Subject: Blurring in space and time & quantum computing
Date: Tue, 31 Dec 2002 17:49:29 +0200 From: Dimi Chakalov <dchakalov@surfeu.at> To: marcofrasca@mclink.it CC: rbk@socrates.berkeley.edu, vstenger@mindspring.com, jon.walgate@qubit.org, l.hardy1@physics.oxford.ac.uk, christopher.timpson@queens.oxford.ac.uk, p.knight@ic.ac.uk, m.plenio@ic.ac.uk, v.vedral@ic.ac.uk, dansuzy@nyc.rr.com, terno@physics.technion.ac.il, David.Miller@cern.ch, John.Ellis@cern.ch BCC: [snip] Dear Dr. Frasca, May I ask two questions. 1. Regarding the blurring in space and time, which is washed out in the thermodynamic limit [Ref. 1]: can you state the condition under which quantum computing [Ref. 2] will be impossible *in principle*? Something like 'if A turns out to be true, quantum computing will be impossible'? 2. Precisely what are the implications for quantum computing from the absence of a theory of Lorentz invariant nonlocality? Please see http://members.aon.at/chakalov/readme1st.html#Schroedinger_1931 http://members.aon.at/chakalov/Peres.html#NB I believe you will agree that (i) we do not have a relativistic theory of quantum measurement and (ii) can not employ the alleged privileged reference frame, http://members.aon.at/chakalov/Krasnikov.html#NB "The hardest thing of all is to find a black cat in a dark room, especially if there is no cat", says Confucius. In the context of quantum computing, there are tons of papers claiming that there *might* be a cat, but I have not found any clear statement of the conditions under which there will be no cat in the dark room. I will be happy to learn the opinion of your colleagues as well. I hope you will agree that, unless we can state a falsifiable hypothesis, we can't claim that are doing science. Wishing you and your colleagues all the best for 2003, Dimi Chakalov
P.S. There is another case of chasing black cats, known as Higgs boson(s), http://members.aon.at/chakalov/LHC.html#summary but let's keep the story simple and pollyannaish.
References [Ref. 1] Marco Frasca, Does decoherence
in the thermodynamic limit exist?,
[Ref. 2] Chris Adami, Jonathan P. Dowling.
Quantum Computation  The Ultimate Frontier,
"The power of quantum computation is that the 2^N terms in superposition (3) can be operated on simultaneously with a unitary quantum operator U (this is known as *quantum parallelism*). Of course, you need to make sure that the entanglement extends to all these qubits, and these qubits only. Should a few qubits become entangled with (3) inadvertently (which means, should you not be aware that this happened), the wonderful properties of the entangled states will have turned from boon to bane: Instead of a coherent superposition you will be handed an uncertain mixture of states, useless for computation. In a manner of speaking, then, all quantum computations ought to be performed in "total darkness" (since photons are perfect qubits on their own), and at zero temperature. Even "looking" at your end result could prove to be hazardous if special precautions are not taken." =====
Subject: Re: Blurring in space and time
& quantum computing
Dear Marco, Regarding my second question, "Precisely what are the implications for quantum computing from the absence of a theory of Lorentz invariant nonlocality?", http://members.aon.at/chakalov/Frasca.html#Q2 please see [Ref. 3]. Peres and Terno wrote: "Relativistic effects affect nearly all notions of quantum information theory" [Ref. 3]. This can be made very clear by recalling that we do not observe the world around us in some absolute Newtonian "time", and therefore the measurement problem (or rather paradox) in QM is indissolubly linked to STR: anything we observe is in our past light cone. For example, if you look at the Sun at the instant t_0 of your wristwatch, you will see the state of the Sun had 8.3 min ago, but you know that the Sun does have a physical state at t_0 which you *will* see after 8.3 min. This future state is 'out there', it will come in 8.3 min. Hence STR and the concept of reality from classical physics are intermingled, as stresses by Schrödinger back in 1935, http://members.aon.at/chakalov/Corbett.html#2 If we think of the entangled qubits as staying 'out there', like the Sun, but in "total darkness", http://members.aon.at/chakalov/Frasca.html#2 we are 'not even wrong', http://members.aon.at/chakalov/Lloyd.html#2 The issue here is not about protecting the entangled qubits from environmental "decoherence". It is about Special Theory of Relativity, as stresses by Schrödinger back in 1931, http://members.aon.at/chakalov/readme1st.html#Schroedinger_1931 Some people get very excited by the possibility for effective shielding from decoherence, http://www.newscientist.com/news/news.jsp?id=ns99993114 http://members.aon.at/chakalov/Vaidman.html The real problems are with STR, however. It goes without saying that we can not build quantum computers operating in the Newtonian time of the socalled unitary "evolution". Nor can we develop some relativistic quantum theory of measurements: there is no room for *nonunitary* dynamics of quantum state in STR, http://members.aon.at/chakalov/LHC.html#Holon Would that life were so simple! More at http://members.aon.at/chakalov/dimi.html#summary To explain the tacit presumption of 'manipulating entanglement locally' in quantum computing, let's consider a Gedankenexperiment called Loop Quantum Teleportation; see my note of March 6, 2000, at http://listserv.arizona.edu/cgibin/wa?A2=ind0003&L=
Think of four participants, Alice > Bob > Carol > David, such that David has not been correlated with Alice & Bob. Suppose it is possible, as a Gedankenexperiment, to link David to Alice like that: Alice > Bob > Carol > David
The idea is to time the whole chain of teleportation by letting David to (re)initiate it by acting on Alice. First, we do a kickstart from Alice, just once, and then David will run the chain as a reverberation cycle. Is this possible, even in a thought experiment? If yes, what would be the timing of events in that cycle, as measured at the point "Alice" with her wristwatch? If not, we go back to my second question above, http://members.aon.at/chakalov/Frasca.html#Q2 See also my forthcoming CD ROM at Regards, Dimi Chakalov
John S. Bell
References [Ref. 3] Asher Peres, Daniel R. Terno.
Quantum information and special relativity.
"Relativistic effects affect nearly all notions of quantum
information theory.
P. 3: "An interesting problem is the relativistic nature
of quantum entanglement when there are several particles. For two particles,
an invariant definition of the entanglement of their spins would be to
compute it in the Lorentz "rest frame" where (XX) = 0. However, this simple
definition is not adequate when there are more than two particles, because
there appears a problem of cluster decomposition: each subset of particles
may have a different rest frame. This is a difficult problem, still
awaiting for a solution. We shall mention only a few partial results."
