Absolute non-violation of a three-setting steering inequality by two-qubit states

Bhattacharya, Some Sankar; Mukherjee, Amit; Roy, Arup; Paul, Biswajit; Mukherjee, Kaushiki; Chakrabarty, Indranil; Jebaratnam, C.; Ganguly, Nirman

doi:10.1007/s11128-017-1734-4

Cited by 13 publications

(12 citation statements)

References 61 publications

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“…Thus, inequality (5) is valid for

and then we obtain the following result which was pointed out in [ 43 ] without proof.…”

Section: Epr Steering Inequalitiessupporting

confidence: 64%

“…Furthermore, a nine-setting steering inequality had also been presented for developing more efficient one-way steering and detecting some Bell nonlocal states. 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.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Thus, inequality (5) is valid for

and then we obtain the following result which was pointed out in [ 43 ] without proof.…”

Section: Epr Steering Inequalitiessupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Einstein-Podolsky-Rosen Steering Inequalities and Applications

Yang

Cao

2018

Entropy

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“…The necessary and sufficient conditions for a state being absolutely unsteerable are not known. However, there is in the literature the following partial result, concerning only steerability with three settings: Theorem 5.5 [7] If is a two-qubit state with spectrum d 1 d 2 , d 3 , d 4 , then is absolutely unsteerable with three settings iff its eigenvalues satisfy…”

Section: Absolutely Unsteerable Statesmentioning

confidence: 99%

Quantumness of States and Unitary Operations

Luc

2020

Found Phys

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This paper investigates various properties that may by possessed by quantum states, which are believed to be specifically “quantum” (entanglement, nonlocality, steerability, negative conditional entropy, non-zero quantum discord, non-zero quantum super discord and contextuality) and their opposites. It also considers their “absolute” counterparts in the following sense: a given state has a given property absolutely if after an arbitrary unitary transformation it still possesses it. The known relations between the listed properties and between their absolute counterparts are summarized. It is proven that the only two-qubit state that has zero quantum discord absolutely is the maximally mixed state. Finally, related conceptual issues concerning the terms “classical” and “quantum” are discussed.

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“…The states, which preserve their non-violation of the steering inequality (5) under arbitrary global unitary action, are called absolutely three-settings unsteerable states. A given two qubit state ρ is absolutely threesettings unsteerable iff [50]…”

Section: Absolute Three-settings Unsteerabilitymentioning

confidence: 99%

“…In the context of absolutely Bell-CHSH local states, the issue of transforming an absolutely Bell-CHSH local state into a nonlocal one has also been presented in a recent study [49]. In a similar spirit, the effect of global unitary interactions on states demonstrating EPR steering has also been studied [50] in the context of steering inequalities derived by Cavalcanti et al [23]. In particular, the issue of non-violation of the steering inequality with three measurement settings per party [23] by any two qubit system under arbitrary global unitary action has been studied in details.…”

Section: Introductionmentioning

confidence: 99%

Environmental Effects on Nonlocal Correlations

Guha

Bhattacharya

Das

et al. 2019

Quanta

Self Cite

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Environmental interactions are ubiquitous in practical instances of any quantum information processing protocol. The interaction results in depletion of various quantum resources and even complete loss in numerous situations. Nonlocality, which is one particular quantum resource marking a significant departure of quantum mechanics from classical mechanics, meets the same fate. In the present work we study the decay in nonlocality to the extent of the output state admitting a local hidden state model. Using some fundamental quantum channels we also demonstrate the complete decay in the resources in the purview of the Bell–Clauser–Horne–Shimony–Holt inequality and a three-settings steering inequality. We also obtain bounds on the parameter of the depolarizing map for which it becomes steerability breaking pertaining to a general class of two qubit states.Quanta 2019; 8: 57–67.

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Absolute non-violation of a three-setting steering inequality by two-qubit states

Cited by 13 publications

References 61 publications

Einstein-Podolsky-Rosen Steering Inequalities and Applications

Einstein-Podolsky-Rosen Steering Inequalities and Applications

Quantumness of States and Unitary Operations

Environmental Effects on Nonlocal Correlations

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