Nonlocality without entanglement: Quantum theory and beyond

Abstract

Quantum nonlocality without entanglement (Q-NWE) captures nonlocal behavior of multipartite product states as they may entail global operation for optimal decoding of the classical information encoded in the state ensemble that allows local preparation. In this Rapid Communication we show that the phenomena of NWE is not specific to quantum theory only, but rather a class of generalized probabilistic theories that can exhibit such behavior. In fact, several manifestations of NWE, e.g., asymmetric local discrimination, suboptimal local discrimination, the notion of separable but locally unimplementable measurements arise generically in operational theories other than quantum theory. We propose a framework to compare the strength of NWE in different theories and show that such behavior in quantum theory is limited, suggesting a specific topological feature of quantum theory, namely, the continuity of state space structure. Our work adds the erstwhile missing foundational appeal to the study of NWE phenomena along with its information-theoretic relevance.

Local Quantum State Marking

“…This constitutes the framework for the problem of local state discrimination (LSD) [14][15][16][17][18][19][20][21]. During the last two decades LSD has been studied in great detail resulting in a plethora of interesting conclusions [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Apart from LSD, and more general quantum state discrimination problems, [38][39][40] several other discrimination tasks, eg.…”

Locking and unlocking of quantum nonlocality without entanglement in local discrimination of quantum states

“…On the other hand, in the case of discriminating non-orthogonal non-entangled states, NLWE occurs when the globally optimal discriminations such as minimum-error discrimination 10 – 13 or optimal unambiguous discrimination 14 – 17 cannot be implemented by LOCC 18 – 21 . We also note that some non-local phenomena without entanglement can occur in the generalized probabilistic theories beyond quantum theory 22 .…”

Entanglement protection via periodic environment resetting in continuous-time quantum-dynamical processes

“…The rebit shares many of the same properties of the standard (complex) qubit so in some cases one is able to make direct comparisons between polygons, rebit and qubit. The polygon theories were first introduced in [24] and have been used to study various concepts, such as non-locality [24][25][26], incompatibility [29], self-testing [26], etc., ever since.…”