Limits on sequential sharing of nonlocal advantage of quantum coherence

TL;DR

This paper investigates the maximum number of observers who can sequentially share nonlocal advantage of quantum coherence in high-dimensional quantum systems, establishing a fundamental limit of one observer under optimal measurement conditions.

Contribution

It provides a theoretical analysis of the sharing limits of nonlocal quantum coherence in high-dimensional states, considering unsharp measurements and their disturbance-information trade-offs.

Findings

At most one observer can demonstrate NAQC with the other party.

The limit holds even with optimal weak measurements.

Results illuminate the relationship between nonlocal correlations and quantum measurements in high dimensions.

Abstract

Sequential sharing of nonlocal correlation is inherently related to its application. We address the question as to how many observers can share the nonlocal advantage of quantum coherence (NAQC) in a $(d\times d)$-dimensional state, where $d$ is a prime or a power of a prime. We first analyze the trade-off between disturbance and information gain of the general $d$-dimensional unsharp measurements. Then in a scenario where multiple Alices perform unsharp measurements on one party of the state sequentially and independently and a single Bob measures coherence of the conditional states on the other party, we show that at most one Alice can demonstrate NAQC with Bob. This limit holds even when considering the weak measurements with optimal pointer states. These results may shed light on the interplay between nonlocal correlations and quantum measurements on high-dimensional systems and the hierarchy of different quantum correlations.