All entangled states display some hidden nonlocality

Abstract

A well-known manifestation of quantum entanglement is that it may lead to correlations that are inexplicable within the framework of a locally causal theory-a fact that is demonstrated by the quantum violation of Bell inequalities. The precise relationship between quantum entanglement and the violation of Bell inequalities is, however, not well understood. While it is known that entanglement is necessary for such a violation, it is not clear whether all entangled states violate a Bell inequality, even in the scenario where one allows joint operations on multiple copies of the state and local filtering operations before the Bell experiment. In this paper we show that all entangled states, or more precisely, all not-fully-separable states of arbitrary Hilbert space dimension and arbitrary number of parties, violate a Bell inequality when combined with another state which on its own cannot violate the same Bell inequality. This result shows that quantum entanglement and quantum nonlocality are in some sense equivalent, thus giving an affirmative answer to the aforementioned open question. It follows from our result that two entangled states that are apparently useless in demonstrating quantum nonlocality via a specific Bell inequality can be combined to give a Bell violation of the same inequality. Explicit examples of such activation phenomenon are provided.

Entanglement and Nonlocality are Inequivalent for Any Number of Parties

“…A number of such operationally meaningful nonlocality scenarios were introduced after Bell's seminal work: the network approach [14], Bell scenarios defined on copies of a state [15] (see also Ref. [16]) or sequential measurements [11][12][13]. In these approaches, states that are local in the standard setup may display nonlocal properties.…”

“…Let us finally remark that several operationally meaningful nonlocality scenarios besides the standard one considered here, consisting of single-copy measurements by each party, have been introduced [11][12][13][14][15][16]. A notable…”

Quantum correlation versus Bell-inequality violation under the amplitude damping channel

“…However, according to Eq. (19), the final state remains entangled for arbitrarily long time, i.e., the duration τ N → ∞. To clearly see the change of the entanglement as time goes on, we plot the degree of Bell-CHSH inequality violation, negativity, and quantum discord as a function of the time t in Fig.…”

“…Nowadays, quantum entanglement and Bell's inequality violation, which are two special aspects of quantum correlation, are among the most fundamental concepts in quantum theory providing powerful resources for modern quantum information processing [8][9][10]. In this context, considerable effort has been devoted to the investigation of quantum entanglement and Bell's inequality violation [11][12][13][14][15][16][17][18][19][20][21]. F. Verstraete and M.M.…”

Activating the Violation of Steering Inequality for Two‐Qubit X States

“…That is, there exists the case when Alice can steer Bob's state but Bob cannot steer Alice's state, which is referred to as one-way steerable and has been demonstrated theoretically [16] and experimentally. [20,21] All entangled states display some hidden nonlocality, which can be activated or superactivated to violate a certain kind of Bell inequality by combining the quantum state with another one [22][23][24] or with itself. [19] There are two typical quantum information resources which can be superactivated in quantum theory, one is bound entanglement and the other is nonlocality.…”