Evolution equation for geometric quantum correlation measures

Abstract

A simple relation is established for the evolution equation of quantum information processing protocols such as quantum teleportation, remote state preparation, Bell-inequality violation and particularly dynamics of the geometric quantum correlation measures. This relation shows that when the system traverses the local quantum channel, various figures of merit of the quantum correlations for different protocols demonstrate a factorization decay behavior for dynamics. We identified the family of quantum states for different kinds of quantum channels under the action of which the relation holds. This relation simplifies the assessment of many quantum tasks.

Evolution equation for quantum coherence

“…For instance, the Pauli channel and Gell-Mann channel given in ref. 41 , and the generalized amplitude damping channel 31 . Notably, covers the bit flip, phase flip, bit-phase flip, phase damping, and depolarizing channels which embody typical noisy sources in quantum information, while covers the structured reservoirs with Lorentzian and Ohmic-type spectral densities.…”

“…Looking for general law determining the evolution equation of coherence can facilitate the design of effective coherence preservation schemes. Remarkably, the evolution equations for certain entanglement monotones (or their bounds) 32 33 34 35 36 37 38 39 40 and geometric discords 41 were found to obey the factorization relation (FR) for specific initial states. Then, it is natural to ask whether there exists similar FR for various coherence monotones.…”

Quantum correlation of qubit-reservoir system in dissipative environments

“…To begin with, we provide a brief review for the geometric discord based on the Hilbert-Schmidt norm by Dakić et al . 12 , 27 where is the square of Hilbert-Schmidt norm of Hermitian operators and Θ denotes the set of zero-discord states. In general, a given state is classically correlated when it can be written as where are sets of orthogonal states of party A and B , with non-negative probabilities p ij satisfying .…”

Two Definitions of the Gell-Mann Channels—A Comparative Analysis

“…The answer to the second question is in the affirmative. There are, indeed, two recent articles by Hu and Fan [1,2] dealing with 3-dimensional Gell-Mann channels. They are defined with the use of the Kraus operators, and then it is assumed that their eigenvectors are the Gell-Mann matrices.…”

“…For the Gell-Mann channel given by its eigenvalue equations, we found its time-local generator together with the conditions under which this generator has the corresponding GKSL form. The EV Gell-Mann channels can be used in the theory of quantum coherences and quantum correlation measures [1,2]. It was shown that, under certain circumstances, the evolution equations of coherences and correlation measures obey the factorization relation.…”