Asymmetry of Locally Available and Locally Transmitted Information in Thermal Two-Qubit States
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ASYMMETRY OF LOCALLY AVAILABLE AND LOCALLY TRANSMITTED INFORMATION IN THERMAL TWO-QUBIT STATES E. O. Kiktenko
UDC 530.145.1
Abstract. 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. Keywords and phrases: quantum discord, Heisenberg XY -interaction, locally available information. AMS Subject Classification: 81V99, 81Q99
CONTENTS 1. 2. 3. 4. 5. 6.
Introduction . . . . . . . . . . . . . . . . . . Approaches to Description of Asymmetry of Asymmetric System of Two Qubits . . . . . Asymmetry of the Ground State . . . . . . Asymmetry of Thermal States . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . .
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Introduction
One of the most important problems of quantum information theory is the quantitative description of quantum correlations between subsystems of composite quantum systems, which are a resource for the implementation of various problems of quantum information technologies (see [1, 2, 23]). A key role in these applications is played by quantum entanglement, the property of composite quantum systems that does not have a classical analog, in which their common wave function cannot be represented in the factorized form (for pure states) or their density matrix cannot be represented as the sum of factorized density matrices (for mixed states). Despite the simplicity of the formal definition, the presence of entanglement in the general case of a mixed two-state state meets substantial computational difficulties. In order to characterize the total correlation value (including both quantum and classical components), quantum mutual information is used, determining the capacity of quantum channels using entanglement (see [9]). This value is a generalization of classical mutual information to
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