scholarly journals Quantum Correlation via Skew Information and Bell Function Beyond Entanglement in a Two-Qubit Heisenberg XYZ Model: Effect of the Phase Damping

2020 ◽  
Vol 10 (11) ◽  
pp. 3782 ◽  
Author(s):  
Abdel-Baset A. Mohamed ◽  
Ahmed Farouk ◽  
Mansour F. Yassen ◽  
Hichem Eleuch
Keyword(s):  
Sudden Change ◽  
Quantum Correlations ◽  
Physical Parameters ◽  
Phase Damping ◽  
Change Behavior ◽  
Skew Information ◽  
Local Correlations ◽  
Non Local ◽  
Moriya Interaction ◽  
Non Locality

In this paper, we analyze the dynamics of non-local correlations (NLCs) in an anisotropic two-qubit Heisenberg XYZ model under the effect of the phase damping. An analytical solution is obtained by applying a method based on the eigenstates and the eigenvalues of the Hamiltonian. It is observed that the generated NLCs are controlled by the Dzyaloshinskii–Moriya interaction, the purity indicator, the interaction with the environment, and the anisotropy. Furthermore, it is found that the quantum correlations, as well as the sudden death and sudden birth phenomena, depend on the considered physical parameters. In particular, the system presents a special correlation: the skew-information correlation. The log-negativity and the uncertainty-induced non-locality exhibit the sudden-change behavior. The purity of the initial states plays a crucial role on the generated nonlocal correlations. These correlations are sensitive to the DM interaction, anisotropy, and phase damping.

scholarly journals Multipartite Quantum Systems and Representations of Wreath Products

2020 ◽  
Vol 226 ◽  
pp. 02013
Author(s):  
Vladimir Kornyak
Keyword(s):  
Hilbert Space ◽  
Quantum Correlations ◽  
Wreath Products ◽  
Quantum Systems ◽  
Efficient Computation ◽  
Multipartite Quantum Systems ◽  
Irreducible Components ◽  
Local Correlations ◽  
Non Local ◽  
Multipartite System

The multipartite quantum systems are of particular interest for the study of such phenomena as entanglement and non-local correlations. The symmetry group of the whole multipartite system is the wreath product of the group acting in the “local” Hilbert space and the group of permutations of the constituents. The dimension of the Hilbert space of a multipartite system depends exponentially on the number of constituents, which leads to computational difficulties. We describe an algorithm for decomposing representations of wreath products into irreducible components. The C implementation of the algorithm copes with representations of dimensions in quadrillions. The program, in particular, builds irreducible invariant projectors in the Hilbert space of a multipartite system. The expressions for these projectors are tensor product polynomials. This structure is convenient for efficient computation of quantum correlations in multipartite systems with a large number of constituents.

The accelerated Gisin state: its non-locality, quantum correlations and efficiency to perform quantum masking

2021 ◽  
Vol 21 (15&16) ◽  
pp. 1274-1295
Author(s):  
A.G. Abdelwahab ◽  
A. Ghwail ◽  
N. Metwally ◽  
M.H. Mahran ◽  
A. -S. F. Obada
Keyword(s):  
Quantum Correlations ◽  
Local Behavior ◽  
Quantum Uncertainty ◽  
Acceleration Parameter ◽  
Masking Condition ◽  
Local Quantum Uncertainty ◽  
Local Quantum ◽  
Non Local ◽  
Classical Correlations ◽  
Non Locality

The local and non local behavior of the accelerated Gisin state are investigated either before or after filtering process. It is shown that, the possibility of predicting the non-local behavior is forseen at large values of the weight of the Gisin and acceleration parameters. Due to the filtering process, the non-locality behavior of the Gisin state is predicted at small values of the weight parameter. The amount of non classical correlations are quantified by means of the local quantum uncertainty (LQU)and the concurrence, where the LQU is more sensitive to the non-locality than the concurrence. The phenomenon of the sudden changes is displayed for both quantifiers. Our results show that, the accelerated Gisin state could be used to mask information, where all the possible partitions of the masked state satisfy the masking criteria. Moreover, there is a set of states, which satisfy the masking condition, that is generated between each qubit and its masker qubit. For this set, the amount of the non-classical correlations increases as the acceleration parameter increases . Further, the filtering process improves these correlations, where their maximum bounds are much larger than those depicted for non-filtered states.

scholarly journals Implications of superstrong non-locality for cryptography

2006 ◽  
Vol 462 (2071) ◽  
pp. 1919-1932 ◽  
Author(s):  
Harry Buhrman ◽  
Matthias Christandl ◽  
Falk Unger ◽  
Stephanie Wehner ◽  
Andreas Winter
Keyword(s):  
Quantum Mechanics ◽  
Oblivious Transfer ◽  
Secure Computation ◽  
Bit Commitment ◽  
Local Correlations ◽  
Non Local ◽  
Non Locality

Non-local boxes are hypothetical ‘machines’ that give rise to superstrong non-local correlations, leading to a stronger violation of Bell/Clauser, Horne, Shimony & Holt inequalities than is possible within the framework of quantum mechanics. We show how non-local boxes can be used to perform any two-party secure computation. We first construct a protocol for bit commitment and then show how to achieve oblivious transfer using non-local boxes. Both have been shown to be impossible using quantum mechanics alone.

scholarly journals CTC assisted PR box type correlation can lead to signaling

2014 ◽  
Vol 14 (13&14) ◽  
pp. 1251-1260
Author(s):  
Indranil Chakrabarty ◽  
Tanumoy Pramanik ◽  
Arun K Pati ◽  
Pankaj Agrawal
Keyword(s):  
Quantum Correlations ◽  
Quantum Mechanical ◽  
Local Correlations ◽  
No Signaling ◽  
Non Local

It is known that there exist non-local correlations that respect no-signaling criterion, but violate Bell-type inequalities more than quantum-mechanical correlations. Such super quantum correlations were introduced as the Popescu-Rohrlich (PR) box. We consider such non-local boxes with two/three inputs and two/three outputs. We show that these super quantum correlations can lead to signaling when at least one of the input bit has access to a word line along a closed time-like curve.

An anomaly of non-locality

2007 ◽  
Vol 7 (1&2) ◽  
pp. 157-170 ◽  
Author(s):  
A.A. Methot ◽  
V. Scarani
Keyword(s):  
Bell Inequalities ◽  
Present Knowledge ◽  
Quantum States ◽  
Entangled States ◽  
Low Dimensions ◽  
Local Correlations ◽  
Non Local ◽  
Entangled Quantum States ◽  
Maximally Entangled States ◽  
Non Locality

Ever since the work of Bell, it has been known that entangled quantum states can produce non-local correlations between the outcomes of separate measurements. However, for almost forty years, it has been assumed that the most non-local states would be the maximally entangled ones. Surprisingly it is not the case: non-maximally entangled states are generally more non-local than maximally entangled states for all the measures of non-locality proposed to date: Bell inequalities, the Kullback-Leibler distance, entanglement simulation with communication or with non-local boxes, the detection loophole and efficiency of cryptography. In fact, one can even find simple examples in low dimensions, confirming that it is not an artefact of a specifically constructed Hilbert space or topology. This anomaly shows that entanglement and non-locality are not only different concepts, but also truly different resources. We review the present knowledge on this anomaly, point out that Hardy's theorem has the same feature, and discuss the perspectives opened by these discoveries.

scholarly journals Discrimination of Non-Local Correlations

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 104 ◽  
Author(s):  
Alberto Montina ◽  
Stefan Wolf
Keyword(s):  
Communication Complexity ◽  
Simple Algorithm ◽  
Running Time ◽  
Numerical Tests ◽  
Quantum Non Locality ◽  
Local Correlations ◽  
Non Local ◽  
Np Complete ◽  
Very High ◽  
Non Locality

In view of the importance of quantum non-locality in cryptography, quantum computation, and communication complexity, it is crucial to decide whether a given correlation exhibits non-locality or not. As proved by Pitowski, this problem is NP-complete, and is thus computationally intractable unless NP is equal to P. In this paper, we first prove that the Euclidean distance of given correlations from the local polytope can be computed in polynomial time with arbitrary fixed error, granted the access to a certain oracle; namely, given a fixed error, we derive two upper bounds on the running time. The first bound is linear in the number of measurements. The second bound scales with the number of measurements to the sixth power. The former holds only for a very high number of measurements, and is never observed in the performed numerical tests. We, then, introduce a simple algorithm for simulating the oracle. In all of the considered numerical tests, the simulation of the oracle contributes with a multiplicative factor to the overall running time and, thus, does not affect the sixth-power law of the oracle-assisted algorithm.

scholarly journals Randomness and Non-Locality

2016 ◽  
Vol 15 (03) ◽  
pp. 1640005 ◽  
Author(s):  
Gabriel Senno ◽  
Ariel Bendersky ◽  
Santiago Figueira
Keyword(s):  
Quantum Information ◽  
Information Science ◽  
Quantum Information Science ◽  
Recent Advances ◽  
Local Correlations ◽  
Distant Measurement ◽  
Non Local ◽  
Non Locality

The concepts of randomness and non-locality are intimately intertwined outcomes of randomly chosen measurements over entangled systems exhibiting non-local correlations are, if we preclude instantaneous influence between distant measurement choices and outcomes, random. In this paper, we survey some recent advances in the knowledge of the interplay between these two important notions from a quantum information science perspective.

scholarly journals Evaluating probabilistic forecasts of football matches: the case against the ranked probability score

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Edward Wheatcroft
Keyword(s):  
Scoring Rules ◽  
Brier Score ◽  
Sporting Events ◽  
Forecast Performance ◽  
Scoring Rule ◽  
Probability Score ◽  
Probabilistic Forecasts ◽  
Non Local ◽  
Evaluating Forecasts ◽  
Non Locality

Abstract A scoring rule is a function of a probabilistic forecast and a corresponding outcome used to evaluate forecast performance. There is some debate as to which scoring rules are most appropriate for evaluating forecasts of sporting events. This paper focuses on forecasts of the outcomes of football matches. The ranked probability score (RPS) is often recommended since it is ‘sensitive to distance’, that is it takes into account the ordering in the outcomes (a home win is ‘closer’ to a draw than it is to an away win). In this paper, this reasoning is disputed on the basis that it adds nothing in terms of the usual aims of using scoring rules. A local scoring rule is one that only takes the probability placed on the outcome into consideration. Two simulation experiments are carried out to compare the performance of the RPS, which is non-local and sensitive to distance, the Brier score, which is non-local and insensitive to distance, and the Ignorance score, which is local and insensitive to distance. The Ignorance score outperforms both the RPS and the Brier score, casting doubt on the value of non-locality and sensitivity to distance as properties of scoring rules in this context.

scholarly journals Non-local and local ghost fields in quantum correlations

1995 ◽  
Vol 36 (3) ◽  
pp. 139-147 ◽  
Author(s):  
Krzysztof Wódkiewicz
Keyword(s):  
Quantum Correlations ◽  
Non Local
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