Conservation of information and the foundations of quantum mechanics
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In this article, a recent approach to the foundations of quantum mechanics inspired by quantum information theory is presented, based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features.Abstract:
We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory [1, 2]. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems.read more
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Entanglement and thermodynamics in general probabilistic theories
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Ruling out Higher-Order Interference from Purity Principles
TL;DR: Any theory satisfying Causality, Purity Preservation, Pure Sharpness, and Purification—four principles that formalise the fundamental character of purity in nature—exhibits at most second-order interference, and it is proved that systems in such theories correspond to Euclidean Jordan algebras.
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Microcanonical thermodynamics in general physical theories
TL;DR: A duality is derived between the resource theory of microcanonical thermodynamics and the resource theories of pure bipartite entanglement, which are equivalent in terms of state convertibility if and only if the dynamics allowed by theory satisfy a suitable condition, which is called unrestricted reversibility.
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Operational axioms for diagonalizing states
TL;DR: In this article, a set of axioms that guarantee that every state can be diagonalized are presented, and a constructive algorithm for diagonalizing every given state is presented. But the authors do not address the question of how to reconstruct the notions of majorization and entropy.
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A no-go theorem for theories that decohere to quantum mechanics
TL;DR: In this article, it was shown that any post-quantum theory must either satisfy causality, purification, or both of the two natural physical principles of information propagation and purification.
References
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Quantum Computation and Quantum Information
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Quantum Computation and Quantum Information
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
Journal ArticleDOI
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
TL;DR: Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete.
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Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
Charles H. Bennett,Gilles Brassard,Claude Crépeau,Richard Jozsa,Asher Peres,William K. Wootters +5 more
TL;DR: An unknown quantum state \ensuremath{\Vert}\ensure Math{\varphi}〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations.
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A single quantum cannot be cloned
TL;DR: In this article, the linearity of quantum mechanics has been shown to prevent the replication of a photon of definite polarization in the presence of an excited atom, and the authors show that this conclusion holds for all quantum systems.