Generalized non-additive entropies and quantum entanglement

Abstract

We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system, the formalism allows to avoid fake entanglement for data based on the Bell-CHSH observable, and, in general, on any set of Bell constraints. Particular results obtained with the Tsallis entropy and with an introduced exponential entropic form are also discussed.

5 pages

References in corpus (11)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
• Information-theoretic aspects of quantum inseparability of mixed states
• Negative entropy and information in quantum mechanics
• Nonextensivity and multifractality in low-dimensional dissipative systems
• Operationally Invariant Information in Quantum Measurements
• Separability and distillability of multiparticle quantum systems
• Quantum entanglement inferred by the principle of maximum Tsallis entropy
• Quantum Entanglement and Entropy
• Quantum Entanglement and the Maximum Entropy States from the Jaynes Principle

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