Nonlocal advantage of quantum coherence in high-dimensional states

Abstract

By local measurements on party A of a system AB and classical communication between its two parties, one can achieve a nonlocal advantage of quantum coherence (NAQC) on party B. For the l 1 norm of coherence and the relative entropy of coherence, we generalized the framework of NAQC for two qubits and derived the criteria which capture NAQC in the (d × d)-dimensional states when d is a power of a prime. We also presented a new framework for formulating NAQC, and showed through explicit examples its capacity on capturing the NAQC states. Moreover, we proved that any bipartite state with NAQC is quantum entangled, thus the obtained criteria can also be used as an entanglement witness.

Sharing of nonlocal advantage of quantum coherence by sequential observers

“…Sequential sharing of nonlocal quantum correlations could be of relevance in practical information theoretic protocols involving secret key generation among multiple parties, and randomness certification [40,41]. In the present work, we investigate the sequential sharing of nonlocal advantage of quantum coherence (NAQC) [9] which is a correlation stronger than Bell nonlocality [13,14]. We consider a bipartite entangled state in the C 2 ⊗ C 2 Hilbert space where multiple Alices perform sequential POVMs on half of the entangled pair, and a single Bob measures coherence on the other half in a particular basis.…”

“…The states which manifest NAQC form a subset of Bell non-local correlations and thereby NAQC is proved to be the strongest among all such correlations for all bipartite quantum states. Recently, non-local advantage of quantum coherence has been probed for higher dimensional quantum states, and the interrelation between coherence and steerability is explored further [14]. The complementarity between various coherence steering criteria has also been proposed recently [15].…”

Restrain the losses of the entanglement and the non-local advantage of quantum coherence for accelerated quantum systems

“…From Figs. (7) and (9), one may conclude that, the powerful of the local symmetric operator, PT is clearly exhibited, where one can keep the non-local coherent advantage survival and consequently the efficiency of the accelerated state increases for any value of the acceleration. By applying the local symmetric operator on both qubits, the vanishing phenomena of N La disappears.…”

“…In this contribution, we consider the l 1 -norm and the relative entropy of coherence as a measure of quantum coherence, where these measures satisfy the criteria suggested by Baumgratz et al [5]. For a combined system AB, we quantify the non-local advantage N La on party B by local measurements on party A and classical communication between its two parties [9]. However, it is well known that the Unruh effect on the accelerated systems causes degradation of entanglement [10] and consequently, the coherence between the accelerated subsystems decreases.…”

Steered Quantum Coherence and Quantum Criticality in the XY Model with Dzyaloshinsky–Moriya Interaction

“…[64] With this motivation, we consider the steered quantum coherence (SQC) which is defined based on the mutually unbiased bases (i.e., the sets of reference basis mutually unbiased to each other) 65] and exists in almost all bipartite states. [66][67][68] By inspecting its behaviors in the transverse field XY model with Dzyaloshinsky-Moriya (DM) interaction, we aim to reveal its figure of merit in characterizing quantum criticality.…”