Genuine hidden nonlocality without entanglement: from the perspective of local discrimination

TL;DR

This paper demonstrates the existence of non-entangled quantum state sets exhibiting genuine hidden nonlocality, advancing understanding of quantum nonlocality without entanglement and its potential applications in data hiding.

Contribution

It constructs entanglement-free sets with genuine hidden nonlocality and develops a method to address local irredundancy in systems with composite dimensions.

Findings

Existence of entanglement-free sets with genuine hidden nonlocality.

A new method to solve local irredundancy in composite systems.

Implications for quantum data hiding applications.

Abstract

Quantum nonlocality without entanglement is a fantastic phenomenon in quantum theory. This kind of quantum nonlocality is based on the task of local discrimination of quantum states. Recently, Bandyopadhyay and Halder [Phys. Rev. A 104, L050201 (2021)] studied the problem: is there any set of orthogonal states which can be locally distinguishable, but under some orthogonality preserving local measurement, each outcome will lead to a locally indistinguishable set. We say that the set with such property has hidden nonlocality. Moreover, if such phenomenon can not arise from discarding subsystems which is termed as local irredundancy, we call it genuine hidden nonlocality. There, they presented several sets of entangled states with genuine hidden nonlocality. However, they doubted the existence of a set without entanglement but with genuine hidden nonlocality. In this paper, we eliminate this doubt by constructing a series of sets without entanglement but whose nonlocality can be genuinely activated. We derive a method to tackle with the local irredundancy problem which is a key tricky for the systems whose local dimensions are composite numbers. As Bandyopadhyay and Halder have been pointed out, sets with genuine hidden nonloclity would lead to some applications on the data hiding.