| Subject: Quantum
computing in dark
Date: Tue, 14 Mar 2006 10:56:15 +0200 From: Dimi Chakalov <dimi@chakalov.net> To: Peter L Knight <p.knight@imperial.ac.uk> CC: Norbert Lütkenhaus <nlutkenhaus@iqc.ca>, Miloslav Dusek <dusek@optnw.upol.cz>, Martin Hendrych <hendrych@optnw.upol.cz>, Karl Svozil <svozil@tuwien.ac.at>, Martin Plenio <m.plenio@imperial.ac.uk>, S Virmani <s.virmani@imperial.ac.uk>, Terry Rudolph <tez@imperial.ac.uk> Dear Peter, If you were designing a brand new car, wouldn't you try the prototype on a rough road? In case you are optimistic about "quantum computing", see the price one has to pay for relativistic locality [Ref. 1]. Regarding Fig. 1b in Karl Svozil's paper, see http://www.god-does-not-play-dice.net/right.html#Note_1 If you and/or any of your colleagues still believe in "quantum computing", please take part in the 'flipping a quantum coin' quiz at http://www.god-does-not-play-dice.net/Adler.html#Kracklauer Kind regards, Dimi
"In what follows we shall investigate, as a second and arguably conceptually more gratifying alternative, the feasibility to either measure or counterfactually infer all required entities simultaneously. By 'simultaneous' measurement we mean that all single measurements are pairwise spatially separated and temporally coincide in some reference frame (presumably in the centre-of-mass frame of the particles involved). Note also that, due to the apparent randomness and parameter independence of the single outcomes in the correlation experiment, relativistic locality is possible." [See Fig. 1b and Eq. 3] ========= Subject:
What role does entanglement play in quantum computers?
RE: "What role does entanglement play in quantum computers? This question is in general not entirely answered yet." (quant-ph/0401019 v3) Dear Dr. Eisert, Please see http://www.God-does-not-play-dice.net/Knight.html Comments will be appreciated. Sincerely, Dimi Chakalov
Note: Let me quote from "Quantum Computing", quant-ph/0401019 v3, written by Jens Eisert and Michael Wolf: pp. 4-5: "qubits can be in a superposition
of all classically possible states".
"This possibility is called quantum parallelism and it is certainly one of the reasons for the computational power of a quantum computer. The mathematical structure behind the composition of quantum systems is the one of the tensor product." I will now provide my understanding of "quantum computing". The mere suggestion that "qubits can be in a superposition of all classically possible states" is just a wild guess, which cannot be verified by experiment or observation due to its counterfactual nature. The question here, raised by Ernst Specker, is whether we can provide a complete (or global) presentation of a quantum system by a set of all observable (or local) states of that same system. As explained eloquently by K. Svozil (reference here), "in quantum mechanics, every single orthonormal basis of a Hilbert space corresponds to locally comeasurable elements of physical reality. The (undenumerable) class of all orthonormal basis of a Hilbert space corresponds to a global description of the conceivable observables -- Schrödinger’s catalogue of expectation values (52)." It turns out that, in the case of Hilbert space with dimension greater than two, we cannot compile such set in principle. It just does not exist, as we could have anticipated from Schrödinger’s 1935 paper. The proponents of "quantum computing" are making all efforts to avoid the crucial implications from Kochen-Specker theorem, but if they use an entangled state of quantum particles, I'm afraid they are in deep murky waters. What I meant by 'quantum computing in dark' (please see above) is that they employ a "cat", called Macavity, which shows up only when there is no one to look at it (T.S. Eliot, "Macavity, the Mystery Cat"). Here, Macavity stands for 'the complete (global) presentation of a quantum system by its observable (local) states', along the line of thought of Ernst Specker. See also the story of John's jackets here, and recall the dictum 'the whole is more than the sum of its parts'. The task undertaken by Ernst Specker is theoretically feasible only and exclusively only in the inanimate macro-world, in which the lack of global or complete knowledge is purely epistemological. In the living and quantum worlds, it is a question of new ontology. See its manifestation in Einstein's GR here. To understand the whole issue in 2-D Hilbert space, and the alleged "unitary evolution" performed by the hypothetical quantum computer [Ref. 1], please see the 'flipping a quantum coin' quiz here. Now, consider a quantum coin as a "qubit". It has two entangled states, which can be observed by Alice and Bob. Suppose also that if Alice observes 'head', Bob will have to observe 'tail', and if Alice observes 'tail', Bob will have to observe 'head'. As we know from EPR paper of 1935, if Alice observes 'head', she could formulate the following educated guess: If some non-local observer could "see" Bob and me simultaneously, then this non-local observer would "see" that the instant tA at which I have already observed 'head', and the instant tB at which Bob has already observed 'tail', are simultaneous in all reference frames. Alice is certainly not a blond girl. However, notice that the so-called non-local observer should be able to see her and Bob simultaneously, like a 3-D nanny watching 2-D kids in Flatland, firstly, and secondly -- the whole guess of Alice is grounded entirely on counterfactuals, just like the Bell "argument". Thus, the whole "quantum computing" is inevitably contaminated with counterfactuals from the outset. The proponents speculate that if they chain many such 'quantum coins', they should be able to "run the computation on all classically possible input states at the same time" (see above; emphasis added). However, if they chain just four entangled coins (cf. K. Svozil above), the so-called quantum parallelism will be collapsed to "one path through the system", as noticed by Saul Youssef. Why? See again Fig. 1b and Eq. 3 in K. Svozil above, and recall that the four entangled coin(s) do not, and cannot possess any individual properties whatsoever, as explained by GianCarlo Ghirardi and Luca Marinatto here. To use again the story of John's jackets, we can say that John can indeed cast four of his jackets in our past light cone, but in order to make a quantum computer, you'd have to manipulate John himself, which isn't possible, simply because John does not live in the Hilbert space nor in Minkowski spacetime. He is a different reality: potential reality. To sum up, I believe "quantum computing" is sheer parapsychology. It is true that its mathematical structure "is the one of the tensor product", as stressed by Jens Eisert and Michael Wolf, but, in order to understand the real problems, don't hide behind "tensor product" but see the 'flipping a quantum coin' quiz here, and cast your vote. I wrote to Jens Eisert, because I liked what he and his co-author wrote about the quantum entanglement. It is indeed a big can of worms. Coincidently nor not, they finished their quant-ph/0401019 v3 with a startling prediction from 1949: "Where a calculator on the ENIAC is equipped with 18,000 vacuum tubes and weighs 30 tons, computers in the future may have only 1,000 tubes and perhaps only weigh 1 1/2 tons." (Popular Mechanics, March 1949) Similar optimistic predictions about "quantum computers" may be very instructive. More can be read below. Comments are welcomed. Alternatively, you may reply like Andrew Steane. Since "the border between classical and quantum phenomena is just a question of money" (reference here), and the military establishment is never short of taxpayers' money, you can, at least for now, play with the "error correction" of your "quantum computer". Not for long though.
[Ref. 1] Michael A. Nielsen
et al., Quantum Computation as Geometry,
quant-ph/0603161
v1. ========= Subject: Entanglement distillation, if any
Dear Peter, Regarding your recent entanglement distillation procedure and loophole-free test of Bell inequalities [Ref. 1]: I wonder if you remember my numerous email notes sent three years ago, in which I expressed my profound skepticism. I believe there is a hidden parameter (called 'global
mode of spacetime'), which is *not* present in the linear combination
of
All this boils down to (i) the Lorentz-invariant non-locality, http://www.God-does-not-play-dice.net/Tresser.html#collapse http://www.God-does-not-play-dice.net/Hartle.html#Bell and (ii) the hypothetical "decoherence", http://www.God-does-not-play-dice.net/Halliwell.html#addendum See also the concept of "hidden" time, proposed by Pavel Kurakin et al. [Refs. 2 and 3]. If you believe can overcome problems (i) and (ii) above, and are optimistic about entanglement distillation and manipulating entanglement locally, please write me back. Kindest regards, Dimi
John S. Bell
References [Ref. 1] Sonja Daffer, Peter L. Knight,
Generating optimal states for a homodyne Bell test, quant-ph/0504084 v1,
April 13, 2005,
"The procedure presented here offers the opportunity for
another possible experiment, as it utilizes a subset of an entanglement
distillation procedure. Of course, any observed violation of a Bell inequality
is sensitive to inefficiencies in the experiment that tend to deplete correlations."
[Ref. 2]
Pavel
V. Kurakin, Hidden variables and hidden time in quantum theory, quant-ph/0504089
v1,
[Ref. 3] Pavel Kurakin, George Malinetskii,
Howard Bloom, Conversational (dialogue) model of quantum transitions, quant-ph/0504088
v1,
Note: To understand on the problems (i) and (ii) above, read the recent paper by Michael A. Nielsen, Cluster-state quantum computation, quant-ph/0504097 v1 [Ref. 4]. He claims that we can 'have our cake and eat it': "the basic dynamical operations are non-unitary quantum measurements, yet they can still be used to simulate arbitrary quantum dynamics, including unitary dynamics." On March 6, 2000, I have suggested a simple Gedankenexperimenht to verify this staggering presumption (or rather religious belief). It's called Loop Quantum Teleportation, and employs quantum teleportation, unitary dynamics, and STR. Read it here. More on the alleged "unitary dynamics" here and here. Back in November
2002, Peter Knight was hugely optimistic about "a truly useful quantum
processor" [Ref. 5]. Would that life were so simple!
D. Chakalov
[Ref. 4] Michael
A. Nielsen, Cluster-state quantum computation, quant-ph/0504097 v1,
"The purpose of the present paper is to review recent work on measurement-based quantum computation, i.e., models for quantum computation having the remarkable property that all the basic dynamical operations are non-unitary quantum measurements, yet they can still be used to simulate arbitrary quantum dynamics, including unitary dynamics. "Such models of quantum computation
thus challenge the conventional understanding of quantum measurement as
a process that inherently destroys quantum coherence."
[Ref. 5] Quantum
computing making 'tremendous progress', by Michael Brooks, New Scientist,
09:30 29 November 2002,
"The advances made in the field belie
the difficulty of manipulating quantum information, according to Peter
Knight, a quantum information researcher at Imperial
College, London. But he believes there is now cause for optimism about
developing a truly useful quantum processor. "There's been tremendously
rapid progress in the last year. I was hugely impressed at how things have
developed," he says."
======= Subject: Probabilities
of failure for quantum error correction
Dear Dr. Scott, It seems to me that, in order to gain control over the cascade of quantum error correction operations [Ref. 1], you need to maintain *strictly* unitary operations by projective measurements [Refs. 1-4], which, in turns, requires controlling the quantum beast over a *finite* time interval, as measured by your wristwatch, which, in turns, requires a detailed unambiguous description of the process of embedding a quantum "event" into Minkowski spacetime. To the best of my knowledge, nobody has managed to achieve this crucial last step. If we try to solve it, we need to go beyond QM: the ket is not merely a description [Ref. 4], but the underlying quantum reality that can "enter" the Minkowski cone in Lorentz-invariant fashion, as I tried to elaborate on my web site. Hence if I'm on the right track, the only "quantum computer" is the one above your neck, http://www.God-does-not-play-dice.net/Mallios.html#note If true, I think the potential implications could hardly be overestimated. On the negative side, all your efforts to build some inanimate "quantum computer" will fail. Given your affiliation with the military, I wouldn't be surprised if you do not reply. But if you do, please be assured that I will be happy to elaborate. Kindest regards, Dimi Chakalov
References [Ref. 1] Andrew
J. Scott, Probabilities of failure for quantum error
"Error correction is achieved through
a two-step process: a projective measurement followed by a unitary operation
conditioned on the measurement outcome.
"This work was supported in part
by ONR Grant No. N00014-00-1-0578 and by ARO Grant No. DAAD19-01-1-0648."
[Ref. 2] Bryan Eastin,
A brief review of error correction concepts necessary for fault tolerant
quantum computation,
"Generalized Error Correction. "A complete syndrome circuit implements the unitary [XXX]. "This unitary enables the correction
of arbitrary errors on a mixed
[Ref. 3] Andrew
M. Steane, Quantum error correction (February 1996),
"Note that we define the term 'error' to mean in general any contribution to the evolution of a quantum system which is unpredictable. Usually therefore the errors will be continuous rather than discrete, and will affect all the qubits rather than a subset. However, during error correction the system is projected onto a subspace of its Hilbert space which contains only state vectors with a specific error syndrome. Therefore the continuous error process is rendered discrete (collapsed) by the projective measurement. "The main *proviso* to all the above
is that the correction process can itself be carried out without errors.
This is clearly a huge assumption."
[Ref. 4] Andrew
Steane, On the Interpretation of Quantum Mechanics
"The most obvious way to think about Schrodinger's cat is to adopt one of the following hypotheses: (i) completely unitary dynamics leading
to highly complicated quantum
"The first is the hypothesis in which Schrodinger's equation is perfectly ok and describes all physical interactions all the time, so the final state of nucleus, poison, cat, other observers, old uncle Tom Cobbley and all is a quantum superposition state. The second is the hypothesis that some as yet not fully understand non-linear dynamics occurs in physical systems of sufficient mass or complexity, leading to a final state in which the cat is either alive or dead, and certainly not in a superpussition. The third is a framework such as the de Broglie Bohm pilot wave theory, or the decoherent histories approach. "It seems to me that Occam's razor
("don't accumulate unneccesary hypotheses") would shave away (ii) and (iii)
if we could be convinced that (i) is a clear and elegant description of
the world around us. I do not find (iii) appealing because those approaches
seem to me highly inelegant, especially when the attempt is made to render
them Lorentz invarient.
"In my point of
view, quantum states such as |u a w> + |e d c> are perfectly legitimate.
An apparent difficulty is that we might imagine we don't encounter states
like |u a w> + |e d c> in our conscious experience. Once we recall that
the ket is merely a description, not the underlying reality, this problem
vanishes. The reality is that we experience cats either alive or dead,
and the state |u a w> + |e d c> is the description of our experience, furnished
by our physical theory. We can tell when this description is a quantum
superposition and when a mixture by appealing to Postulate 1. The only
way this can lead to problems is if your conscious experience does not
have an environment, but this never happens and indeed is probably a self-contradictory
circumstance."
======= Subject: Re:
Probabilities of failure for quantum error correction
P.S. Andrew
Steane has instructed his email client to bounce back my
What do you think? D.C. =======
Subject: The
glorified chimpanzees
Dear Dr. Rudolph, I agree with your opinion on quantum information and 'glorified chimpanzees' (Quantum Physics from A to Z, quant-ph/0505187 v1). I also noticed that you have graduate students, "Yep, I now have my own graduate
students to make miserable..."
I believe kids have the right to know the whole truth. If you agree, please pass the link below to your grad students, http://www.God-does-not-play-dice.net/Knight.html Kindest regards, D. Chakalov
There is no quantum information. There is only a quantum way of handling information. The border between classical and quantum phenomena is just a question of money. The speed of the collapse is bull... A.Z. to Paul Kwiat: You will never catch up. So don't bother trying. Have fun! Quoting A.Z. on unscientific business: I don't know, I just work here. Terry Rudolph: Without Zeilingers, Vedrals and other glorified chimpanzees there is no need for information whatsoever.
=======
Subject: Macavity
and LOCC
Dear Martin, Regarding your latest "An introduction to entanglement measures", quant-ph/0504163 v1 [Ref. 1]: I believe there are generic limitations of 'Local Operations and Classical Communication' (LOCC) on "the additional power provided by entanglement", which make the latter a purely intellectual exercise devoid of any practical implementation whatsoever. It's like trying to "see" a dark room with a torch. Just like the cat Macavity, http://www.God-does-not-play-dice.net/Helfer.html I believe we're dealing with a brand new animal which "exists" as long as no one is "looking" at it with LOCC. Hence the interconversion of all, i.e. pure and mixed, bi-partite entangled states [Ref. 2] passes through the invisible Macavity state called 'entanglement'. Any time you look at it with your LOCC "torch", it's gone. Why? Because all we can observe with *inanimate* devices is inevitably in our past light cone, http://www.God-does-not-play-dice.net/Willem.html#STR More at http://www.God-does-not-play-dice.net/Lloyd.html#beard http://www.God-does-not-play-dice.net/Knight.html Perhaps this is the reason why I didn't get a job under the roof of Prof. Peter L. Knight, http://www.God-does-not-play-dice.net/points.html#acknowledgements Shame, because all we needed was just above our neck. Kindest regards, Dimi
References [Ref. 1] Martin
B. Plenio and Shashank Virmani, An introduction to entanglement measures,
quant-ph/0504163 v1, 21 April 2005,
[Ref. 2] M.B. Plenio,
Reversible entanglement manipulation, 08 February 2005,
Problem The concept of entanglement as a
resource motivates the study of its transformation properties under certain
classes of operations such as local operations and classical communication
(LOCC).
The following are open questions: Are ppt-operations sufficient to ensure asymptotically reversibly interconversion of all, i.e. pure and mixed, bi-partite entangled states [BFC]? What is the smallest non-trivial
class of operations that permits asymptotically reversibly interconversion
of all, i.e. pure and mixed, bi-partite entangled states [Bet]?
Note 2: To understand the whole bundle of issues from the invisible cat Macavity (negative energy density effects), read the recent review article by Larry Ford "Spacetime in Semiclassical Gravity", gr-qc/0504096 v1, particularly Sec. 6, "The Dark Energy Problem" [Ref. 3]. Larry Ford uses the so-called semiclassical approximation of gravity, in which the gravitational field is classical, but is (somehow) coupled to quantum matter fields. This is all we have, since a complete theory of quantum gravity is still out of sight. Needless to say, I believe we should place Macavity in the "unzipped" virtual gravitational reality: the global mode of spacetime. Since the gravitational field is classical, but is (somehow) coupled to quantum matter fields, we need to understand the very transition from quantum to classical, and back. But you have to "hold on something" to move between these two totally different realms, right? If you agree, make sure that you never turn on your LOCC "torch", for you'll never see Macavity nor the phenomenon called 'entanglement'. It can be "observed" only with a human brain, as I argued two years ago. To sum up, in order to explain the transition from quantum to classical and back, we need to 'hold onto' something. Let's call it [X]. It is a very peculiar "dark" object, since it disappears by 'looking at it'; just like the invisible cat Macavity. Let's place [X] in the global mode of spacetime, and ask the following question: what if [X] is composed of two gravitational waves that cancel each other à la Cramer? The ultimate task is to suggest a cancellation mechanism for the dynamical dark energy: the remnant from the cancellation of the two virtual "waves" would have to be 'vanishing small but not zero'. That's valid for the current epoch from the evolution of the universe. To explain the coincidence problem, we have to provide the cancellation mechanism for the dynamical dark energy with the option to produce arbitrary large "remnant value", e.g., during the inflationary stage. All these speculations are needed to clarify what we need to achieve in the first step of our theory of quantum gravity: the emergence of 3-D space. This is the crux of the task. Recall that the intrinsic properties of 3-D space are presented in dichotomies: 'big vs. small', 'inside vs. outside' (more on this puzzle here). Perhaps the emergence of 3-D space has to include some brand new 'space inversion' symmetry (see 'how to catch a lion in Sahara' here), which could be used to model the dynamical dark energy. Just a guess. All I can suggest at this moment is to set the task in simple words: define the emergence of a finite volume of 3-D space, that is, a sphere with radius r ranging in the open interval (0, [inf.]). First, start with the classical world of tables and chairs, say, with r = 0.01 cm, which is "about the geometric mean of the size of the observable universe and the Planck length." [Ref. 4] We need new physics to fix such a cutoff [Ref. 3]. Secondly, think of two virtual gravitational waves that cancel each other à la Cramer, with a real remnant r = 0.01 cm in the local mode of spacetime. This is a genuine 3-D space with two fixed "directions" in the local mode of spacetime, toward the Large and the Small. Obviously, some essential ideas are missing here, and a lot of work is needed to make them clear. Sorry. At the end of the day, we should obtain an asymptotically flat 3-D space with lots of virtual "dark stuff", and with a virtual "tail" of 'negative mass' in the global mode of spacetime. The "tail" should be seen in the local mode of spacetime as a "mirror" tachyonic world; see also Ya.P. Terletsky here. The deadline is November 2015, exactly 100 years after Einstein proposed his General Relativity. He honestly acknowledged that we "entirely shun the vague word 'space' of which we must honestly acknowledge we cannot form the slightest conception." Of course, it is very likely that by 2015 many of the ideas above may turn out to be wrong: there is too much from 'the unknown unknown' here. But if we don't leave for India,
how can we discover America? D. Chakalov
[Ref. 3] L.H. Ford, Spacetime in Semiclassical Gravity, gr-qc/0504096 v1. p. 6: "We could take a more radical
approach and seek some physical principle which effectively fixes the value
of the regulator parameter to a definite, nonzero value. However, for the
first term on the right hand side of Eq. (2) to be the dark energy, we
would have to take [y] =[app.] (0.01cm)2. It is very hard to
imagine what new physics would introduce a cutoff on a scale of the order
of 0.01cm."
[Ref. 4] L.H. Ford, What does Quantum Field Theory in Curved Spacetime Have to Say about the Dark Energy? gr-qc/0210096 v1. p. 3: "It is not clear how to find
a result which is the geometric mean of these two extremes in a natural
way. In other words, a cosmologically interesting energy density arises
from a scale of the order of 10-2cm, which is about the geometric
mean of the size of the observable universe and the Planck length. It is
far from clear why such a length scale should arise."
|
