Generalized Steering Robustness of Bipartite Quantum States

Zheng, Chunming; Guo, Zhihua; Cao, Huaixin

doi:10.1007/s10773-018-3704-8

Cited by 10 publications

(7 citation statements)

References 26 publications

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“…A related quantification of steering, the generalized steering robustness, is proposed in [250], in a similar way as what is done for the generalized entanglement robustness [251,252]. This quantification is proven to have desirable characteristics for a proper steering measure.…”

Section: Steering Robustnessmentioning

confidence: 99%

Certification and applications of quantum nonlocal correlations

Piceno-Martínez,

Rosales-Zárate,

Ornelas-Cruces

2023

J. Phys. Photonics

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Entanglement and Einstein-Podolsky-Rosen (EPR) steering are nonlocal quantum correlations, which are relevant resources for quantum information protocols. EPR steering, or quantum steering, refers to the correlation where a party might “steer”, or modify, the state of another, which is spatially separated. Entanglement is a symmetric resource while steering is asymmetrical, since it depends on the direction of the effect. Due to these different characteristics and the therefore different possible applications, there has been both theoretical and experimental research on forms to certify the distinct quantum nonlocal correlations. In recent years, alongside the investigation on quantum correlations between two systems, there has been a great interest in investigating multipartite/multimode entanglement as well as steering, since they include a high dimension and it may be possible to store more information than in a single qubit. In this review, we will summarize the different criteria and measures that have been developed for the characterization of these two kinds of correlations. We first focus on bipartite entanglement and steering. We then review the progress that has been made in the investigation of multipartite quantum correlations. We revise the theoretical work in quantum nonlocal correlation witnesses and measures, which respectively allow one to certify that the system is entangled or presents EPR steering, and give a quantification of the content of these correlations in the system. Then, we briefly review the experiments that have been designed and that demonstrate multipartite quantum correlations. We also include applications in quantum information protocols, in particular in quantum teleportation and quantum cryptography.

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Section: Steering Robustnessmentioning

confidence: 99%

Certification and applications of quantum nonlocal correlations

Piceno-Martínez,

Rosales-Zárate,

Ornelas-Cruces

2023

J. Phys. Photonics

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“…As an intermediary property between Bell nonlocality and entanglement, EPR steering was first observed by Schrödinger [2] in the context of the well-known EPR paradox [1,[20][21][22]. It is also is an important resources in quantum information and then has been recently discussed, please refer to [17,[23][24][25][26][27][28][29][30][31]. Especially, mathematical definitions of Bell nonlocality and EPR steerability of bipartite states were proposed and their characterizations were given in [17] by Cao and Guo. Although entanglement was first recognized as the characteristic trait of quantum mechanics [1], its role has been debated since it does not capture all the quantum features of a quantum system [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Some Measurement-Based Characterizations of Separability of Bipartite States

2021

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Importance of quantum entanglement has been demonstrated in various applications. Usually, separability of a bipartite state is defined by its algebraic structure, i.e. a convex combination of product states. But it seems to be hard to check separability (equivalently, entanglement) of a state from its algebraic structure. In this note, we give some characterizations of separability of bipartite states based on POVM measurements. For bipartite pure states, we prove the separability, Bell locality, unsteerability and classical correlation are the same. As a consequence, every entangled pure bipartite state is always Bell nonlocal, steerable and quantum correlated.

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“…Bhattacharya et al [ 43 ] present absolute non-violation of a three-setting steering inequality by two-qubit states. Recently, some characterizations of EPR steering are given in [ 44 ] and the generalized steering robustness was introduced and some interesting properties were established in [ 45 ], which suggests a way of quantifying quantum steering. Very recently, Bell nonlocality and EPR steering of bipartite states were discussed mathematically in [ 46 ], including mathematical definitions and characterizations of these two quantum correlations, the convexity and closedness of the sets of all Bell local states and all EPR unsteerable states, respectively.…”

Section: Introductionmentioning

confidence: 99%

Einstein-Podolsky-Rosen Steering Inequalities and Applications

Yang

Cao

2018

Entropy

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Einstein-Podolsky-Rosen (EPR) steering is very important quantum correlation of a composite quantum system. It is an intermediate type of nonlocal correlation between entanglement and Bell nonlocality. In this paper, based on introducing definitions and characterizations of EPR steering, some EPR steering inequalities are derived. With these inequalities, the steerability of the maximally entangled state is checked and some conditions for the steerability of the X-states are obtained. IntroductionGenerally, quantum correlations means the correlations between subsystems of a composite quantum system, including Bell nonlocality, steerability, entanglement and quantum discord.Einstein-Podolsky-Rosen (EPR) steering was first observed by Schrodinger [1] in the context of famous Einstein-Podolsky-Rosen (EPR) paradox [2][3][4][5]. It was realized that EPR steering, as a form of bipartite quantum correlation, is an intermediate between entanglement and Bell nonlocality. Wiseman et al. [6] shown the inequivalence between entanglement, steering, and nonlocality when considering the projective measurements. Then, Quintino et al. [7] further considered the general measurements and proved that these three quantum relations are inequivalent. Interestingly, steering can be characterized by a simple quantum information processing task, namely, entanglement verification with an untrusted party [6][7][8][9][10]. In addition, steering has been found useful in several applications, such as one-sided device-independent quantum key distribution [11]; subchannel discrimination [12]; temporal steering and security of quantum key distribution with mutually unbiased bases against individual attacks [13]; temporal steering in four dimensions with applications to coupled qubits and magnetoreception [14]; no-cloning of quantum steering [15]; and spatio-temporal steering for testing nonclassical correlations in quantum networks [16]. Recently, detection and characterization of steering have attracted increasing attention [3,6,8,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Many of the standard Bell inequalities (e.g., CHSH ) are not effective for detection of quantum correlations which allow for steering, because for a wide range of such correlations they are not violated. Various steering inequalities have been derived, such as linear steering inequalities [33][34][35]; inequalities based on multiplicative variances [3,17,33]; entropy uncertainty relations [36,37]; fine-grained uncertainty relations [38], temporal steering inequality [39]. Besides, Zukowski et al. [40] presented some Bell-like inequalities which have lower bounds for non-steering correlations than for local causal models. These inequalities involve all possible measurement settings at each side. Based on the data-processing inequality for an extended Rényi relative entropy, Zhu et al. [41] introduced a family of steering inequalities, which detect steering much more efficiently than those inequalities known before. Chen et al. [42] showed that Bell nonlo...

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Generalized Steering Robustness of Bipartite Quantum States

Cited by 10 publications

References 26 publications

Certification and applications of quantum nonlocal correlations

Certification and applications of quantum nonlocal correlations

Some Measurement-Based Characterizations of Separability of Bipartite States

Einstein-Podolsky-Rosen Steering Inequalities and Applications

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