Coherence migration in high-dimensional bipartite systems

Abstract

The conservation law for first-order coherence and mutual correlation of a bipartite qubit state is first proposed by Svozilík et al. [Phys. Rev. Lett. 115, 220501 (2015)], and their theories laid the foundation for the study of coherence migration under unitary transformations. In this paper, we generalize the framework of first-order coherence and mutual correlation to an arbitrary $(m \otimes n)$-dimensional bipartite composite state by introducing an extended Bloch decomposition form of the state. We also generalize two kinds of unitary operators in high-dimensional systems, which can bring about coherence migration and help to obtain the maximum or minimum first-order coherence. Meanwhile, coherence migration in open quantum systems are investigated. We take depolarizing channels as examples and establish that the reduced first-order coherence of the principal system over time is completely transformed into mutual correlation of the $(2 \otimes 4)$-dimensional system-environment bipartite composite state. It is expected that our results may provide a valuable idea or method for controlling the quantum resource such as coherence and quantum correlations.

Visualizing and witnessing first-order coherence, Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame

“…Meanwhile, coherence can also be used to depict the interference capability of interacting fields in quantum optics research. [8][9][10][11][12] Beyond this, there have been various efforts to ascertain the interrelations between coherence and correlations, [13][14][15][16][17][18][19][20] and these relations are essential for predicting the coherent transfer in researched quantum systems. Various coherence measures have been established to quantify coherence.…”