intellectuals from academia, researcher, professional community and industry. While this book would dwell on the foundations of Quantum Machine Learning as a part of transparency, scalability, integrity, security, it will also focus on contemporary topics for Research and Development on QML.

Topic 4. Quantum Error Mitigation(QEM)

4.1 Introduction to quantum errors and noise

4.2 Quantum error mitigation techniques

4.3 Integrating QEM to the QML framework

Topic 5. Quantum Error Correction(QEC)

5.1. Introduction to quantum error correction

5.2 Quantum error correction techniques

5.3 Fault-tolerant quantum computing

Publisher:

Editors

Howdy Marc Fischer,

I applaud your clear statement that "random" and "stochastic" are terms to be applied to human perceptions and efforts, since the underlying dynamics of fluids in turbulence is deterministic. Very rare observation, very welcome! (The fluid knows.)

As far as "quantum mechanics is genuinely indetermistic," some of us think the jury is still out on that because your comments on turbulence apply to human limitations, including ignorance, there also.

Given the experience of "QUANTUM MECHANICAL random fluctuations" by turbulent processes that is possible, I doubt that they could affect the state of the turbulence as having too little energy. "Random" absorption of a photon by a molecule that enhanced the molecule's internal energy would have an effect, of course, by increasing the thermal-motion energy of the fluid, but I doubt it could be noticed in turbulence, even by the flow being triggered to new behavior. This affect is very different from application of human precision in initial conditions that enters mathematical expressions with such strong leverage because of the mathematical non-linearity.

I also applaud the association you have made as one of the ways to trigger insight, but too often the answer in a specific case is no.

Happy Trails, Len

A related development is, by Torsten Asselmeyer-Maluga, https://arxiv.org/pdf/1910.09966.pdf

Thanks to 'Juan Weisz' and 'L. I. Plimak' for your quick answers!

I just want to add that the reason for my question was an article ( https://arxiv.org/pdf/1612.00676.pdf ), in which physicists were surveyed about their attitudes concerning the foundations of quantum mechanics. I was shocked to see (in Fig.6) that 29% considered the measurement problem as solved by decoherence, and 17% considered it even as a pseudoproblem. I my opinion, the measurement problem is absolutely important, but still unsolved.

Hello, Mr. Steinburg, there is a very fundamental difference between how classical and quantum mechanics are being described. In classical mechanics, a particle or an electron can be deterministically described but not in the quantum world. Because the uncertainty principle says we cannot measure both position and momentum at the same time. We don't know the initial state of a particle with sufficient accuracy. In quantum mechanics, what we do is, we measure the probability of finding a particle. As there is no deterministic way to describe a particle in quantum mechanics, we use wave function to describe a body. So, within the range, we can find a particle anywhere. So, if the range is +infite to - infinite (say in the universe), then the particle is within anywhere in that range. We do not know about the position of the particle unless we measure it. Going back to your example, in the quantum world, you do not name a million object with a single word, rather you give a name to a single entity but unless you observe that, that word does not deterministically say anything about your desired entity. The example of the electron that you gave follows the same, we will not have any unique electron unless you measure that. That is why electron in the orbital is described by electron cloud in the atom. However, another question that you came up with that whether the electron is in the orbit and in the universe at the same time, that actually is solved by the issue of the measurement range. We not measuring electron of Mg or Al, in the universe, but we are measure within a substance. But yes, if the electron is free within the universe, the electron is anywhere in the universe. We will only know about that electron when we measure it. So, back to your first question, in quantum mechanics, in a superposition state, a particle can experience an infinite number of states within a range. The probability of finding a particle with a range can be, 0, 0.1, 0.001, 0.000...million..zillion..01 up to 0.999999...million...zillion....9, 9.99 to 1. I hope, that will suffice your query. Thank you.

In spin systems in particular, commonly used protocols for dynamical decoupling include the Carr-Purcell and the Carr-Purcell-Meiboom-Gill schemes. They are based on the Hahn spin echo technique of applying periodic pulses to enable refocusing and hence extend the coherence times of qubits.

Yes, Dinesh wants everything to be Classical Mechanics,

unfortunately he is very wrong.

classical Mechanics is identified with Newton and followers,

Lagrage and Hamilton. Special theory of relativity is also included.

Then Classical field theory covers Maxwell theory of Electromagnetism, and the General theory of relativity.

In summary almost everything that is non quantum is called

Classical.

The quantum markes a sharp break in methods and results.

In fact irreducible randomness is a characteristic, which

Dinesh would rather not admit.

Thermodynamics and Statistical Mechanics also admit randomness, although at not so fundamental level, unless it is quantum statistical mechanics.

Thank you Stam Nicolis for reply.

I edited the title to be Vacuum Space Time rather than Vacuum Space where time is assumed. You make a number of points that should be considered.

In quantum systems phase space may differ from space time depending on the system. When vacuum space time is represented as the quantum system under consideration then the phase space must be the same as space time or be contained with in it.

I will argue that the ground state of quantum space time can be uniquely defined by isotropic CMB in flat space, a view shared by some famous names, but not generally accepted in the research community.

In your explanation the other operator M is represented in my system as a fast moving vehicle which locally meets the measurement requirement. In most cases and in all of those described by GR, the moving vehicle referenced to isotropic CMB will not generate a high probability of excited states in vacuum space time.

Unusual cases of very high speed and kinetic energy are most interesting to me. This is where local quantum effects cannot be ignored in GR. I have argued that the probability of excited states become significant and become superimposed upon each other and upon the ground state.

As kinetic field energy continues to increase some limit is reached at which a state vector reduction may occur. Physically it is represented as a change of spin angular momentum of the space time quanta from h to 2h. This is the hierarchy of Plancks that occur in other theories and research of the past 40 years.

If a state vector reduction occurs as R, the unitary evolution U continues locally as kinetic energy continues to increase, but this is not described by GR because h has become a local variable and local space time is in a squeezed quantum state. In this representation the velocity relative to CMB is approaching a substantial fraction of light speed, and the kinetic field energy is sufficient to change the quantum state of local space time as the vehicle passes through it.

In the present question I am asking if quantized vacuum space time can undergo a state vector reduction.

The so-called "entropy " doesn't exist at all.

During the process of deriving the so-called entropy, in fact, ΔQ/T can not be turned into dQ/T. That is, the so-called "entropy " doesn't exist at all.

The so-called entropy was such a concept that was derived by mistake in history.

It is well known that calculus has a definition,

any theory should follow the same principle of calculus; thermodynamics, of course, is no exception, for there's no other calculus at all, this is common sense.

Based on the definition of calculus, we know:

to the definite integral ∫T f(T)dQ, only when Q=F(T), ∫T f(T)dQ=∫T f(T)dF(T) is meaningful.

As long as Q is not a single-valued function of T, namely, Q=F( T, X, …), then,

∫T f(T)dQ=∫T f(T)dF(T, X, …) is meaningless.

1) Now, on the one hand, we all know that Q is not a single-valued function of T, this alone is enough to determine that the definite integral ∫T f(T)dQ=∫T 1/TdQ is meaningless.

2) On the other hand, In fact, Q=f(P, V, T), then

∫T 1/TdQ = ∫T 1/Tdf(T, V, P)= ∫T dF(T, V, P) is certainly meaningless. ( in ∫T , T is subscript ).

We know that dQ/T is used for the definite integral ∫T 1/TdQ, while ∫T 1/TdQ is meaningless, so, ΔQ/T can not be turned into dQ/T at all.

that is, the so-called "entropy " doesn't exist at all.

Dear Sofia,

Sorry for the long delay.

SW: Nooooo! Oh, I thought that we know what we mean (in the domain of fundaments of QM) by the phrase "common cause". So, you don't know this expression. I'll explain you.

I know it well but perhaps in a different form so I'll explain my version. In some studies we might find that two parameters, say A and B, have a relationship and if A occurs before B we might conclude that "A causes B". However that may not be the case because it may be that both A and B have been caused by a third influence C which preceded both, thus the correct picture would be "C causes A and C causes B".

SW: Consider two or more entangled particles - let's speak of two for simplicity, A and B. Common cause of the results produced by A and B when measured, is a hidden variable Λ which takes values at the preparation step, i.e. when a pair is prepared, both A and B are attributed a value of λ of Λ, the same for both particles.

Yes, that seems to be the same as my general version.

SW: The word "common" means common to the two particles in the pair, not common to two subsequent pairs.

Yes, that is what I said, so the idea of delaying one measurement so that the pairs overlap in time doesn't have any consequence as far as I can see, what is common to one pair remains separate from what is common to the other pair. George: "Right, but the wave-function that defines one pair of entangled electrons is independent of the wave-function that defines the next pair, there isn't a single hidden variable, local or non-local, associated with one pair that would influence the other pair." Wooow! My God! Let's make order! The wave-function, George, is one and the same all along the experiment. In each trial and trial of the experiment the pair is prepared in the same way, i.e. the same wave-function. For instance, if the wave-function is, say 2-½( α|x>A |x>B + β|y>A|y>B ), each pair of particles exits the preparation region in the state 2-½( α|x>A |x>B + β|y>A|y>B).

OK, it is my terminology that is probably a little off the conventional. I understand that that one equation defines the nature of the pair but what I was saying was that two trials are independent so in a sense two separate examples of the same wavefunction. I'm not familiar with the correct jargon here.

SW: The wave-function is not a hidden variable!

Oh certainly not. If anything, I think it is called "hidden" specifically because it would be a physical parameter which does not appear in the wave-function.

SW: If the issue is not clear to you I invite you to tell me. Please reformulate according to the correct terminlogy and concepts.

It is quite clear and entirely agreed, my layman language is causing confusion.

Not knowing the correct terminology gives me a problem, see if these diagrams help:

SW: So, as you say that you admit that there are no HVs, you rule out common causes.

Not quite, that is where I have a doubt. I've added two diagrams

In the first, we have a spacetime diagram showing the worldlines of two entangled photons (red lines) from where they are generated "G" to their measurement at "A" and "B". Each measurement involves an interaction (horizontal green lines) with an instrument which constitutes a local environment E_a and E_b respectively. The interaction causes decoherence giving a definite result. The idea of "hidden variables" would be a parameter "hv" carried by the photons but not visible, this it seems has been ruled out by experiment.

My question then is whether there might be a back door as shown in the second diagram. The state of the environments is dependent only on what lay within their past light cones (slanting green lines). While they don't fully overlap, the conditions of everything of relevance at some time in the past (blue horizontal line) determines each, E_a by the conditions in region P-Q and E_b by the region R-S. Now the possibility is that there might be a common cause "C.C." which influenced the whole of the region P-S.

What that requires is not that "decoherence causes the measured value" but that "the state of the environment E_a is a common cause of both decoherence and the value measured as A", and similarly for E_b and B.

I'm not arguing that this is the case, just wondering how confidently it can be eliminated.

Let us take an extreme position and see if we can make progress

If we assume, that instead of quantum coherence being a subsequent add-on to the living process, that it is, in fact, intrinsic to the living process. And if we further assume that quantum coherence in living systems is intrinsically robust, and necessarily so, in order to perform its biological function. Then we may be able to address the problem a different way: by paring the issue down to its very basics we may simplify it enough to see the way forward:-

If it is true that consciousness correlates with a macroscopic quantum coherent state.

And if it is also true that this coherent state can effect change in the world of classical physics

Then, given the evidence of our own ontology, the beginning of life on this planet would have coincided with the moment that quantum coherence found a way of breaking through the de-coherence barrier and maintaining coherence employing Occam's razor] as a direct consequence of the way in which

that change is effected.

If this argument holds, and if the soliton instrumental in the

process of catalysis maintains coherence through the process then, we should discover that cognition is not an aspect of life, -but definitive of it.

Dear Sofia,

I have written about crises, about philosophy, about history of physics, about free will since these issues are directly relevant to your question. It is impossible to answer correctly on your question without an understanding of the Kant philosophy. Your question is VERY difficult without understanding of the Kant philosophy and the answer on this question will be simple and unambiguous if you, as Einstein, will saturate himself with the Kant philosophy. You write: “In the 21th century the result may be at all passed to a completely automatic process. But not this is the issue, whether the observer is human or a machine”. This opinion is typical for most modern scientists who sure that we can know the Nature as ’thing-in-itself’ and who don't make the distinction between ’res cogitans’ (thinking entities) and ’res extensa’ (extended entities). I draw your attention on the problem of free will in quantum mechanics since this problem is actual only if the observer is human since no machine can have free will. If the observer is a machine and the act of the observation in quantum mechanics is a real interaction of quantum system with a macroscopic body or apparatus, as you think, then the Nobel prize winner Gerard 't Hooft tries to solve a nonexistent problem of free will and numerous publications refuting realism (for example The BIG Bell Test Collaboration, Challenging local realism with human choices. Nature 557, 212216 (2018)) make no sense. I tried to draw the attention in my letter to an Associate Editor of Nature (see attached file) that the believers in quantum mechanics belong to different confessions: the believers of one confession refute realism whereas the believers of other confession don’t want to hear that quantum mechanics contradict realism. Your questions and remarks witness that you belong to the latter confession as well as most physicists of Soviet school. You are sure that quantum mechanics describes real processes. Therefore it's not obvious for you that the "collapse" of the wave-function occurs under influence of the mind of the observer. It was not obvious for most physicists but was obvious for Einstein, Schrodinger, Bell and other critics of quantum mechanics. It is obvious according to the Born interpretation of the wave-function. In order to understand the collapse of the wave-function occurs under influence of the mind of the observer it is needed to put the question: ”Why the realistic understanding of the wave function proposed by Schrodinger was rejected and Born’s interpretation was accepted?” The answer is obvious: ”We cannot think that a real density can change due to an observation whereas we know from our everyday experience that a probability of observation changes at first

observation”. For example, your friend takes away a one dice without looking from a box with one white dice and one black dice. You know before observation of the remaining dice that your friend will see the white dice with the probability 0.5. The probability will become 1 when you will see the black dice and 0 when you will see the white dice, regardless of distance between you and your friend. Thus, the wave function describes first of all the state of the mind of the observer, according to Born’s interpretation. We can think that only observer’s knowledge changes because of observation in the case of the dices. But the wave-particle duality observed for example in the doubleslit interference experiment cannot be described if only observer’s knowledge changes. Therefore Dirac postulated in 1930 ”that a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured”. The wave function describes the states of both the mind of the observer and quantum system according to the Dirac jump or the collapse of the wave-function. This renouncement of the distinction between reality and our knowledge of reality creates the illusion that quantum mechanics can describe the wave-particle duality and other paradoxical quantum phenomena. But it is very strange that only few scientists understood that this renouncement of realism leads to the logical absurdity.

A clue is found in the squeezed quantum states of lasers like the ones used in LIGO facilities, where the uncertainty principle is affected, lowering the uncertainty of energy, momentum, time, and distance.

Uncertainty is a factor in decay modes and half times of unstable particles, suggesting again that smaller uncertainty provides greater stability.

The mystery vanishes in the de Broglie-Bohm theory. The fate on the cat depends on the initial position of the particle inside the wave density only which deliver an radioactive decay or not . An observer plays no role. There is no measuring effect on the cat until you modify the experiment/wave function.

See for example the youtube videos:

https://www.youtube.com/watch?v=cpNSc-X6I8c

https://www.youtube.com/watch?v=lwFfpQMcj4Y

I am not actually expert in this field and I am not sure whether the following paper is of your help, I just referred this if I could learn something from you and others.

Entanglement-free Heisenberg-limited phase estimation

BL Higgins, DW Berry, SD Bartlett, HM Wiseman, GJ Pryde, Nature 450 (7168), 393

Danielle,

I wonder in your theory what is the width of a photon? It turns out that is has macroscopic dimensions? (X=lambda and even more d+2X) All current data show that it is pointlike. At least in your theory it can react with electron which is much smaller.

Very important - does your photon splits in two in DSE and why is never observed splitted?

It is necessary to split the four-dimensional manifold into 3-space and time. If 4-space is flat (Minkowski space), this splitting is most light in the reference system, which moves with a constant velocity. The 3-space is orthogonal to the time in his case. If we use the curved space-time of GR, this operation is possible only locally (for every 4-point). We split the space-time (locally) into 3-space (it can rotate, deform and move with acceleration), the time can depend on the velocity of the 3-space rotation and of the gravitational potential of every point). This operation is showed in detail in Zelmanov theory of the physical observable values. May be, it is possible to find another analogical theories, which are built on the space, whose metric is the sum of the fundamental metric tensor and the product of the unit 4-vector velocity, which is connected with a observer. But Zelmanov theory contents exact method of calculations of all spatial characteristics (gravitational force, rotation, deforming and 3-curvature tensor). It lets also to calculate the temp of the time.

It may be helpful to think about depolarizing channels in another way:  with some probability the qubit is discarded and replaced with a qubit in a maximally mixed state; otherwise it is unchanged.  So the state of the qubit becomes a mixture of the original state and the maximally mixed state.

In the Bloch sphere picture, the original state is represented by some vector, and the maximally mixed state is represented by the zero vector.  A mixture of the two will be presented by a linear combination of the two vectors, which will be in the same direction as the vector for the original state, but shorter.

The question puts me in the situation to answer two times yes - where both answers are based on reasons that belong much more to those who reject this theory as to them accepting it.

1. I am much more a convinced fan of the determinist views of physics as of the non-determinist theories. The paradox is that as a determinist I agree more with the existence of a wave function of the universe as with its non-existence. A general coherence, or what remained, matches better with my intuition of strict and many-dimensional chain of causalities.

2. I cannot accept the big-bang  as possible begin of the whole universe. I accept it just as one accepts the hypothesis of a local event that determines all the visible universe and maybe much more, but just a small neighborhood of us relatively to the universe. Seen like this, the big bang is also a theory with local applicability, as all other physical theories before. But exactly because of its locality, I have a reason less to deny the existence of the universal wave function, although the circularity Ψ(U)=Ψ(Ψ,U) would locally persist!

Isn't this a funny situation?

@Leyvraz  Non-Markovianity has been linked quantitatively to different distance measures (e.g., trace distance, Bures distance, Hilbert-Schmidt distance). However these measures vary  due to inherently differet characteristics,  and as such there is no  unique definition of non-Markovianity in quantum systems. In a sense, if there is a measure that responds to deviations from the continuous, memoryless, completely positive semi-group feature of Markovian evolution, then it is may qualify as a tool to quantify non-Markovianity. The concepts of divisibility and distinguishability  have been very useful  in identifying  measures which violate the complete positivity during the evolution of a  system. So to answer your question: there is no single quantity that I have in mind.....as long as "it" is linked to the breakdown of the complete positivity during  evolution, it will do ok. Even the increase of trace distance during time intervals (for instance) may be  taken as a sufficient but not necessary signature of  non-Markovianity. This shows the complexities of non-Markovian dynamics.

It is challenging as well to quantify Non-locality, and there are attempts to involve  the  Bell inequality and variations thereof  to quantify the boundaries of non-local events. So we have hurdles in defining the problem even before resorting to solving it!

Perhaps it is a good start to seek a link (implicit or otherwise) between non-Markovianity and non-locality. To this end, it would be interesting to seek  the role of mathematical mappings known as the assignment or extension maps within the context of this problem. Assignment maps provide description as to how a subsystem is embedded within a larger system. These maps can take on negative values in some instances, and the  quantum system proceeds to evolve with signatures of non-Markovian dynamics for a given period of time. Will further examination of the Assignment maps help establish a link  between increased non-Markovianity and non-locality? What is the role of the Minkowski space & geometric algebra in this regard? Are they better platforms with which to examine this problem, which appears ill defined at the moment.

I cannot give quite a satisfactory answer. However, I do believe an essential ingredient is the fact that the interaction of any photon with any particular atom in the beam splitter is exceedingly small. The reflection arises as a collective, or coherent, effect. For this reason, at least, the large number of atoms does not necessarily lead to decoherence. As for temperature, I would argue that room temperature does not lead to the presence of optical thermal photons, so that for an optical photon things are OK. In other words, thermal lattice vibrations do not interact with the incident photon, because of a considerable energy and frequency mismatch.

Initially I might have said: it is because no energy gets transferred from the photon to the beam splitter. This, however, is not true, since there are plenty of instances in which decoherence arises without energy transfer. 

It is somewhat disheartening that, apparently, many physicists are not even capable  to correctly describe a Stern-Gerlach spin-component measurement. In such a measurement, a specific COMPONENT of the quantum-mechanical spin of, e.g., an atom is measured - let's say the z-component. in this experiment, the measuring device does NOT exhibit full rotational symmetry, but only symmetry under rotations around the z-axis; (the device typically will involve an external magnetic field parallel to the z-axis, which breaks full rotational invariance, but preserves the symmetry of rotations around the z-axis). Hence, in the course of a measurement, only the z-component of the total spin of the observed system is conserved! The total spin, as measured by \vec{S}\cdot\vec{S}, is NOT conserved in the measurement. (For two atoms, each with spin 1/2, prepared in a spin-singlet initial state (i.e., s=0), the state AFTER a measurement of the z-component of one of the two atoms is a superposition of states of spin s=0 and spin s=1; but the z-component of the total spin remains 0!)

Obviously, it is IMPOSSIBLE to measure ALL components of a quantum-mechanical spin in a single measurement, because the operators representing these components do not commute among each other.

When one observes photons, instead of atoms, one measures HELICITIES of photons (rather than "spin"). The direction of propagation of the photons (as determined, for example, by some optical fiber through which they propagate) then breaks rotational symmetry. It is therefore inaccurate to say that the observed correlations between the helicities of two photons is a consequence of the initial state of the two photons having "spin = 0"!

Re. entropy and QM, this paper is interesting: http://cdn.intechopen.com/pdfs-wm/29594.pdf