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arXiv:1406.0530 · Physical Review Letters

Necessary and Sufficient Quantum Information Characterization of Einstein-Podolsky-Rosen Steering

Marco Piani, John Watrous

Published Feb 12, 2015• 465 citations
arXivHTMLPDF

Abstract

Steering is the entanglement-based quantum effect that embodies the "spooky action at a distance" disliked by Einstein and scrutinized by Einstein, Podolsky, and Rosen. Here we provide a necessary and sufficient characterization of steering, based on a quantum information processing task: the discrimination of branches in a quantum evolution, which we dub subchannel discrimination. We prove that, for any bipartite steerable state, there are instances of the quantum subchannel discrimination problem for which this state allows a correct discrimination with strictly higher probability than in the absence of entanglement, even when measurements are restricted to local measurements aided by one-way communication. On the other hand, unsteerable states are useless in such conditions, even when entangled. We also prove that the above steering advantage can be exactly quantified in terms of the steering robustness, which is a natural measure of the steerability exhibited by the state.

DOI
10.1103/physrevlett.114.060404

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Steering is the entanglement-based quantum effect that embodies the "spooky action at a distance" disliked by Einstein and scrutinized by Einstein, Podolsky, and Rosen. Here we provide a necessary and sufficient characterization of steering, based on a quantum information processing task: the discrimination of branches in a quantum evolution, which we dub subchannel discrimination. We prove that, for any bipartite steerable state, there are instances of the quantum subchannel discrimination problem for which this state allows a correct discrimination with strictly higher probability than in the absence of entanglement, even when measurements are restricted to local measurements aided by one-way communication. On the other hand, unsteerable states are useless in such conditions, even when entangled. We also prove that the above steering advantage can be exactly quantified in terms of the steering robustness, which is a natural measure of the steerability exhibited by the state.
Abstract Einstein–Podolsky–Rosen (EPR) steering describes a quantum nonlocal phenomenon in which one party can nonlocally affect the other’s state through local measurements. It reveals an additional concept of quantum non-locality, which stands between quantum entanglement and Bell nonlocality. Recently, a quantum information task named as subchannel discrimination (SD) provides a necessary and sufficient characterization of EPR steering. The success probability of SD using steerable states is higher than using any unsteerable states, even when they are entangled. However, the detailed construction of such subchannels and the experimental realization of the corresponding task are still technologically challenging. In this work, we designed a feasible collection of subchannels for a quantum channel and experimentally demonstrated the corresponding SD task where the probabilities of correct discrimination are clearly enhanced by exploiting steerable states. Our results provide a concrete example to operationally demonstrate EPR steering and shine a new light on the potential application of EPR steering.
Quantum steering, also called Einstein-Podolsky-Rosen steering, is the intriguing phenomenon associated with the ability of spatially separated observers to steer---by means of local measurements---the set of conditional quantum states accessible by a distant party. In the light of quantum information, all steerable quantum states are known to be resources for quantum information processing tasks. Here, via a quantity dubbed steering fraction, we derive a simple, but general criterion that allows one to identify quantum states that can exhibit quantum steering (without having to optimize over the measurements performed by each party), thus making an important step towards the characterization of steerable quantum states. The criterion, in turn, also provides upper bounds on the largest steering-inequality violation achievable by arbitrary finite-dimensional maximally entangled states. For the quantification of steerability, we prove that a strengthened version of the steering fraction is a convex steering monotone and demonstrate how it is related to two other steering monotones, namely, steerable weight and steering robustness. Using these tools, we further demonstrate the superactivation of steerability for a well-known family of entangled quantum states, i.e., we show how the steerability of certain entangled, but unsteerable quantum states can be recovered by allowing joint measurements on multiple copies of the same state. In particular, our approach allows one to explicitly construct a steering inequality to manifest this phenomenon. Finally, we prove that there exist examples of quantum states (including some which are unsteerable under projective measurements) whose steering-inequality violation can be arbitrarily amplified by allowing joint measurements on as little as three copies of the same state. For completeness, we also demonstrate how the largest steering-inequality violation can be used to bound the largest Bell-inequality violation and derive, analogously, a simple sufficient condition for Bell nonlocality from the latter.
Einstein-Podolsky-Rosen (EPR) steering is the ability that an observer persuades a distant observer to share entanglement by making local measurements. Determining a quantum state is steerable or unsteerable remains an open problem. Here, we derive a new steering inequality with infinite measurements corresponding to an arbitrary two-qubit T state, from consideration of EPR steering inequalities with N projective measurement settings for each side. In fact, the steering inequality is also a sufficient criterion for guaranteering that the T state is unsteerable. Hence, the steering inequality can be viewed as a necessary and sufficient criterion to distinguish whether the T state is steerable or unsteerable. In order to reveal the fact that the set composed of steerable states is the strict subset of the set made up of entangled states, we prove theoretically that all separable T states can not violate the steering inequality. Moreover, we put forward a method to estimate the maximum violation from concurrence for arbitrary two-qubit T states, which indicates that the T state is steerable if its concurrence exceeds 1/4.
EPR steering is a form of bipartite quantum correlation that is intermediate between entanglement and Bell nonlocality. It is detected via the violation of steering inequalities, which provide sufficient conditions for the steerability of quantum states. Furthermore, there is a sufficient criterion for guaranteeing that a two-qubit state is unsteerable. But there are some two qubit states that can not determine the steerability of the steering inequality and the sufficient criteria. Here we introduce a way of quantifying this phenomenon and use it to study the steerability of two qubit states. This article recommend a platonic solid measurement schemes. And then discuss the problem, namely expanding the scope of steerable, which guarantees that the state is steerable.
Einstein-Podolsky-Rosen (EPR) steering describes the ability of one observer to nonlocally "steer" the other observer's state through local measurements. EPR steering exhibits a unique asymmetric property; i.e., the steerability can differ between observers, which can lead to one-way EPR steering in which only one observer obtains steerability in the steering process. This property is inherently different from the symmetric concepts of entanglement and Bell nonlocality, and it has attracted increasing interest. Here, we experimentally demonstrate asymmetric EPR steering for a class of two-qubit states in the case of two measurement settings. We propose a practical method to quantify the steerability. We then provide a necessary and sufficient condition for EPR steering and clearly demonstrate one-way EPR steering. Our work provides new insight into the fundamental asymmetry of quantum nonlocality and has potential applications in asymmetric quantum information processing.
Einstein-Podolsky-Rosen steering is a form of bipartite quantum correlation that is intermediate between entanglement and Bell nonlocality. It allows for entanglement certification when the measurements performed by one of the parties are not characterized (or are untrusted) and has applications in quantum key distribution. Despite its foundational and applied importance, Einstein-Podolsky-Rosen steering lacks a quantitative assessment. Here we propose a way of quantifying this phenomenon and use it to study the steerability of several quantum states. In particular, we show that every pure entangled state is maximally steerable and the projector onto the antisymmetric subspace is maximally steerable for all dimensions; we provide a new example of one-way steering and give strong support that states with positive-partial transposition are not steerable.