Dynamical behavior of maximal steered coherence and concurrence under decoherence

Abstract

In this work, by employing quantum steering ellipsoid (QSE) pictures, we investigate the dynamical characteristics of maximal steered coherence (MSC) and concurrence for an arbitrary Bell-diagonal state when the qubit-system suffers from canonical noisy channels, such as phase damping, bit flip and bit-phase flip channels. It has been found that the MSC is equal to the longest semiaxis length of the QSEs. Remarkably, the QSEs have an invariant semiaxis length under these mentioned unital channels. The dynamical behavior of MSC is dependent of the initial ellipsoid shape, and MSC is frozen to the length of invariant semiaxis ultimately. The time of frozen MSC can be derived by means of QSEs. Moreover, one can obtain that the concurrence depends on the sum of three semiaxis lengths of QSEs under these unital channels. Interestingly, the concurrence will be sudden death, if the sum of three semiaxis lengths is equal to 1. Additionally, we conclude that the time of entanglement sudden death can be deduced via QSE pictures.

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

“…The sufficient and necessary condition for a QSE to denote a bipartite state was derived by Milne et al [41] It is worth mentioning that the QSE provides an intuitive depiction and indication for quantum correlations. Examples include steered coherence, [42][43][44] discord, [38,[45][46][47] entanglement [38,41,48] and EPR steering. [49][50][51][52][53][54] Zhang et al [55] experimentally verified the QSE of two-qubit states and also demonstrated volume monogamy relations of the QSE.…”

“…However, these efforts are limited to inertial systems. [42][43][44][45]57] The non-inertial frame provides nontrivial tools for understanding relativistic quantum information and black holes, and is a rapidly developing field. [58] Relevant explorations in the non-inertial frame have been widely carried out.…”

Nonlocal quantum correlations under amplitude damping decoherence

“…It has been widely studied the effect of decoherence on entanglement both in theory and experiment [22,23,[26][27][28]. However, there are only a few theoretical studies on other nonlocal quantum correlations [34][35][36][37]. These studies deal with the entanglement sudden death (ESD) [22,23,26,27] and Bell nonlocality sudden death (BNSD) [37], however, the study of EPR steering sudden death (SSD) is still missing.…”