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34
The generally covariant locality principle  A new paradigm for local quantum physics
 COMMUN.MATH.PHYS
, 2001
"... A new approach to the modelindependent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a locally cova ..."
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Cited by 66 (13 self)
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A new approach to the modelindependent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a locally covariant quantum field theory. Such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories, on one side, of globally hyperbolic spacetimes with isometric embeddings as morphisms and, on the other side, of ∗algebras with unital injective ∗endomorphisms as morphisms. Moreover, locally covariant quantum fields can be described in this framework as natural transformations between certain functors. The usual HaagKastler framework of nets of operatoralgebras over a fixed spacetime backgroundmanifold, together with covariant automorphic actions of the isometrygroup of the background spacetime, can be regained from this new approach as a special case. Examples of this new approach are also outlined. In case that a locally covariant quantum field theory obeys the
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 28 (3 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
Entanglement and open systems in algebraic quantum field theory
 Studies in History and Philosophy of Modern Physics 32: 1–31
, 2001
"... Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum "eld theory (AQFT) provides a rigoro ..."
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Cited by 21 (4 self)
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Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum "eld theory (AQFT) provides a rigorous framework within which to analyse entanglement in the context of a fully relativistic formulation of quantum theory. What emerges from the analysis are new practical and theoretical limitations on an experimenter's ability to perform operations on a "eld in one spacetime region that can disentangle its state from the state of the "eld in other spacelikeseparated regions. These limitations show just how deeply entrenched entanglement is in relativistic quantum "eld theory, and yield a fresh perspective on the ways in which the theory di!ers conceptually from both standard nonrelativistic quantum theory and classical relativistic "eld theory. � 2001 Elsevier
On The Statistical Independence of Algebras of Observables
 J. Math. Phys
"... . We reexamine various notions of statistical independence presently in use in algebraic quantum theory, establishing alternative characterizations for such independence, some of which are also valid without assuming that the observable algebras mutually commute. In addition, in the context which h ..."
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Cited by 18 (8 self)
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. We reexamine various notions of statistical independence presently in use in algebraic quantum theory, establishing alternative characterizations for such independence, some of which are also valid without assuming that the observable algebras mutually commute. In addition, in the context which holds in concrete applications to quantum theory, the equivalence of three major notions of statistical independence is proven. Introduction The notions of "independence of two systems" are legion in quantum theory. This is quite understandable, since the physical concept is central in many aspects of quantum theory, and the various formalizations of independence capture different qualitative and quantitative aspects for possibly different ends. 1 Those notions which have appeared in the literature and have formulations in algebraic quantum theory have been extensively reviewed in [24], where their logical interrelationships have been discussed. However, some issues of logical relation wer...
Continuity of symplectically adjoint maps and the algebraic structure of Hadamard vacuum representations for quantum fields on curved spacetime
, 1996
"... We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space dominating the symplectic form, then they are bounded with ..."
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Cited by 17 (5 self)
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We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space dominating the symplectic form, then they are bounded with respect to a oneparametric family of scalar products canonically associated with the initially given one, among them being its “purification”. As a typical example we consider a scalar field on a globally hyperbolic spacetime governed by the KleinGordon equation; the classical system is described by a symplectic space and the temporal evolution by symplectomorphisms (which are symplectically adjoint to their inverses). A natural scalar product is that inducing the classical energy norm, and an application of the above result yields that its “purification ” induces on the oneparticle space of the quantized system a topology which coincides with that given by the twopoint functions of quasifree Hadamard states. These findings will be shown to lead to new results concerning the structure of the local (von Neumann) observablealgebras in representations of quasifree Hadamard states of the KleinGordon field in an arbitrary globally hyperbolic spacetime, such as local definiteness, local primarity and Haagduality (and also split and type III1properties). A brief review of this circle of notions, as well as of properties of Hadamard states, forms part of the article.
Microlocal analysis of quantum fields on curved spacetimes: Analytic wavefront sets and ReehSchlieder theorems
, 2002
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The quantum moment problem and bounds on entangled multiprover games
 In Proceedings of 23rd IEEE Conference on Computational Complexity
, 2008
"... We study the quantum moment problem: Given a conditional probability distribution together with some polynomial constraints, does there exist a quantum state ρ and a collection of measurement operators such that (i) the probability of obtaining a particular outcome when a particular measurement is p ..."
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Cited by 16 (2 self)
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We study the quantum moment problem: Given a conditional probability distribution together with some polynomial constraints, does there exist a quantum state ρ and a collection of measurement operators such that (i) the probability of obtaining a particular outcome when a particular measurement is performed on ρ is specified by the conditional probability distribution, and (ii) the measurement operators satisfy the constraints. For example, the constraints might specify that some measurement operators must commute. We show that if an instance of the quantum moment problem is unsatisfiable, then there exists a certificate of a particular form proving this. Our proof is based on a recent result in algebraic geometry, the noncommutative Positivstellensatz of Helton and McCullough [Trans. Amer. Math. Soc., 356(9):3721, 2004]. A special case of the quantum moment problem is to compute the value of oneround multiprover games with entangled provers. Under the conjecture that the provers need only share states in finitedimensional Hilbert spaces, we prove that a hierarchy of semidefinite programs similar to the one given by Navascués, Pironio and Acín [Phys. Rev. Lett., 98:010401, 2007] converges to the entangled value of the game. It follows that the class of languages recognized by a multiprover interactive proof system where the provers share entanglement is recursive.
Interpreting the Quantum
, 1997
"... This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of informa ..."
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Cited by 16 (1 self)
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This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the informationtheoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the informationtheoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information.
Some aspects of quantum entanglement for CAR systems
 Lett. Math. Phys
, 2002
"... We show some distinct features of quantum entanglement for bipartite CAR systems such as the failure of triangle inequality of von Neumann entropy and the possible change of our entanglement degree under local operations. Those are due to the nonindependence of CAR systems and never occur in any alg ..."
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Cited by 11 (9 self)
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We show some distinct features of quantum entanglement for bipartite CAR systems such as the failure of triangle inequality of von Neumann entropy and the possible change of our entanglement degree under local operations. Those are due to the nonindependence of CAR systems and never occur in any algebraic independent systems. We introduce a new notion halfsided entanglement. Mathematical Subject Classifications (2000). 94A17, 46L30. Key words. CAR Systems, entropy inequality, quantum entanglement.