Characterizing Bell nonlocality and steering in generalized probabilistic theories

Huaixin Cao, Zhihua Guo

E. Buffenoir

Martin Plávala

We derive general conditions for the compatibility of channels in general probabilistic theory. We introduce formalism that allows us to easily formulate steering by channels and Bell nonlocality of channels as generalizations of the well-known concepts of steering by measurements and Bell nonlocality of measurements. The generalization does not follow the standard line of thinking stemming from the Einstein-Podolsky-Rosen paradox, but introduces steering and Bell nonlocality as entanglement-assisted incompatibility tests. We show that all of the proposed definitions are, in the special case of measurements, the same as the standard definitions, but not all of the known results for measurements generalize to channels. For example, we show that for quantum channels, steering is not a necessary condition for Bell nonlocality. We further investigate the introduced conditions and concepts in the special case of quantum theory and we provide many examples to demonstrate these concepts and their implications.

Marco Túlio Quintino, Tamás Vértesi, Daniel Cavalcanti +4 more

Einstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely, projective measurements. Here we prove that entanglement, one-way steering, two-way steering, and nonlocality are genuinely different considering general measurements, i.e., single round positive-operator-valued measures. Finally, we show that the use of sequences of measurements is relevant for steering tests, as they can be used to reveal ``hidden steering.''

Yuri Ozhigov

Jing‐Ling Chen, Changliang Ren, Changbo Chen +2 more

Recently quantum nonlocality has been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell's nonlocality. Among which, Bell's nonlocality is the strongest type. Bell's nonlocality for quantum states is usually detected by violation of some Bell's inequalities, such as Clause-Horne-Shimony-Holt inequality for two qubits. Steering is a manifestation of nonlocality intermediate between entanglement and Bell's nonlocality. This peculiar feature has led to a curious quantum phenomenon, the one-way Einstein-Podolsky-Rosen steering. The one-way steering was an important open question presented in 2007, and positively answered in 2014 by Bowles et al., who presented a simple class of one-way steerable states in a two-qubit system with at least thirteen projective measurements. The inspiring result for the first time theoretically confirms quantum nonlocality can be fundamentally asymmetric. Here, we propose another curious quantum phenomenon: Bell nonlocal states can be constructed from some steerable states. This novel finding not only offers a distinctive way to study Bell's nonlocality without Bell's inequality but with steering inequality, but also may avoid locality loophole in Bell's tests and make Bell's nonlocality easier for demonstration. Furthermore, a nine-setting steering inequality has also been presented for developing more efficient one-way steering and detecting some Bell nonlocal states.