Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is correspondingly easier to be demonstrated without the detection loophole. In this work, we trigger an extraordinary approach to investigate Bell's nonlocality, which is strongly based on the EPR steering. We present a theorem, showing that for any two-qubit state
τ, if its mapped state
ρ is EPR steerable, then the state
τ must be Bell nonlocal. The result not only pinpoints a deep connection between EPR steering and Bell's nonlocality, but also sheds a new light to realize a loophole-free Bell-test experiment (without the CHSH inequality) through the violation of steering inequality.
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.
Steering is a form of quantum nonlocality that is intimately related to the famous Einstein-Podolsky-Rosen (EPR) paradox that ignited the ongoing discussion of quantum correlations. Within the hierarchy of nonlocal correlations appearing in nature, EPR steering occupies an intermediate position between Bell nonlocality and entanglement. In continuous variable systems, EPR steering correlations have been observed by violation of Reid's EPR inequality, which is based on inferred variances of complementary observables. Here we propose and experimentally test a new criterion based on entropy functions, and show that it is more powerful than the variance inequality for identifying EPR steering. Using the entropic criterion our experimental results show EPR steering, while the variance criterion does not. Our results open up the possibility of observing this type of nonlocality in a wider variety of quantum states.