Information Content of Elementary Systems as a Physical Principle

Por • 30 mar, 2014 • Sección: Ambiente

L. Czekaj, M. Horodecki, P. Horodecki, R. Horodecki

Abstract: Quantum physics has remarkable characteristics such as quantum correlations, uncertainty relations, no cloning, which make for an interpretative and conceptual gap between the classical and the quantum world. To provide more unified framework the generalized probabilistic theories were formulated. Recently, it turned out that such theories include so called “postquantum” ones which share many of the typical quantum characteristics but predict supraquantum effects such as correlations stronger than quantum ones. As a result we reveal even more dramatic gap between classical/quantum and post-quantum world. Therefore it is imperative to search for information principles characterizing physical theories. In recent years, different principles has been proposed, however all of the principles considered so far has been correlation ones. Here, we introduce an elementary system information content principle (ICP) whose basic ingredient is the phenomenon of Heisenberg uncertainty. The principle states that the amount of non-redundant information which may be extracted from a given single system is bounded by a perfectly decodable information content of the system. We show that this new principle is respected by classical and quantum theories and is violated by hidden variable theories as well as post-quantum ones: p-theory and polygon theories. Remarkably, ICP is sometimes more sensitive than Tsirelson’s bound: it allows to rule out even some theories which do not violate Tsirelson’s bound. Especially the ability of the ICP to rule out some specific hidden variable bit theories makes it to our knowledge unique among the informational principles known so far. The elementary system character of ICP suggests that it might be one of the foundational bricks of Nature.

arXiv:1403.4643v1 [quant-ph]

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