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Asymmetry of locally available and locally transmitted information in thermal two-qubit states. (English. Russian original) Zbl 07282999
J. Math. Sci., New York 252, No. 1, 43-59 (2021); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 151, 45-61 (2018).
Summary: In the paper, we consider thermal states of two particles with spin 1/2 (qubits) located in an inhomogeneous transverse magnetic field and interacting according to the Heisenberg $$XY$$-model. We introduce the concepts of magnitude and direction of asymmetry of the entropy of a state and the magnitude and asymmetry of a flow of locally transmitted information. We show that for the system considered, the asymmetry of entropy is directed from the particle in a weaker magnetic field toward the particle in a stronger magnetic field, and this direction coincides with the direction of the excess flow of locally transmitted information. We also demonstrate that this asymmetry direction is consistent with the direction of the excess flow of locally available information: measurements over the particle in a weaker magnetic field provide a greater level of locally available information than measurements over the particle in a stronger magnetic field.
##### MSC:
 81P45 Quantum information, communication, networks (quantum-theoretic aspects) 81R25 Spinor and twistor methods applied to problems in quantum theory 78A30 Electro- and magnetostatics 81P43 Quantum discord 81P17 Quantum entropies 81P15 Quantum measurement theory, state operations, state preparations
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