Non-Local Advantage of Quantum Coherence

A bipartite state is said to be steerable if and only if it does not have a single system description, i.e., the bipartite state cannot be explained by a local hidden state model. Several steering inequalities have been derived using different local uncertainty relations to verify the ability to control the state of one subsystem by the other party. Here, we derive complementarity relations between coherences measured on mutually unbiased bases using various coherence measures such as the $l_1$-norm, relative entropy and skew information. Using these relations, we derive conditions under which non-local advantage of quantum coherence can be achieved and the state is steerable. We show that not all steerable states can achieve such advantage.Comment: 8 pages, protocol modified, To appear in PRA-Rapid Communication

Fine-grained EPR-steering inequalities

We derive a new steering inequality based on a fine-grained uncertainty relation to capture EPR-steering for bipartite systems. Our steering inequality improves over previously known ones since it can experimentally detect all steerable two-qubit Werner state with only two measurement settings on each side. According to our inequality, pure entangle states are maximally steerable. Moreover, by slightly changing the setting, we can express the amount of violation of our inequality as a function of their violation of the CHSH inequality. Finally, we prove that the amount of violation of our steering inequality is, up to a constant factor, a lower bound on the key rate of a one-sided device independent quantum key distribution protocol secure against individual attacks. To show this result, we first derive a monogamy relation for our steering inequality.Comment: 5 pages, Accepted for publication as a Rapid Communication in Physical Review

Experimental detection of steerability in Bell local states with two measurement settings

Steering, a quantum property stronger than entanglement but weaker than non-locality in the quantum correlation hierarchy, is a key resource for one-sided device-independent quantum key distribution applications, in which only one of the communicating parties is trusted. A fine-grained steering inequality was introduced in [PRA 90 050305(R) (2014)], enabling for the first time the detection of steering in all steerable two-qubit Werner states using only two measurement settings. Here we numerically and experimentally investigate this inequality for generalized Werner states and successfully detect steerability in a wide range of two-photon polarization-entangled Bell local states generated by a parametric down-conversion source.Comment: 9 pages, 7 figures (including Appendix