Asymmetry of Locally Available and Locally Transmitted Information in Thermal Two-Qubit States

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 the 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 flux 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.