Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0302049 · Physical Review A

Consistency of the Shannon entropy in quantum experiments

PierGianLuca Porta Mana

Published Jun 21, 2004• 21 citations
arXivHTMLPDF

Abstract

The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analysed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be paid to logical and experimental contexts. This last remark is shown to apply regardless of the quantum or classical nature of the experiments.

DOI
10.1103/physreva.69.062108

Related papers

The properties of the Shannon entropy are not violated in quantum measurements

PierGianLuca Porta Mana

Brukner and Zeilinger [Phys. Rev. A 63 (2001) 022113] have claimed that two properties of the Shannon conditional entropy are violated in quantum experiments. It is shown here that the analysis by which they support their claim is flawed by the fact that they mix (probabilities and) entropies relative to different contexts, i.e., different experimental arrangements. It is also argued that the context-dependency of the Shannon entropy has nothing to do with the quantum or classical nature of experiments.

•Feb 6, 2003•1 citation

Quantum logical entropy: fundamentals and general properties

Boaz Tamir, Ismael L. Paiva, Zohar Schwartzman-Nowik +1 more

Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how this fundamental concept and other related definitions can be applied to the study of quantum systems with the use of quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.

arXiv:2108.02726•4open•Jan 1, 2022•8 citations

BELL'S INEQUALITY AND CONTEXTUAL INFORMATION

Feryal Safinejad, Afshin Shafiee, Reza Maleeh

The properties of the Shannon entropy (concavity and strong additivity) are satisfied in both classical and quantum experiments, if the context of experiment is considered appropriately. We show that these properties hold true in a classical model with the feature of being contextual, where a correlation is observed between events. Our results show that the classical example is similar to an entangled singlet state for spin-½ particles. But, contrary to general opinion, [Formula: see text] is not a necessary and sufficient condition for violating Bell's inequality, since it has been obtained on the basis of a common cause pattern. In other words, it is possible to reconstruct the amount of information contained in a quantum entangled state according to the common cause criterion satisfying local realism.

International Journal of Quantum Information•Aug 1, 2006•0 citations

Consistency of the Shannon entropy in quantum experiments (12 pages)

PierGianLuca Porta Mana

Physical Review A•Jan 1, 2004•1 citation

ℏ→0 limit of the entanglement entropy

Giuseppe Mussardo, Jacopo Viti

It may be naively assumed that certain entanglement measures, like the entanglement entropy of a pure state, approach zero in the classical limit. Here, however, the authors show that the limit is both well-behaved and nonzero: for a bipartite system of N particles, it coincides with the Shannon entropy of N bits. These results have been demonstrated previously in the context of quantum field theory, but here the authors use fully analytic methods to provide a general physical interpretation.

arXiv:2112.06840•Physical Review A•Mar 2, 2022•9 citations

Uncertainty relations expressed by Shannon-like entropies

Vladimír Majerník, Eva Majerníková, Serge Shpyrko

Abstract Besides the well-known Shannon entropy, there is a set of Shannon-like entropies which have applications in statistical and quantum physics. These entropies are functions of certain parameters and converge toward Shannon entropy when these parameters approach the value 1. We describe briefly the most important Shannon-like entropies and present their graphical representations. Their graphs look almost identical, though by superimposing them it appears that they are distinct and characteristic of each Shannon-like entropy. We try to formulate the alternative entropic uncertainty relations by means of the Shannon-like entropies and show that all of them equally well express the uncertainty principle of quantum physics.

Open Physics•Sep 1, 2003•23 citations
The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analysed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be paid to logical and experimental contexts. This last remark is shown to apply regardless of the quantum or classical nature of the experiments.
Brukner and Zeilinger [Phys. Rev. A 63 (2001) 022113] have claimed that two properties of the Shannon conditional entropy are violated in quantum experiments. It is shown here that the analysis by which they support their claim is flawed by the fact that they mix (probabilities and) entropies relative to different contexts, i.e., different experimental arrangements. It is also argued that the context-dependency of the Shannon entropy has nothing to do with the quantum or classical nature of experiments.
Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how this fundamental concept and other related definitions can be applied to the study of quantum systems with the use of quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.
The properties of the Shannon entropy (concavity and strong additivity) are satisfied in both classical and quantum experiments, if the context of experiment is considered appropriately. We show that these properties hold true in a classical model with the feature of being contextual, where a correlation is observed between events. Our results show that the classical example is similar to an entangled singlet state for spin-½ particles. But, contrary to general opinion, [Formula: see text] is not a necessary and sufficient condition for violating Bell's inequality, since it has been obtained on the basis of a common cause pattern. In other words, it is possible to reconstruct the amount of information contained in a quantum entangled state according to the common cause criterion satisfying local realism.
Abstract Besides the well-known Shannon entropy, there is a set of Shannon-like entropies which have applications in statistical and quantum physics. These entropies are functions of certain parameters and converge toward Shannon entropy when these parameters approach the value 1. We describe briefly the most important Shannon-like entropies and present their graphical representations. Their graphs look almost identical, though by superimposing them it appears that they are distinct and characteristic of each Shannon-like entropy. We try to formulate the alternative entropic uncertainty relations by means of the Shannon-like entropies and show that all of them equally well express the uncertainty principle of quantum physics.