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

scholarly journals A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 282 ◽  
Author(s):  
Andrea Coladangelo
Keyword(s):  
Optimal Strategy ◽  
Elementary Proof ◽  
Quantum Correlations ◽  
Entangled State ◽  
Finitely Presented Groups ◽  
Self Testing ◽  
Question And Answer ◽  
Questions And Answers ◽  
Non Local ◽  
Finitely Presented

We describe a two-player non-local game, with a fixed small number of questions and answers, such that an ϵ-close to optimal strategy requires an entangled state of dimension 2Ω(ϵ−1/8). Our non-local game is inspired by the three-player non-local game of Ji, Leung and Vidick \cite{ji2018three}. It reduces the number of players from three to two, as well as the question and answer set sizes. Moreover, it provides an (arguably) elementary proof of the non-closure of the set of quantum correlations, based on embezzlement and self-testing. In contrast, previous proofs \cite{slofstra2019set, dykema2017non, musat2018non} involved representation theoretic machinery for finitely-presented groups and C∗-algebras.

scholarly journals Monogamy of non-local quantum correlations

2008 ◽  
Vol 465 (2101) ◽  
pp. 59-69 ◽  
Author(s):  
Ben Toner
Keyword(s):  
Probability Distributions ◽  
Bell Inequality ◽  
Arbitrary Dimension ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Interactive Proof ◽  
Proof Systems ◽  
Non Local ◽  
A New Technique ◽  
Tsirelson Bound

We describe a new technique for obtaining Tsirelson bounds, which are upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signalling, we obtain a Tsirelson bound by maximizing over all no-signalling probability distributions. This maximization can be cast as a linear programme. In a setting where three parties, A, B and C, share an entangled quantum state of arbitrary dimension, we (i) bound the trade-off between AB's and AC's violation of the Clauser–Horne–Shimony–Holt inequality and (ii) demonstrate that forcing B and C to be classically correlated prevents A and B from violating certain Bell inequalities, relevant for interactive proof systems and cryptography.

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 MEASUREMENT IN CONTROL AND DISCRIMINATION OF ENTANGLED PAIRS UNDER SELF-DISTORTION

2011 ◽  
Vol 09 (supp01) ◽  
pp. 165-179
Author(s):  
FRANCISCO DELGADO
Keyword(s):  
Magnetic Field ◽  
Quantum Correlations ◽  
Inhomogeneous Magnetic Field ◽  
Original State ◽  
Communication Processes ◽  
Local Measurements ◽  
Non Local ◽  
And Behavior ◽  
And Control ◽  
Measurement And Control

Quantum correlations and entanglement are fundamental resources for quantum information and quantum communication processes. Developments in these fields normally assume stable resources, not susceptible of distortion. That is not always the case, Heisenberg interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e. g. quantum computation or quantum cryptography). The presence of parasite magnetic fields modifies the expected properties and behavior for which the pair was intended. Quantum measurement and control help to discriminate the original state in order to correct it or reconstruct it using some procedures which do not alter their quantum nature. Different kinds of quantum entangled pairs driven by a Heisenberg Hamiltonian with an additional inhomogeneous magnetic field become distorted. They can be reconstructed by adding an external magnetic field with fidelity close to one. In addition, each state can be efficiently discriminated. Combining both processes, first reconstruction without discrimination and after discrimination with adequate non-local measurements, it is possible to (a) improve the discrimination, and (b) reprepare faithfully the original state. The complete process gives fidelities better than 0.9. Some results about a class of equivalence for the required measurements are found, allowing to select the experimentally most adequate.

scholarly journals Causation does not explain contextuality

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 63 ◽  
Author(s):  
Sally Shrapnel ◽  
Fabio Costa
Keyword(s):  
Quantum Mechanics ◽  
Causal Structure ◽  
Quantum Correlations ◽  
Global Constraints ◽  
Local Constraints ◽  
The Past ◽  
Interpretations Of Quantum Mechanics ◽  
The World ◽  
Non Local ◽  
Initial States

Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot be explained by non-contextual ontological models, where physical properties are assumed to exist prior to and independently of the act of measurement. However, all such contextuality proofs assume a traditional notion of causal structure, where causal influence flows from past to future according to ordinary dynamical laws. This leaves open the question of whether the apparent contextuality of quantum mechanics is simply the signature of some exotic causal structure, where the future might affect the past or distant systems might get correlated due to non-local constraints. Here we show that quantum predictions require a deeper form of contextuality: even allowing for arbitrary causal structure, no model can explain quantum correlations from non-contextual ontological properties of the world, be they initial states, dynamical laws, or global constraints.

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.

scholarly journals Remote State Design for Efficient Quantum Metrology with Separable and Non-Teleporting States

2021 ◽  
Vol 3 (1) ◽  
pp. 228-241
Author(s):  
Rahul Raj ◽  
Shreya Banerjee ◽  
Prasanta K. Panigrahi
Keyword(s):  
Parameter Estimation ◽  
Quantum Information ◽  
Fisher Information ◽  
Quantum Information Processing ◽  
Quantum Fisher Information ◽  
Quantum Correlations ◽  
Quantum States ◽  
Quantum Metrology ◽  
High Quantum ◽  
Non Local

Measurements leading to the collapse of states and the non-local quantum correlations are the key to all applications of quantum mechanics as well as in the studies of quantum foundation. The former is crucial for quantum parameter estimation, which is greatly affected by the physical environment and the measurement scheme itself. Its quantification is necessary to find efficient measurement schemes and circumvent the non-desirable environmental effects. This has led to the intense investigation of quantum metrology, extending the Cramér–Rao bound to the quantum domain through quantum Fisher information. Among all quantum states, the separable ones have the least quantumness; being devoid of the fragile non-local correlations, the component states remain unaffected in local operations performed by any of the parties. Therefore, using these states for the remote design of quantum states with high quantum Fisher information can have diverse applications in quantum information processing; accurate parameter estimation being a prominent example, as the quantum information extraction solely depends on it. Here, we demonstrate that these separable states with the least quantumness can be made extremely useful in parameter estimation tasks, and further show even in the case of the shared channel inflicted with the amplitude damping noise and phase flip noise, there is a gain in Quantum Fisher information (QFI). We subsequently pointed out that the symmetric W states, incapable of perfectly teleporting an unknown quantum state, are highly effective for remotely designing quantum states with high quantum Fisher information.

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 An artificial spiking quantum neuron

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Lasse Bjørn Kristensen ◽  
Matthias Degroote ◽  
Peter Wittek ◽  
Alán Aspuru-Guzik ◽  
Nikolaj T. Zinner
Keyword(s):  
Time Series Prediction ◽  
Dynamical Evolution ◽  
Building Blocks ◽  
Quantum Correlations ◽  
Neuromorphic Hardware ◽  
Local Measurements ◽  
Non Local ◽  
Elementary Building ◽  
Learning Protocols

AbstractArtificial spiking neural networks have found applications in areas where the temporal nature of activation offers an advantage, such as time series prediction and signal processing. To improve their efficiency, spiking architectures often run on custom-designed neuromorphic hardware, but, despite their attractive properties, these implementations have been limited to digital systems. We describe an artificial quantum spiking neuron that relies on the dynamical evolution of two easy to implement Hamiltonians and subsequent local measurements. The architecture allows exploiting complex amplitudes and back-action from measurements to influence the input. This approach to learning protocols is advantageous in the case where the input and output of the system are both quantum states. We demonstrate this through the classification of Bell pairs which can be seen as a certification protocol. Stacking the introduced elementary building blocks into larger networks combines the spatiotemporal features of a spiking neural network with the non-local quantum correlations across the graph.

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