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116
Quantum Equilibrium and the Origin of Absolute Uncertainty
, 1992
"... The quantum formalism is a "measurement" formalisma phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr6dinger's equation for a system of ..."
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Cited by 142 (50 self)
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The quantum formalism is a "measurement" formalisma phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr6dinger's equation for a system of particles when we merely insist that "particles " means particles. While distinctly nonNewtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that an appearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by "p = IV [ 2.,, A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.
Unknown quantum states: the quantum de Finetti representation
 J. Math. Phys
"... We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanc ..."
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Cited by 46 (7 self)
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We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable densityoperator assignments and provides an operational definition of the concept of an “unknown quantum state ” in quantumstate tomography. This result is especially important for informationbased interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than states of nature. We further demonstrate that the theorem fails for real Hilbert spaces and discuss the significance of this point. I.
Characterizing quantum theory in terms of informationtheoretic constraints
 Foundations of Physics
, 2003
"... We show that three fundamental informationtheoretic constraints—the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibil ..."
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Cited by 35 (2 self)
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We show that three fundamental informationtheoretic constraints—the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment—suffice to entail that the observables and state space of a physical theory are quantummechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment. KEY WORDS: quantum theory; informationtheoretic constraints. Of John Wheeler’s ‘‘Really Big Questions,’ ’ the one on which most progress has been made is It from Bit?—does information play a significant role at the foundations of physics? It is perhaps less ambitious than some of the other Questions, such as How Come Existence?, because it does not necessarily require a metaphysical answer. And unlike, say, Why the Quantum?, it does not require the discovery of new laws of nature: there was room for hope that it might be answered through a better understanding of the laws as we currently know them, particularly those of quantum physics. And this is what has happened: the better understanding is the quantum theory of information and computation. 1
Time–entanglement between mind and matter
 Mind and Matter
, 2003
"... This contribution explores Wolfgang Pauli’s idea that mind and matter are complementary aspects of the same reality. We adopt the working hypothesis that there is an undivided timeless primordial reality (the primordial “one world”). Breaking its symmetry, we obtain a contextual description of the ..."
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Cited by 17 (3 self)
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This contribution explores Wolfgang Pauli’s idea that mind and matter are complementary aspects of the same reality. We adopt the working hypothesis that there is an undivided timeless primordial reality (the primordial “one world”). Breaking its symmetry, we obtain a contextual description of the holistic reality in terms of two categorically different domains, one tensed and the other tenseless. The tensed domain includes, in addition to tensed time, nonmaterial processes and mental events. The tenseless domain refers to matter and physical energy. This concept implies that mind cannot be reduced to matter, and that matter cannot be reduced to mind. The nonBoolean logical framework of modern quantum theory is general enough to implement this idea. Time is not taken to be an a priori concept, but an archetypal acausal order is assumed which can be represented by a oneparameter group of automorphisms, generating a time operator which parametrizes all processes, whether material or nonmaterial. The timereversal symmetry is broken in the nonmaterial domain, resulting in a universal direction of time for the material domain as well.
Quantum entanglement and projective ring geometry
 SIGMA 2, Paper 66
, 2006
"... The paper explores the basic geometrical properties of the observables characterizing twoqubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal quantum entanglement in such systems, we demonstrate that the 1 ..."
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Cited by 16 (10 self)
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The paper explores the basic geometrical properties of the observables characterizing twoqubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal quantum entanglement in such systems, we demonstrate that the 15×15 multiplication table of the associated fourdimensional matrices exhibits a sofarunnoticed geometrical structure that can be regarded as three pencils of lines in the projective plane of order two. All lines in each pencil carry mutually commuting operators; in one of the pencils, which we call the kernel, the observables on two lines share a base of maximally entangled states. The three operators on any line in each pencil represent a row or column of some Mermin’s “magic ” square, thus revealing an inherent geometrical nature of the latter. In the complement of the kernel, the eight vertices/observables are joined by twelve lines which form the edges of a cube. A substantial part of the paper is devoted to showing that the nature of this geometry has much to do with the structure of the projective lines defined over the rings that are the direct product of n copies of the Galois field GF(2), with n = 2, 3 and 4.
Quantum Mechanics is About Quantum Information
, 2005
"... I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive—just as, following Einstein’s spec ..."
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Cited by 9 (1 self)
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I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive—just as, following Einstein’s special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical entity in its own right.
NonBoolean Descriptions for MindMatter Problems
"... A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmat ..."
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A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmatter distinction. Such a description in terms of a locally Boolean but globally nonBoolean structure makes allowance for the fact that Boolean descriptions play a privileged role in science. If we accept the insight that there are no ultimate building blocks, the existence of holistic correlations between contextually chosen parts is a natural consequence. The main problem of a genuinely nonBoolean description is to find an appropriate partition of the universe of discourse. If we adopt the idea that all fundamental laws of physics are invariant under time translations, then we can consider a partition of the world into a tenseless and a tensed domain. In the sense of a regulative principle, the material domain is defined as the tenseless domain with its homogeneous time. The tensed domain contains the mental domain with a tensed time characterized by a privileged position, the Now. Since this partition refers to two complementary descriptions which are not given apriori,wehavetoexpectcorrelations between these two domains. In physics it corresponds to Newton’s separation of universal laws of nature and contingent initial conditions. Both descriptions have a nonBoolean structure and can be encompassed into a single nonBoolean description. Tensed and tenseless time can be synchronized by holistic correlations. 1.
Quantum information and computation
 arXiv:quantph/0512125. Forthcoming in Butterfield and Earman (eds.) Handbook of Philosophy of Physics
, 2005
"... This Chapter deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, ..."
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Cited by 7 (1 self)
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This Chapter deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information
Perturbation growth and structure in uncertain flows
 I, II. J. Atmospheric Sci
"... Perturbation growth in uncertain systems is examined and related to previous work in which linear stability concepts were generalized from a perspective based on the nonnormality of the underlying linear operator. In this previous work the linear operator, subject to an initial perturbation or a sto ..."
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Cited by 7 (4 self)
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Perturbation growth in uncertain systems is examined and related to previous work in which linear stability concepts were generalized from a perspective based on the nonnormality of the underlying linear operator. In this previous work the linear operator, subject to an initial perturbation or a stochastic forcing distributed in time, was either fixed or time varying, but in either case the operator was certain. However, in forecast and climate studies, complete knowledge of the dynamical system being perturbed is generally lacking; nevertheless, it is often the case that statistical properties characterizing the variability of the dynamical system are known. In the present work generalized stability theory is extended to such uncertain systems. The limits in which fluctuations about the mean of the operator are correlated over time intervals, short and long, compared to the timescale of the mean operator are examined and compared with the physically important transitional case of operator fluctuation on timescales comparable to the timescales of the mean operator. Exact and asymptotically valid equations for transient ensemble mean and moment growth in uncertain systems are derived and solved. In addition, exact and asymptotically valid equations for the ensemble mean response of a stable uncertain system to deterministic forcing are derived and solved. The ensemble mean response of the forced stable uncertain system obtained from this analysis is interpreted under the ergodic assumption as equal to the time mean of the state of the uncertain system as recorded by an averaging instrument. Optimal perturbations are obtained for the ensemble mean of an uncertain system in the case of harmonic forcing. Finally, it is shown that the remarkable systematic increase in asymptotic growth rate with moment in uncertain systems occurs only in the context of the ensemble. 1.
Strong NPHardness of the Quantum Separability Problem
, 2009
"... Given the density matrix ρ of a bipartite quantum state, the quantum separability problem asks whether ρ is entangled or separable. In 2003, Gurvits showed that this problem is NPhard if ρ is located within an inverse exponential (with respect to dimension) distance from the border of the set of se ..."
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Given the density matrix ρ of a bipartite quantum state, the quantum separability problem asks whether ρ is entangled or separable. In 2003, Gurvits showed that this problem is NPhard if ρ is located within an inverse exponential (with respect to dimension) distance from the border of the set of separable quantum states. In this paper, we extend this NPhardness to an inverse polynomial distance from the separable set. The result follows from a simple combination of works by Gurvits, Ioannou, and Liu. We apply our result to show (1) an immediate lower bound on the maximum distance between a bound entangled state and the separable set (assuming P ̸ = NP), and (2) NPhardness for the problem of determining whether a completely positive tracepreserving linear map is entanglementbreaking. 1