Sharing of Non-Local Advantage of Quantum Coherence by sequential observers

TL;DR

This paper establishes an upper limit on how many sequential observers can independently demonstrate non-local advantage of quantum coherence in an entangled qubit system, revealing fundamental constraints on quantum steering.

Contribution

It provides the first quantitative bound on the number of observers capable of demonstrating NAQC sequentially, considering different coherence measures and measurement strategies.

Findings

Maximum of two Alices can show NAQC with $l_1$-norm coherence.

Only one Alice can reveal NAQC with other coherence measures.

The bounds depend on the coherence measure used and measurement settings.

Abstract

Non-local Advantage of Quantum Coherence(NAQC) or steerability of local quantum coherence is a strong non-local resource based on coherence complementarity relations. In this work, we provide an upper bound on the number of observers who can independently steer the coherence of the observer in the other wing in a scenario where half of an entangled pair of spin-$\frac{1}{2}$ particles is shared between a single observer (Bob) in one wing and several observers (Alices) on the other, who can act sequentially and independently of each other. We consider one-parameter dichotomic POVMs for the Alices and mutually unbiased basis in which Bob measures coherence in case of the maximally entangled bipartite qubit state. We show that not more than two Alices can exhibit NAQC when $l_1$-norm of coherence measure is probed, whereas for two other measures of coherence, only one Alice can reveal NAQC within the same framework.