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302
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
private communication
"... Stability problem; Cauchy–Jensen mappings; Euler–Lagrange mappings; Fixed point alternative. In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the wellknown Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive ma ..."
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Cited by 27 (4 self)
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Stability problem; Cauchy–Jensen mappings; Euler–Lagrange mappings; Fixed point alternative. In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the wellknown Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. In this paper we introduce generalized additive mappings of Jensen type mappings and establish new theorems about the Ulam stability of additive and alternative additive mappings. This study was financially supported by research fund of Chungnam National University in 2007. Euler–Lagrange Additive Mappings
An introduction to quantum filtering
, 2006
"... Abstract. This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation ..."
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Cited by 24 (13 self)
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Abstract. This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation
Strong Singularity For Subalgebras Of Finite Factors
 Internat. J. Math
"... In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type II 1 factors arising from countable discrete groups. We give simple criteria for strong singularity, and use them to construct strongly singula ..."
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Cited by 23 (6 self)
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In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type II 1 factors arising from countable discrete groups. We give simple criteria for strong singularity, and use them to construct strongly singular subalgebras. We particularly focus on groups which act on geometric objects, where the underlying geometry leads to strong singularity. 2000 Mathematics Subject Classification Numbers: 46L10, 22D25 Partially supported by the Australian Research Council Partially supported by the National Science Foundation. 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
A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN
, 1998
"... The aim of this paper is to provide a viable measuretheoretic framework for the study of random phenomena involving a large number of economic entities. The work is based on the fact that processes which are measurable with respect to hyperfinite Loeb product spaces capture the limiting behaviors ..."
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Cited by 20 (10 self)
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The aim of this paper is to provide a viable measuretheoretic framework for the study of random phenomena involving a large number of economic entities. The work is based on the fact that processes which are measurable with respect to hyperfinite Loeb product spaces capture the limiting behaviors of triangular arrays of random variables and thus constitute the `right' class for general stochastic modeling. The primary concern of the paper is to characterize those hyperfinite processes satisfying the exact law of large numbers by using the basic notions of conditional expectation, orthogonality, uncorrelatedness and independence together with some unifying multiplicative properties of random variables. The general structure of the processes is also analyzed via a biorthogonal expansion of the KarhunenLoeve type and via the representation in terms of the simpler hyperfinite Loeb counting spaces. A universality property for atomless Loeb product spaces is formulated to show the abun...
Amenability for dual Banach algebras
 Run 2] [Sel] [Spr] [Woo 1] [Woo 2] V. Runde, Lectures on Amenability. Lecture Notes in Mathematics 1774
, 2002
"... We define a Banach algebra A to be dual if A = (A∗) ∗ for a closed submodule A ∗ of A ∗. The class of dual Banach algebras includes all W ∗algebras, but also all algebras M(G) for locally compact groups G, all algebras L(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Ban ..."
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Cited by 19 (6 self)
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We define a Banach algebra A to be dual if A = (A∗) ∗ for a closed submodule A ∗ of A ∗. The class of dual Banach algebras includes all W ∗algebras, but also all algebras M(G) for locally compact groups G, all algebras L(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception than the rule. We confirm this impression. We first show that under certain conditions an amenable dual Banach algebra is already superamenable and thus finitedimensional. We then develop two notions of amenability — Connesamenability and strong Connesamenability — which take the w ∗topology on dual Banach algebras into account. We relate the amenability of an Arens regular Banach algebra A to the (strong) Connesamenability of A ∗ ∗ ; as an application, we show that there are reflexive Banach spaces with the approximation property such that L(E) is not Connesamenable. We characterize the amenability of inner amenable locally compact groups in terms of their algebras of pseudomeasures. Finally, we give a proof of the known fact that the amenable von Neumann algebras are the subhomogeneous ones which avoids the equivalence of amenability and nuclearity for C ∗algebras.
Modular Groups of Quantum Fields in Thermal States
, 1998
"... For a quantum field in a thermal equilibrium state we discuss the group generated by time translations and the modular action associated with an algebra invariant under halfsided translations. The modular flows associated with the algebras of the forward light cone and a spacelike wedge admit a sim ..."
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Cited by 19 (3 self)
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For a quantum field in a thermal equilibrium state we discuss the group generated by time translations and the modular action associated with an algebra invariant under halfsided translations. The modular flows associated with the algebras of the forward light cone and a spacelike wedge admit a simple geometric description in two dimensional models that factorize in lightcone coordinates. At large distances from the domain boundary compared to the inverse temperature the flow pattern is essentially the same as time translations, whereas the zero temperature results are approximately reproduced close to the edge of the wedge and the apex of the cone. Associated with each domain there is also a one parameter group with a positive generator, for which the thermal state is a ground state. Formally, this may be regarded as a certain converse of the Unruheffect.
Generic metrics, irreducible rankone PU(2) monopoles, and transversality
 Comm. Anal. Geom
"... Our main purpose in this article is to prove that the moduli space of solutions to the PU(2) monopole equations is a smooth manifold of the expected dimension for simple, generic parameters such as (and including) the Riemannian metric on the given fourmanifold: see Theorem 1.3. In [16] we proved t ..."
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Cited by 18 (7 self)
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Our main purpose in this article is to prove that the moduli space of solutions to the PU(2) monopole equations is a smooth manifold of the expected dimension for simple, generic parameters such as (and including) the Riemannian metric on the given fourmanifold: see Theorem 1.3. In [16] we proved transversality using an