Nonlocality without entanglement: Quantum theory and beyond

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.

Figure 1

Polygonal models $\mathbb{P}\left(4\right)$ (left) and $\mathbb{P}\left(5\right)$ (right). Normalized state plane (at $z=1$) is depicted. Pentagon model is self-dual, whereas squit is not. In both models ${\omega }_i$'s represent pure states. In the squit model there are only two extremal measurements, ${\mathcal{M}}_i\equiv \{e_i,e_{i+1}|e_i+e_{i+1}=u\}$ with $i\in \{0,1\}$, whereas the other has five extremal measurements, ${\mathcal{M}}_i\equiv \{e_i,{\overline{e}}_i|e_i+{\overline{e}}_i=u\}$ with $i\in \{0,...,4\}$. In both models $e_i$'s are ray extremal effects, whereas ${\overline{e}}_i$'s are extremal effects of $\mathcal{E}\left(5\right)$ but not ray extremal.