scholarly journals Exploring Multipartite Steering Effect Using Bell Operators

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 19
Author(s):  
Li-Yi Hsu ◽  
Shoichi Kawamoto
Keyword(s):  
Quantum Correlation ◽  
Numerical Results ◽  
Quantum Network ◽  
Joint Measurability ◽  
Einstein Podolsky Rosen ◽  
Bell Nonlocality ◽  
The One ◽  
Necessary And Sufficient ◽  
Qubit States ◽  
Epr Steering

While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein–Podolsky–Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are illustrated as examples. Finally, the steering criteria in a star-shaped quantum network is studied to see how the result is applied to a genuine multipartite steering case.

scholarly journals Einstein-Podolsky-Rosen Steering Inequalities and Applications

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 683 ◽  
Author(s):  
Ying Yang ◽  
Huaixin Cao
Keyword(s):  
Quantum System ◽  
Quantum Correlation ◽  
Entangled State ◽  
Intermediate Type ◽  
Maximally Entangled State ◽  
Nonlocal Correlation ◽  
Composite Quantum System ◽  
Einstein Podolsky Rosen ◽  
Bell Nonlocality ◽  
Epr Steering

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.

scholarly journals The Einstein–Podolsky–Rosen Steering and Its Certification

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 422 ◽  
Author(s):  
Yi-Zheng Zhen ◽  
Xin-Yu Xu ◽  
Li Li ◽  
Nai-Le Liu ◽  
Kai Chen
Keyword(s):  
Local Effects ◽  
Basic Framework ◽  
Quantum Protocols ◽  
Einstein Podolsky Rosen ◽  
Non Local ◽  
Bell Nonlocality ◽  
Epr Steering

The Einstein–Podolsky–Rosen (EPR) steering is a subtle intermediate correlation between entanglement and Bell nonlocality. It not only theoretically completes the whole picture of non-local effects but also practically inspires novel quantum protocols in specific scenarios. However, a verification of EPR steering is still challenging due to difficulties in bounding unsteerable correlations. In this survey, the basic framework to study the bipartite EPR steering is discussed, and general techniques to certify EPR steering correlations are reviewed.

scholarly journals Deriving Einstein–Podolsky–Rosen steering inequalities from the few-body Abner Shimony inequalities

2018 ◽  
Vol 33 (12) ◽  
pp. 1850064
Author(s):  
Jie Zhou ◽  
Hui-Xian Meng ◽  
Shu-Han Jiang ◽  
Zhen-Peng Xu ◽  
Changliang Ren ◽  
...  
Keyword(s):  
Quantum Nonlocality ◽  
Hidden Variable ◽  
Einstein Podolsky Rosen ◽  
Bell Nonlocality ◽  
Epr Steering ◽  
Local Hidden Variable

For the Abner Shimony (AS) inequalities, the simplest unified forms of directions attaining the maximum quantum violation are investigated. Based on these directions, a family of Einstein–Podolsky–Rosen (EPR) steering inequalities is derived from the AS inequalities in a systematic manner. For these inequalities, the local hidden state (LHS) bounds are strictly less than the local hidden variable (LHV) bounds. This means that the EPR steering is a form of quantum nonlocality strictly weaker than Bell nonlocality.

scholarly journals Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality

2014 ◽  
Vol 113 (16) ◽  
Author(s):  
Marco Túlio Quintino ◽  
Tamás Vértesi ◽  
Nicolas Brunner
Keyword(s):  
Joint Measurability ◽  
Einstein Podolsky Rosen ◽  
Bell Nonlocality

scholarly journals DETECTING EINSTEIN–PODOLSKY–ROSEN STEERING FOR CONTINUOUS VARIABLE WAVEFUNCTIONS

2013 ◽  
Vol 11 (02) ◽  
pp. 1350019 ◽  
Author(s):  
HONG-YI SU ◽  
JING-LING CHEN ◽  
CHUNFENG WU ◽  
DONG-LING DENG ◽  
C. H. OH
Keyword(s):  
Continuous Variable ◽  
Entangled States ◽  
Sufficient Condition ◽  
Bell’S Inequality ◽  
Necessary And Sufficient Condition ◽  
Bell's Inequality ◽  
Entropic Inequality ◽  
Einstein Podolsky Rosen ◽  
Necessary And Sufficient ◽  
Epr Steering

By use of Reid's criterion and the entropic criterion, we investigate the Einstein–Podolsky–Rosen (EPR) steering for some entangled continuous variable wavefunctions. We find that some entangled states that violate Bell's inequality will not violate Reid's EPR inequality nor the entropic inequality. This implies that neither criterion gives a necessary and sufficient condition to detect the EPR steering.

Does Global Justice Require More than Just Global Institutions?

2016 ◽  
Vol 3 (1) ◽  
pp. 19-31
Author(s):  
Kok-Chor Tan
Keyword(s):  
Global Justice ◽  
The Other ◽  
Global Institutions ◽  
Institutional Approach ◽  
The One ◽  
Necessary And Sufficient ◽  
Strong Reading

The ‘institutional approach’ to justice holds that persons’ responsibility of justice is primarily to support, maintain, and comply with the rules of just institutions. Within the rules of just institutions, so long as their actions do not undermine these background institutions, individuals have no further responsibilities of justice. But what does the institutional approach say in the non-ideal context where just institutions are absent, such as in the global case? One reading of the institutional approach, in this case, is that our duties are primarily to create just institutions, and that when we are doing our part in this respect, we may legitimately pursue other personal or associational ends. This ‘strong’ reading of our institutional duty takes it to be both a necessary and sufficient duty of justice of individuals that they do their part to establish just arrangements. But how plausible is this? On the one hand this requirement seems overly inflexible; on the other it seems overly lax. I clarify the motivation and context of this reading of the institutional duty, and suggest that it need not be as implausible as it seems.

scholarly journals AN ANALYTIC SOLUTION FOR ONE-DIMENSIONAL DISSIPATIONAL STRAIN-GRADIENT PLASTICITY

2009 ◽  
Vol 50 (3) ◽  
pp. 407-420
Author(s):  
ROGER YOUNG
Keyword(s):  
Boundary Condition ◽  
Strain Gradient ◽  
Analytic Solution ◽  
Strain Gradient Plasticity ◽  
Numerical Results ◽  
Gradient Plasticity ◽  
One Dimensional ◽  
Numerical Result ◽  
Formulation Analysis ◽  
The One

AbstractAn analytic solution is developed for the one-dimensional dissipational slip gradient equation first described by Gurtin [“On the plasticity of single crystals: free energy, microforces, plastic strain-gradients”, J. Mech. Phys. Solids48 (2000) 989–1036] and then investigated numerically by Anand et al. [“A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results”, J. Mech. Phys. Solids53 (2005) 1798–1826]. However we find that the analytic solution is incompatible with the zero-sliprate boundary condition (“clamped boundary condition”) postulated by these authors, and is in fact excluded by the theory. As a consequence the analytic solution agrees with the numerical results except near the boundary. The equation also admits a series of higher mode solutions where the numerical result corresponds to (a particular case of) the fundamental mode. Anand et al. also established that the one-dimensional dissipational gradients strengthen the material, but this proposition only holds if zero-sliprate boundary conditions can be imposed, which we have shown cannot be done. Hence the possibility remains open that dissipational gradient weakening may also occur.

CONTROLLED AND REMOTE IMPLEMENTATION OF A SPLIT QUANTUM ROTATION AND SENDER-ENCODED SECRET SHARING

2010 ◽  
Vol 24 (04n05) ◽  
pp. 431-437 ◽  
Author(s):  
LIBING CHEN ◽  
YUHUA LIU ◽  
HONG LU
Keyword(s):  
Secret Sharing ◽  
Quantum Secret Sharing ◽  
Ghz State ◽  
Quantum Network ◽  
Entanglement Property ◽  
Theoretical Scheme ◽  
Einstein Podolsky Rosen ◽  
Unit Probability

A quantum rotation can be divided into M pieces and teleported from a sender onto M distant receivers via the control of N agents in a quantum network. We utilize the entanglement property of a (2M + N + 1)-qubit Einstein–Podolsky–Rosen (EPR) — Greenberger–Horne–Zeilinger (GHZ) state to design a theoretical scheme for implementing these rotations remotely with unit fidelity and unit probability. The feature of the scheme is that, apart from a sender and M receivers, N agents are included in the process as controllers. Should any one of the N agents not cooperate, the receivers could not gain the original rotations. This scheme can be used to sender-encoded quantum secret sharing. It definitely has the strong security.

scholarly journals Qualitative analysis of an autocatalytic chemical reaction model with decay

2014 ◽  
Vol 144 (2) ◽  
pp. 427-446 ◽  
Author(s):  
Jun Zhou ◽  
Junping Shi
Keyword(s):  
Steady State ◽  
Chemical Reaction ◽  
Reaction Diffusion ◽  
Steady State Solution ◽  
Reaction Model ◽  
Existence Of A Solution ◽  
Positive Steady State ◽  
Chemical Reaction Model ◽  
The One ◽  
Necessary And Sufficient

In this paper, we revisit a reaction—diffusion autocatalytic chemical reaction model with decay. For higher-order reactions, we prove that the system possesses at least two positive steady-state solutions; hence, it has bistable dynamics similar to the system without decay. For the linear reaction, we determine the necessary and sufficient condition to ensure the existence of a solution. Moreover, in the one-dimensional case, we prove that the positive steady-state solution is unique. Our results demonstrate the drastic difference in dynamics caused by the order of chemical reactions.

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