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arXiv:1707.08285 · Physical Review A

Revealing hidden quantum steerability using local filtering operations

Tanumoy Pramanik, Young‐Wook Cho, Sang-Wook Han, Sang‐Yun Lee, Yong‐Su Kim, Sung Moon

Published Mar 1, 2019• 37 citations
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Abstract

Nonlocal quantum correlation is at the heart of the bizarre nature of quantum physics. While there are various classes of nonlocal quantum correlation, steerability of a quantum state by local measurements provides unique operational features. Here, we theoretically and experimentally investigate the ``hidden'' property of quantum steerability. In particular, we find that there are initially unsteerable states which can reveal the steerability by using local filters on individual quantum systems. It is remarkable that a certain set of local filters is more effective in revealing steerability than Bell nonlocality whereas there exists another set of filters that is more effective in revealing Bell nonlocality than steerability. This result suggests the structural difference between entanglement and steerability. Finally, we present a counterintuitive result that mixed states originating from nonmaximally pure entangled states can have hidden steerability while the mixed state from a maximally pure entangled state fails to show steerability.

DOI
10.1103/physreva.99.030101

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Nonlocal quantum correlation is at the heart of the bizarre nature of quantum physics. While there are various classes of nonlocal quantum correlation, steerability of a quantum state by local measurements provides unique operational features. Here, we theoretically and experimentally investigate the ``hidden'' property of quantum steerability. In particular, we find that there are initially unsteerable states which can reveal the steerability by using local filters on individual quantum systems. It is remarkable that a certain set of local filters is more effective in revealing steerability than Bell nonlocality whereas there exists another set of filters that is more effective in revealing Bell nonlocality than steerability. This result suggests the structural difference between entanglement and steerability. Finally, we present a counterintuitive result that mixed states originating from nonmaximally pure entangled states can have hidden steerability while the mixed state from a maximally pure entangled state fails to show steerability.
The nonlocality of certain quantum states can be revealed by using local filters before performing a standard Bell test. This phenomenon, known as hidden nonlocality, has been so far demonstrated only for a restricted class of measurements, namely, projective measurements. Here, we prove the existence of genuine hidden nonlocality. Specifically, we present a class of two-qubit entangled states, for which we construct a local model for the most general local measurements, and show that the states violate a Bell inequality after local filtering. Hence, there exist entangled states, the nonlocality of which can be revealed only by using a sequence of measurements. Finally, we show that genuine hidden nonlocality can be maximal. There exist entangled states for which a sequence of measurements can lead to maximal violation of a Bell inequality, while the statistics of nonsequential measurements is always local.
It is well known that quantum correlations such as quantum nonlocality and steering can be revealed by means of the implementation of local filters or stochastic local operation and classical communication (SLOCC). This means that bipartite quantum states that are entangled but local (unsteerable), can be driven locally to quantum nonlocal (steerable) states. However, there does not exist a criterion telling us whether the revealed quantum correlation is accessible by locally implementing on a single party, or both parties are required to cooperate by implementing local filters. In this work, we proposed a criterion based on the quantum steering ellipsoid and provided examples of two-qubit states with locally inaccessible quantum correlations.
The bipartite state is said to be steerable iff it does not have single system description, i.e., the bipartite state can not be explained by local hidden state model [Phys. Rev. Lett. {\bf 98}, 140402 (2007)]. Several steering inequalities have been derived using different local uncertainty relations to verify the control on the state of one subsystem by other. Here, we derive complementarity kind of relations between coherences measured on mutually unbiased bases using various coherence measures like the l1l_1l1​-norm, relative entropy and skew information. Using these relations, we formulate steering inequalities to check whether one subsystem has control to the coherence of the other entangled subsystem. According to our results, all pure entangled states are maximally steerable but for mixed entangled states, coherence steerability needs stronger non-local correlation than the existing state steering inequalities. We also show that our steering criteria is monogamous.
We show that any Bell local state with a hidden nonlocality that can be revealed by local filtering is more, or equally, entangled than nonlocal states. More precisely, it can be deterministically transformed into a nonlocal state by local operations and classical communication. For such a state, there is a clear anomaly of nonlocality for any measures of entanglement and nonlocality. Moreover, we prove that the hidden nonlocality of any bipartite state more, or equally, entangled than nonlocal states can be revealed by local operations and the sending of two one-bit messages, one in each direction. For some particular states, one bit of communication is even enough.