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27
Quantum mechanics as quantum information (and only a little more), Quantum Theory: Reconsideration of Foundations
, 2002
"... In this paper, I try once again to cause some goodnatured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or ..."
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Cited by 61 (6 self)
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In this paper, I try once again to cause some goodnatured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears better calibrated for a direct assault than quantum information theory. Far from a strained application of the latest fad to a timehonored problem, this method holds promise precisely because a large part—but not all—of the structure of quantum theory has always concerned information. It is just that the physics community needs reminding. This paper, though takingquantph/0106166 as its core, corrects one mistake and offers several observations beyond the previous version. In particular, I identify one element of quantum mechanics that I would not label a subjective term in the theory—it is the integer parameter D traditionally ascribed to a quantum system via its Hilbertspace dimension. 1
Simulating Quantum Mechanics by NonContextual Hidden Variables
, 2000
"... No physical measurement can be performed with infinite precision. This leaves a loophole in the standard nogo arguments against noncontextual hidden variables. All such arguments rely on choosing special sets of quantummechanical observables with measurement outcomes that cannot be simulated non ..."
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Cited by 27 (1 self)
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No physical measurement can be performed with infinite precision. This leaves a loophole in the standard nogo arguments against noncontextual hidden variables. All such arguments rely on choosing special sets of quantummechanical observables with measurement outcomes that cannot be simulated noncontextually. As a consequence, these arguments do not exclude the hypothesis that the class of physical measurements in fact corresponds to a dense subset of all theoretically possible measurements with outcomes and quantum probabilities that can be recovered from a noncontextual hidden variable model. We show here by explicit construction that there are indeed such noncontextual hidden variable models, both for projection valued and positive operator valued measurements.
Quantum Foundations in the Light of Quantum Information
 PROCEEDINGS OF THE NATO ADVANCED RESEARCH WORKSHOP, MYKONOS GREECE
, 2001
"... In this paper, I try to cause some goodnatured trouble. The issue at stake is when will we ever stop burdening the taxpayer with conferences and workshops devoted— explicitly or implicitly—to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to ..."
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Cited by 17 (2 self)
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In this paper, I try to cause some goodnatured trouble. The issue at stake is when will we ever stop burdening the taxpayer with conferences and workshops devoted— explicitly or implicitly—to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears to be better calibrated for a direct assault than quantum information theory. Far from being a strained application of the latest fad to a deepseated problem, this method holds promise precisely because a large part (but not all) of the structure of quantum theory has always concerned information. It is just that the physics community has somehow forgotten this.
Computational universes
 Chaos, Solitons & Fractals
, 2006
"... Suspicions that the world might be some sort of a machine or algorithm existing “in the mind ” of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science h ..."
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Cited by 9 (5 self)
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Suspicions that the world might be some sort of a machine or algorithm existing “in the mind ” of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science have lent support to the thesis, but empirical evidence is needed before it can begin to replace our contemporary world view.
KochenSpecker vectors
 J. Phys. A: Math. Gen
, 2005
"... Abstract. We give a constructive and exhaustive definition of KochenSpecker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in ndim Hilbert space, H n, n ≥ 3 to which it i ..."
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Cited by 5 (0 self)
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Abstract. We give a constructive and exhaustive definition of KochenSpecker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in ndim Hilbert space, H n, n ≥ 3 to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R n, on algorithms that single out those diagrams on which algebraic 01 states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and selfteaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all 4dim KS vector systems containing up to 24 vectors were generated and described, all 3dim vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found.
Generalizations of Kochen and Specker’s theorem and the effectiveness of Gleason’s theorem
 Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35, 177194
, 2004
"... Abstract. Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s th ..."
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Cited by 3 (1 self)
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Abstract. Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated. 1. Gleason’s Theorem and Logical Compactness Kochen and Specker’s (1967) theorem (KS) puts a severe constraint on possible hiddenvariable interpretations of quantum mechanics. Often it is considered an improvement on a similar argument derived from Gleason (1957) theorem (see, for example, Held. 2000). This is true in the sense that KS provide an explicit construction of a finite set of rays on which no twovalued homomorphism exists. However, the fact that there is such a finite set follows from Gleason’s theorem using a simple logical compactness argument (Pitowsky 1998, a similar point is made in Bell 1996). The existence of finite sets of rays with other interesting features
Noncontextuality, finite precision measurement and the Kochen–Specker theorem
, 2003
"... Meyer originally raised the question of whether noncontextual hidden variable models can, despite the KochenSpecker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental ..."
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Cited by 2 (0 self)
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Meyer originally raised the question of whether noncontextual hidden variable models can, despite the KochenSpecker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental
Book Review
, 1996
"... pproximations, that is complete and to the point. His survey of complexity theory is equally clear and well done. The book starts out by discussing the general ideas in terms of the simple twopoint boundary value problem (1) (Lu)(x) =  d 2 u dx 2 (x) + u(x) = f(x) for x # [0 , 1] , (2) du( ..."
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Cited by 1 (0 self)
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pproximations, that is complete and to the point. His survey of complexity theory is equally clear and well done. The book starts out by discussing the general ideas in terms of the simple twopoint boundary value problem (1) (Lu)(x) =  d 2 u dx 2 (x) + u(x) = f(x) for x # [0 , 1] , (2) du(0) dx = du(1) dx = 0. Here f is the given data and is assumed to lie in the unit ball F of square integrable functions; i.e., (3) F = {f : #f# L 2 # 1}. 2 BOOK REVIEWS The next step is to formulate (1)(2) in terms of the Sobolev sp