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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 166 (52 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 67 (9 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 56 (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
Quantum Information Theory and the Foundations of Quantum Mechanics
, 2004
"... This thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. In Part I an attempt is made to shed some light on the nature of information and quantum information theory. It is emphasized that the everyday notion of ..."
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Cited by 28 (7 self)
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This thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. In Part I an attempt is made to shed some light on the nature of information and quantum information theory. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; noun, hence does not refer to a particular or substance. The popular claim ‘Information is Physical ’ is assessed and it is argued that this proposition faces a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. A novel argument is provided against Dretske’s (1981) attempt to base a semantic notion of information on ideas from information theory. The function of various measures of information content for quantum systems is explored and the applicability of the Shannon information in the quantum context maintained against the challenge of Brukner and Zeilinger (2001). The phenomenon of quantum teleportation is then explored as a case study serving to emphasize the value of
Quantum picturalism
, 2009
"... Why did it take us 50 years since the birth of the quantum mechanical formalism to discover that unknown quantum states cannot be cloned? Yet, the proof of the ‘nocloning theorem’ is easy, and its consequences and potential for applications are immense. Similarly, why did it take us 60 years to dis ..."
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Cited by 20 (4 self)
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Why did it take us 50 years since the birth of the quantum mechanical formalism to discover that unknown quantum states cannot be cloned? Yet, the proof of the ‘nocloning theorem’ is easy, and its consequences and potential for applications are immense. Similarly, why did it take us 60 years to discover the conceptually intriguing and easily derivable physical phenomenon of ‘quantum teleportation’? We claim that the quantum mechanical formalism doesn’t support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the arrays of 0s and 1s of the early days of computer programming practice. Using a technical term from computer science, the quantum mechanical formalism is ‘lowlevel’. In this review we present steps towards a diagrammatic ‘highlevel ’ alternative for the Hilbert space formalism, one which appeals to our intuition. The diagrammatic language as it currently stands allows for intuitive reasoning about interacting quantum systems, and trivialises many otherwise involved and tedious computations. It clearly exposes limitations such as the nocloning theorem, and phenomena such as quantum teleportation. As a logic, it supports ‘automation’: it enables a (classical) computer to reason about interacting quantum systems, prove theorems, and design protocols. It allows for a wider variety of underlying theories, and can be easily modified, having the potential to provide the required stepstone towards a deeper conceptual understanding of quantum theory, as well as its
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 20 (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.
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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Cited by 18 (1 self)
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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
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 17 (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.
Experimental delayedchoice entanglement swapping. Nature Phys
, 2012
"... Motivated by the question of which kind of physical interactions and processes are needed for the production of quantum entanglement, Peres has put forward the radical idea of delayedchoice entanglement swapping. There, entanglement can be ‘produced a posteriori, after the entangled particles have ..."
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Cited by 16 (0 self)
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Motivated by the question of which kind of physical interactions and processes are needed for the production of quantum entanglement, Peres has put forward the radical idea of delayedchoice entanglement swapping. There, entanglement can be ‘produced a posteriori, after the entangled particles have been measured and may no longer exist’. Here, we report the realization of Peres’s gedanken experiment. Using four photons, we can actively delay the choice of measurement— implemented through a highspeed tunable bipartitestate analyser and a quantum randomnumber generator—on two of the photons into the timelike future of the registration of the other two photons. This effectively projects the two already registered photons onto one of two mutually exclusive quantum states in which the photons are either entangled (quantum correlations) or separable (classical correlations). This can also be viewed as ‘quantum steering into the past’. In the entanglement swapping 1–3 procedure, two pairs of entangled photons are produced, and one photon from each pair is sent to Victor. The two other photons from each pair are sent to Alice and Bob, respectively. If Victor projects his two photons onto an entangled state, Alice’s and Bob’s photons are entangled although they have never interacted or shared any common past.