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

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 (2021 Phys. Rev. A 104 L050201) 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. The set with such property is called to have 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. Unexpectedly, the constructions of genuine hidden nonlocal sets without entanglement seems to be easier than that with entanglement. Therefore, from this perspective, this kind of nonlocality is rather different from the Bell nonlocality.