Characterizing Bell nonlocality and EPR steering

Cao, Huaixin; Guo, Zhihua

doi:10.1007/s11433-018-9279-4

Cited by 36 publications

(29 citation statements)

References 60 publications

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“…From 2009, a series of experiments [26]- [29] showed that this type of paradox existed in reality. Based on the Hardy paradox and extensions, various theoretical models and experiments were developed [26]- [31], linked with wider applications: Bell inequality, quantum entanglements, single photon detection etc.…”

Section: Hardy Paradoxmentioning

confidence: 99%

Complementary Local and Nonlocal Measurements of Conjugate Transformation - Unified Logic Representation of Conjugate 0-1 Vectors

Zheng¹

2020

Preprint

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Bohr proposed the complementarity principle in 1927 as the foundation of quantum mechanics, since then relevant debates have been critically discussed for many years. Applying a pair of spin particles, Einstein proposed the EPR paradox in 1935. Using nonlocal potential properties, Aharonov and Bohm proposed the AB effect to test complementary measurement results. Under locality conditions, Bell established a Bell inequality under classical logic. Using a pair of particles and double sets of ZMI devices for complementarity measurements, Hardy proposed the Hardy paradox in 1992. During the past 50 years, locality and nonlocality tests on complementarity were hot-topics among the advanced quantum information, computing and measurement directions with various theoretical extensions and solid experimental results.These complementarity approaches separated local/nonlocal parameters to form different equations without an integrated logic framework to describe these equations including both local and nonlocal features consistently. The main results provide a series of paradoxes that conflict with each other. This paper uses conjugate transformation. Based on the m+1 kernel form of 0-1 states, n pairs of conjugate partitions were established. Under a given configuration in N bits, a set of 2n 0-1 feature vectors are applied to construct conjugate transformation operators in logic levels with intrinsic measurements to be a set of measurement operators.The key results of the paper are listed in Theorem 5. Two special functions of vector logic (CNF or DNF expression) and four equivalent expressions of the elementary equation are examples to show local and nonlocal variables in equations consistently. Applying two pairs of conjugate sets <A, B> and their complementary sets <A', B''>, 4 meta measures are established corresponding to <±aA;±bB> quantitative features under measurement operators. The main results of the paper are represented in Lemma (1-4), Theorem (1-5) and Corollary (1-7). From a vector logic viewpoint, conjugate complementary scheme can organize local and nonlocal variables to satisfy the comprehensive properties of modern logic constructions on completeness, non-conflict and consistence in a united logic framework.

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Section: Hardy Paradoxmentioning

confidence: 99%

Complementary Local and Nonlocal Measurements of Conjugate Transformation - Unified Logic Representation of Conjugate 0-1 Vectors

Zheng¹

2020

Preprint

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“…In this section, we will recall mathematical definitions related to steering motivated by the literature (e.g., [ 29 ]) and proposed in [ 46 ], and list related results proved in [ 46 ]. To do this, we use

and

to denote two finite dimensional complex Hilbert spaces, which describe two quantum systems A and B , respectively.…”

Section: Steering Inequalities Of Bipartite Quantum Statesmentioning

confidence: 99%

“…([ 46 ], Theorem 3.3) A state

of the system

is unsteerable from A to B if and only if for every

, there exists a PD

, a set of states

and

PDs

such that for every POVM

of B, it holds that

…”

Section: Steering Inequalities Of Bipartite Quantum Statesmentioning

confidence: 99%

“…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. Lastly, a sufficient condition for a state to be steerable was established, which leads to proofs of the EPR steerability of the maximally entangled states and that of entangled pure states.…”

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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“…2018年, Ren等人 [40] 基于2-测量与3-测量协议的线性导引不等式与CHSH型导引不等式, 从数学上推导出了极大可导引2-比特混合态; 文献 [41]引入并研究了量子导引广义鲁棒性; 文献 [42]给出了不可导引的必要条件和充分条件, 进而建立了一个EPR导引不等式. Cao与Guo [43] 提出了两体量子系统中的Bell非局域性及量子导引的数学定义, 并建立了它们的一系列等价刻画, 得到了可导引性的一些充分条件. 在多体量子导引的实验研究方面, Zeng等人 [44] 在实验上首次观测到了高维非局域量子操控效应, 这是对现有量子非局域效应研究的一次重要补充.…”

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