Dear Wei, Interleaving.
----- Original Message ----- From: "Wei Dai" <[EMAIL PROTECTED]> To: "Stephen Paul King" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Friday, December 27, 2002 4:18 PM Subject: Re: Quantum Probability and Decision Theory > On Thu, Dec 26, 2002 at 08:21:38PM -0500, Stephen Paul King wrote: > > Forgive me if my writting gave you that opinion. I meant to imply that > > any mind, including that of a bat, is quantum mechanical and not classical > > in its nature. My ideas follow the implications of Hitoshi Kitada's theory > > of Local Time. > > Please explain how your ideas follow from Hitoshi Kitada's theory > of Local Time. Keep in mind that most of us are not familiar with that > theory. > [SPK] It is hard for me to condense the theory of Local Time, it is better to refer you to Hitoshi Kitada's papers. You will find them here: http://www.kitada.com/#time > Also, any quantum computer or physical system can be simulated by a > classical computer. [SPK] Bruno has made similar statements and I do not understand how this is true. I have it from multiple sources that this is not true. Do you recall the famous statement by Richard Feynman regarding the "exponential slowdown" of classical system attempting to simulate QM systems? Let me quote from a paper by Karl Svozil et al: http://tph.tuwien.ac.at/~svozil/publ/embed.htm *** 4 Summary We have reviewed several options for a classical ``understanding'' of quantum mechanics. Particular emphasis has been given to techniques for embedding quantum universes into classical ones. The term ``embedding'' is formalized here as usual. That is, an embedding is a mapping of the entire set of quantum observables into a (bigger) set of classical observables such that different quantum observables correspond to different classical ones (injectivity). The term ``observables'' here is used for quantum propositions, some of which (the complementary ones) might not be co-measurable, see Gudder . It might therefore be more appropriate to conceive these ``observables'' as ``potential observables.'' After a particular measurement has been chosen, some of these observables are actually determined and others (the complementary ones) become ``counterfactuals'' by quantum mechanical means; cf. Schrödinger's catalogue of expectation values . For classical observables, there is no distinction between ``observables'' and ``counterfactuals,'' because everything can be measured precisely, at least in principle. We should mention also a caveat. The relationship between the states of a quantum universe and the states of a classical universe into which the former one is embedded is beyond the scope of this paper. As might have been suspected, it turns out that, in order to be able to perform the mapping from the quantum universe into the classical one consistently, important structural elements of the quantum universe have to be sacrificed: · Since per definition, the quantum propositional calculus is nondistributive (nonboolean), a straightforward embedding which preserves all the logical operations among observables, irrespective of whether or not they are co-measurable, is impossible. This is due to the quantum mechanical feature of complementarity. · One may restrict the preservation of the logical operations to be valid only among mutually orthogonal propositions. In this case it turns out that again a consistent embedding is impossible, since no consistent meaning can be given to the classical existence of ``counterfactuals.'' This is due to the quantum mechanical feature of contextuality. That is, quantum observables may appear different, depending on the way by which they were measured (and inferred). · In a further step, one may abandon preservation of lattice operations such as not and the binary and and or operations altogether. One may merely require the preservation of the implicational structure (order relation). It turns out that, with these provisos, it is indeed possible to map quantum universes into classical ones. Stated differently, definite values can be associated with elements of physical reality, irrespective of whether they have been measured or not. In this sense, that is, in terms of more ``comprehensive'' classical universes (the hidden parameter models), quantum mechanics can be ``understood.'' *** What this paper points out is that it is impossible to completely embed a "QM universe" in a classical one. If, as you say, it is possible to simulate quantum computer or physical system by a classical computer, then we find outselves in an odd predicament. Let me quote from some other papers to reinforce my argument. http://www.cs.auckland.ac.nz/~cristian/coinsQIP.pdf ** 1. INTRODUCTION For over fifty years the Turing machine model of computation has defined what it means to ''compute'' something; the foundations of the modern theory of computing are based on it. Computers are reading text, recognizing speech, and robots are driving themselves across Mars. Yet this exponential race will not produce solutions to many intractable and undecidable problems. Is there any alternative? Indeed, quantum computing offers one such alternative (see Ref. 7, 10, 11, 23, 35). To date, quantum computing has been very successful in ''beating'' Turing machines in the race of solving intractable problems, with Shor and Grover algorithms achieving the most impressive successes; the progress in quantum hardware is also impressive. Is there any hope for quantum computing to challenge the Turing barrier, i.e., to solve an undecidable problem, to compute an uncomputable function? According to Feynman's argument (see Ref. 20, a paper reproduced also in Ref. 25, regarding the possibility of simulating a quantum system on a (probabilistic) Turing machine4) the answer is negative. *** We also have: http://xxx.lanl.gov/abs/quant-ph/0204153 A stronger no-cloning theorem Authors: Richard Jozsa (University of Bristol UK) Comments: 4 pages. An error in version 1 corrected. Further interpretational comments added It is well known that (non-orthogonal) pure states cannot be cloned so one may ask: how much or what kind of additional (quantum) information is needed to supplement one copy of a quantum state in order to be able to produce two copies of that state by a physical operation? For classical information, no supplementary information is required. However for pure quantum (non-orthogonal) states, we show that the supplementary information must always be as large as it can possibly be i.e. the clone must be able to be generated from the additional information alone, independently of the first (given) copy. *** I could go on and on. > So in theory, even if human minds are quanum > mechanical, we can simulate a complete human being from conception to > adulthood in a classical computer, and then copy him to another classical > computer, so the no-cloning theorem doesn't prevent copying of minds. > > Besides, the no-cloning theorem only says that there's no method for > duplicating arbitrary quantum systems in such a way that no statistical > test can tell the difference between the original and the copy. There is > no evidence that the information that can't be copied are crucial to the > workings of a human mind. I think current theories of how the brain works > have its information stored in macroscopic states such as neuron > connections and neurotransmitter concentrations, which can be copied. [SPK] There do exist strong arguments that the "macroscopic state" of neurons is not completely classical and thus some degree of QM entanglement is involved. But hand waving arguments aside, I would really like to understand how you and Bruno (and others), given the proof and explanations contained in these above mentioned papers and others, maintain the idea that "any quantum computer or physical system can be simulated by a classical computer." Kindest regards, Stephen