Superactivation of quantum steering

Quintino, Marco Túlio; Brunner, Nicolás; Huber, Marcus

doi:10.1103/physreva.94.062123

Cited by 36 publications

(52 citation statements)

References 48 publications

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“…[26] Whether superactivation is possible with two copies in low-dimensional systems such as two-qubit systems is still an open question. [26] Whether superactivation is possible with two copies in low-dimensional systems such as two-qubit systems is still an open question.…”

Section: Resultsmentioning

confidence: 99%

“…Let us consider the scenario based on n copies of EWL states (ρ E WL ) ⊗n in qubit system, which can be recasted into a single copy of a new bipartite entangled state of 2 n -dimensional systems by locally recoding the qubits, [26] that is…”

Section: Extended Werner Like Statesmentioning

confidence: 99%

“…[19] There are two typical quantum information resources which can be superactivated in quantum theory, one is bound entanglement and the other is nonlocality. [26] Hsieh et al independently derived a sufficient condition of steerability in terms of the fully entangled fraction and showed that the steerability of the isotropic states can be superactivated and amplified by joint measurements. [20,21] All entangled states display some hidden nonlocality, which can be activated or superactivated to violate a certain kind of Bell inequality by combining the quantum state with another one [22][23][24] or with itself.…”

Section: Introductionmentioning

confidence: 99%

“…[20,21] All entangled states display some hidden nonlocality, which can be activated or superactivated to violate a certain kind of Bell inequality by combining the quantum state with another one [22][23][24] or with itself. [26] Hence, it is of great importance to study whether superactivation is possible with two copies in small-dimensional systems such as twoqubit systems. That is, starting from multiple copies of unsteerable quantum entangled states, can we obtain a global quantum state which is steerable by local joint measurements?…”

Section: Introductionmentioning

confidence: 99%

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Activating the Violation of Steering Inequality for Two‐Qubit X States

et al. 2019

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The phenomenon of superactivation of quantum steering, that is, the fact that by combining several copies of the unsteerable quantum state one can get a steerable quantum state, has recently attracted much attention. This property is currently only known for isotropic states, and whether there exists an example other than isotropic states is so far an open question. It is of great importance to learn the activation property of non-isotropic states. In this paper, it is shown that the violation of the local uncertainty relations (LUR) steering inequality can be activated for two-qubit X type entangled mixed states. Although the activation phenomenon proven in this paper cannot guarantee the superactivation of steering for two-qubit X states, it does provide clues for this goal. In addition, previous results indicate that two copies are enough for the superactivation of steering, while the price to pay is a high local dimension, and it is unclear whether superactivation is possible with few copies in low-dimensional systems such as two-qubit systems. By providing examples of activation of LUR steering inequality with two copies in a two-qubit system, the work may open a potential way to the solution of this question.

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Section: Resultsmentioning

confidence: 99%

Section: Extended Werner Like Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Activating the Violation of Steering Inequality for Two‐Qubit X States

et al. 2019

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“…Recently, we became aware of the work of [43] who independently (1) derived a sufficient condition of steerability in terms of the fully entangled fraction and (2) demonstrated the superactivation of steering of the isotropic states. Moreover, after submission of this work, an anonymous referee of QIP2017 brought to our attention that for any given assemblage, its optimal steering fraction is actually identical to its steering robustness S R , as can be seen from the dual semidefinite programming formulation of steering robustness given in Eq.…”

Section: Discussionmentioning

confidence: 99%

Quantum steerability: Characterization, quantification, superactivation, and unbounded amplification

2016

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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 measurementsthe 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.

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Generation of One‐Way Gaussian Steering by Gaussian Channel and Converting One‐Way Gaussian Steering by Beamsplitters

et al. 2017

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Gaussian steering is used to characterize the intrinsic quantum correlation of Gaussian states under Gaussian measurement. Here we study the generation of one‐way Gaussian steering and the conversion of one‐way Gaussian steering. It is found that one‐way Gaussian steering could be generated by using Gaussian channels, either the Gaussian lossy channel or the Gaussian amplification channel. Exploiting the one‐way Gaussian steering in a two‐partite quantum system consists of two subsystems marked with A and B, one‐way Gaussian steering (steering from A to B) can be converted to the other one‐way Gaussian steering (steering from B to A) using linear optics, and vice versa.

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Superactivation of quantum steering

Cited by 36 publications

References 48 publications

Activating the Violation of Steering Inequality for Two‐Qubit X States

Activating the Violation of Steering Inequality for Two‐Qubit X States

Quantum steerability: Characterization, quantification, superactivation, and unbounded amplification

Generation of One‐Way Gaussian Steering by Gaussian Channel and Converting One‐Way Gaussian Steering by Beamsplitters

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