Non-Local Advantage of Quantum Coherence

Abstract

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.

8 pages, protocol modified, To appear in PRA-Rapid Communications

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• Sharing of Non-Local Advantage of Quantum Coherence by sequential observers
• Phase control of entanglement and quantum steering in a three-mode optomechanical system
• Sharing of tripartite nonlocality by multiple observers measuring sequentially at one side
• Experimental investigation of nonlocal advantage of quantum coherence
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• Complementarity Relations Between Quantum Steering Criteria
• Finite-size scaling of coherence and steered coherence in the Lipkin-Meshkov-Glick model
• Complete complementarity relations for quantum correlations in neutrino oscillations
• Limits on sequential sharing of nonlocal advantage of quantum coherence
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• Nonlocal Advantages of Quantum Imaginarity
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