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Conference on Lasers and Electro-Optics

Verifying hidden quantum steering via local filtering operations

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

Published Jan 1, 2019• 0 citations
Publisher

Abstract

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 filtering operations on individual quantum systems.
DOI
10.1364/cleo_at.2019.jtu2a.35

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Verifying hidden quantum steering via local filtering operations

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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.
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.
We introduce and study the notion of steerability for channels. This generalizes the notion of steerability of bipartite quantum states. We discuss a key conceptual difference between the case of states and the case of channels: while state steering deals with the notion of “hidden” states, steerability in the channel case is better understood in terms of coherence of channel extensions, rather than in terms of “hidden” channels. This distinction vanishes in the case of states. We further argue how the proposed notion of lack of coherence of channel extensions coincides with the notion of channel extensions realized via local operations and classical communication. We also discuss how the Choi–Jamiołkowski isomorphism allows the direct application of many results about states to the case of channels. We introduce measures for the steerability of channel extensions.
Quantum steering is a central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables (SEO), first proposed to connect the problem of steerability and measurement incompatibility. We provide an efficient method to compute the extractable steerability that is maximal via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples.
The development of large-scale quantum networks promises to bring a multitude of technological applications as well as shed light on foundational topics, such as quantum nonlocality. It is particularly interesting to consider scenarios where sources within the network are statistically independent, which leads to so-called network nonlocality, even when parties perform fixed measurements. Here we promote certain parties to be trusted and introduce the notion of network steering and network local hidden state (NLHS) models within this paradigm of independent sources. In one direction, we show how the results from Bell nonlocality and quantum steering can be used to demonstrate network steering. We further show that it is a genuinely novel effect by exhibiting unsteerable states that nevertheless demonstrate network steering based upon entanglement swapping yielding a form of activation. On the other hand, we provide no-go results for network steering in a large class of scenarios by explicitly constructing NLHS models.