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 Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marcin Wieśniak
Keyword(s):  
Communication Complexity ◽  
Quantum Communication ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Complexity Reduction ◽  
Main Difficulty ◽  
Quantum Communication Complexity ◽  
Number Of Particles ◽  
Dicke States

AbstractQuantum correlations, in particular those, which enable to violate a Bell inequality, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles N. In case of Dicke states, we show that persistency can reach 0.482N, significantly more than reported in previous studies.

scholarly journals Experimental Connection between the Instrumental and Bell Inequalities

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 27
Author(s):  
Iris Agresti ◽  
Gonzalo Carvacho ◽  
Davide Poderini ◽  
Leandro Aolita ◽  
Rafael Chaves ◽  
...  
Keyword(s):  
Causal Model ◽  
Probability Distributions ◽  
Causal Structure ◽  
Joint Probability ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Causal Processes ◽  
Chsh Inequality ◽  
Joint Probability Distributions ◽  
Selection Of

An investigated process can be studied in terms of the causal relations among the involved variables, representing it as a causal model. Some causal models are particularly relevant, since they can be tested through mathematical constraints between the joint probability distributions of the observables. This is a valuable tool because, if some data violates the constraints of a causal model, the implication is that the observed statistics is not compatible with that causal structure. Strikingly, when non-classical correlations come to play, a discrepancy between classical and quantum causal predictions can arise, producing a quantum violation of the classical causal constraints. The simplestscenario admitting such quantum violation is given by the instrumental causal processes. Here, we experimentally violate an instrumental test on a photonic platform and show how the quantum correlations violating the CHSH inequality can be mapped into correlations violating an instrumental test, despite the different forms of non-locality they display. Indeed, starting from a Bell-like scenario, we recover the violation of the instrumental scenario through a map between the two behaviours, which includes a post-selection of data and then we test an alternative way to violate the CHSH inequality, adopting the instrumental process platform.

scholarly journals Does violation of a Bell inequality always imply quantum advantage in a communication complexity problem?

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 316 ◽  
Author(s):  
Armin Tavakoli ◽  
Marek Żukowski ◽  
Časlav Brukner
Keyword(s):  
Communication Complexity ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Fixed Number ◽  
Communication Strategy ◽  
Small Quantum ◽  
Complexity Problem ◽  
Classical Models ◽  
Quantum Protocol

Quantum correlations which violate a Bell inequality are presumed to power better-than-classical protocols for solving communication complexity problems (CCPs). How general is this statement? We show that violations of correlation-type Bell inequalities allow advantages in CCPs, when communication protocols are tailored to emulate the Bell no-signaling constraint (by not communicating measurement settings). Abandonment of this restriction on classical models allows us to disprove the main result of, inter alia, \cite{BZ02}; we show that quantum correlations obtained from these communication strategies assisted by a small quantum violation of the CGLMP Bell inequalities do not imply advantages in any CCP in the input/output scenario considered in the reference. More generally, we show that there exists quantum correlations, with nontrivial local marginal probabilities, which violate the I3322 Bell inequality, but do not enable a quantum advantange in any CCP, regardless of the communication strategy employed in the quantum protocol, for a scenario with a fixed number of inputs and outputs

scholarly journals ON BELL INEQUALITY VIOLATIONS WITH HIGH-DIMENSIONAL SYSTEMS

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1807-1823 ◽  
Author(s):  
ADETUNMISE C. DADA ◽  
ERIKA ANDERSSON
Keyword(s):  
Quantum Information ◽  
Information Science ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
High Dimensional ◽  
Separable State ◽  
Local Dimension ◽  
Quantum Information Science ◽  
Fundamental Physics

Quantum correlations resulting in violations of Bell inequalities have generated a lot of interest in quantum information science and fundamental physics. In this paper, we address some questions that become relevant in Bell-type tests involving systems with local dimension greater than 2. For CHSH-Bell tests within 2D subspaces of such high-dimensional systems, it has been suggested that experimental violation of Tsirelson's bound indicates that more than 2D entanglement was present. We explain that the overstepping of Tsirelson's bound is due to violation of fair sampling, and can in general be reproduced by a separable state, if fair sampling is violated. For a class of Bell-type inequalities generalized to d-dimensional systems, we then consider what level of violation is required to guarantee d-dimensional entanglement of the tested state, when fair sampling is satisfied. We find that this can be used as an experimentally feasible test of d-dimensional entanglement for up to quite high values of d.

scholarly journals Quantum Correlations and Bell Inequality Violation under Decoherence

2017 ◽  
Author(s):  
Volkan Erol
Keyword(s):  
Quantum Information ◽  
Quantum Discord ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Noisy Channels ◽  
Phase Damping ◽  
Entanglement Measures ◽  
Information Domain

Quantum Correlations are studied extensively in quantum information domain. Entanglement Measures and Quantum Discord are good examples of these actively studied correlations. Detection of violation in Bell inequalities is also a widely active area in quantum information theory world. In this work, we revisit the problem of analyzing the behavior of quantum correlations and violation of Bell inequalities in noisy channels. We extend the problem defined in [1] by observing the changes in negativity measure, quantum discord and a modified version of Horodecki measure for violation of Bell inequalities under amplitude damping, phase damping and depolarizing channels. We report different interesting results for each of these correlations and measures. All these correlations and measures decrease under decoherence channels, but some changes are very dramatical comparing to others. We investigate also separability conditions of example studied states.

scholarly journals Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures: Studying the limits of monogamy

2021 ◽  
Author(s):  
Marcin Wieśniak
Keyword(s):  
Communication Complexity ◽  
Quantum Communication ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Complexity Reduction ◽  
Main Difficulty ◽  
Quantum Communication Complexity ◽  
Number Of Particles ◽  
Dicke States

Abstract Quantum correlations, in particular those, which enable to violate a Bell inequality 1 , open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles N. In case of Dicke states, we show that persistency can reach 0.482N, significantly more than reported in previous studies.

Secure Cloud Quantum Computing with Verification Based on Quantum Interactive Proof

Impact ◽  
2019 ◽  
Vol 2019 (10) ◽  
pp. 30-32
Author(s):  
Tomoyuki Morimae
Keyword(s):  
Quantum Computing ◽  
Quantum Information ◽  
Theoretical Physics ◽  
View Point ◽  
Research Subjects ◽  
Interactive Proof ◽  
Open Problems ◽  
Main Research ◽  
Proof Systems ◽  
Information Group

In cloud quantum computing, a classical client delegate quantum computing to a remote quantum server. An important property of cloud quantum computing is the verifiability: the client can check the integrity of the server. Whether such a classical verification of quantum computing is possible or not is one of the most important open problems in quantum computing. We tackle this problem from the view point of quantum interactive proof systems. Dr Tomoyuki Morimae is part of the Quantum Information Group at the Yukawa Institute for Theoretical Physics at Kyoto University, Japan. He leads a team which is concerned with two main research subjects: quantum supremacy and the verification of quantum computing.

scholarly journals Cyclic quantum causal models

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jonathan Barrett ◽  
Robin Lorenz ◽  
Ognyan Oreshkov
Keyword(s):  
Causal Reasoning ◽  
Causal Structure ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Causal Models ◽  
Causal Order ◽  
Quantum Processes ◽  
Causal Explanations ◽  
Causal Structures

AbstractCausal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory encompassing quantum systems and gravity is expected to allow causally nonseparable processes featuring operations in indefinite causal order, defying that events be causally ordered at all. The first challenge has been addressed through the recent development of intrinsically quantum causal models, allowing causal explanations of quantum processes – provided they admit a definite causal order, i.e. have an acyclic causal structure. This work addresses causally nonseparable processes and offers a causal perspective on them through extending quantum causal models to cyclic causal structures. Among other applications of the approach, it is shown that all unitarily extendible bipartite processes are causally separable and that for unitary processes, causal nonseparability and cyclicity of their causal structure are equivalent.

scholarly journals Demonstrating the power of quantum computers, certification of highly entangled measurements and scalable quantum nonlocality

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Elisa Bäumer ◽  
Nicolas Gisin ◽  
Armin Tavakoli
Keyword(s):  
Quantum Computer ◽  
Outcome Measurement ◽  
Bell State ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Entanglement Swapping ◽  
Quantum Nonlocality ◽  
Quantum Computers ◽  
Classical Models ◽  
Quantum Phenomena

AbstractIncreasingly sophisticated quantum computers motivate the exploration of their abilities in certifying genuine quantum phenomena. Here, we demonstrate the power of state-of-the-art IBM quantum computers in correlation experiments inspired by quantum networks. Our experiments feature up to 12 qubits and require the implementation of paradigmatic Bell-State Measurements for scalable entanglement-swapping. First, we demonstrate quantum correlations that defy classical models in up to nine-qubit systems while only assuming that the quantum computer operates on qubits. Harvesting these quantum advantages, we are able to certify 82 basis elements as entangled in a 512-outcome measurement. Then, we relax the qubit assumption and consider quantum nonlocality in a scenario with multiple independent entangled states arranged in a star configuration. We report quantum violations of source-independent Bell inequalities for up to ten qubits. Our results demonstrate the ability of quantum computers to outperform classical limitations and certify scalable entangled measurements.

scholarly journals Is Einsteinian no-signalling violated in Bell tests?

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 739-753 ◽  
Author(s):  
Marian Kupczynski
Keyword(s):  
Quantum Electrodynamics ◽  
Probability Distributions ◽  
Selection Procedure ◽  
Quantum Correlations ◽  
Spin Projection ◽  
Marginal Probability ◽  
Strong Correlations ◽  
Relativistic Invariance ◽  
Long Range Correlations ◽  
Apparent Violation

AbstractRelativistic invariance is a physical law verified in several domains of physics. The impossibility of faster than light influences is not questioned by quantum theory. In quantum electrodynamics, in quantum field theory and in the standard model relativistic invariance is incorporated by construction. Quantum mechanics predicts strong long range correlations between outcomes of spin projection measurements performed in distant laboratories. In spite of these strong correlations marginal probability distributions should not depend on what was measured in the other laboratory what is called shortly: non-signalling. In several experiments, performed to test various Bell-type inequalities, some unexplained dependence of empirical marginal probability distributions on distant settings was observed. In this paper we demonstrate how a particular identification and selection procedure of paired distant outcomes is the most probable cause for this apparent violation of no-signalling principle. Thus this unexpected setting dependence does not prove the existence of superluminal influences and Einsteinian no-signalling principle has to be tested differently in dedicated experiments. We propose a detailed protocol telling how such experiments should be designed in order to be conclusive. We also explain how magical quantum correlations may be explained in a locally causal way.

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