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Nonadditive conditional entropy and its significance for local realism

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  • Abe, Sumiyoshi
  • Rajagopal, A.K

Abstract

Based on the form invariance of the structures given by Khinchin's axiomatic foundations of information theory and the pseudoadditivity of the Tsallis entropy indexed by q, the concept of conditional entropy is generalized to the case of nonadditive (nonextensive) composite systems. The proposed nonadditive conditional entropy is classically nonnegative but can be negative in the quantum context, indicating its utility for characterizing quantum entanglement. A criterion deduced from it for separability of density matrices for validity of local realism is examined in detail by employing a bipartite spin-1/2 system. It is found that the strongest criterion is obtained in the limit q→∞.

Suggested Citation

  • Abe, Sumiyoshi & Rajagopal, A.K, 2001. "Nonadditive conditional entropy and its significance for local realism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(1), pages 157-164.
    • Handle: RePEc:eee:phsmap:v:289:y:2001:i:1:p:157-164
    DOI: 10.1016/S0378-4371(00)00476-3
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    Cited by:

    1. Ishak, Nur Izzati & Muniandy, S.V. & Chong, Wu Yi, 2021. "Entropy analysis of the discrete-time quantum walk under bit-flip noise channel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    2. Nayak, Anantha S. & Sudha, & Rajagopal, A.K. & Usha Devi, A.R., 2016. "Bipartite separability of symmetric N-qubit noisy states using conditional quantum relative Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 286-295.
    3. Yildiz, Anil & Mern, John & Kochenderfer, Mykel J. & Howland, Michael F., 2023. "Towards sequential sensor placements on a wind farm to maximize lifetime energy and profit," Renewable Energy, Elsevier, vol. 216(C).
    4. Chapeau-Blondeau, François, 2014. "Tsallis entropy for assessing quantum correlation with Bell-type inequalities in EPR experiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 204-215.

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