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 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 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.

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 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 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 Robust Bell inequalities from communication complexity

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 72 ◽  
Author(s):  
Sophie Laplante ◽  
Mathieu Laurière ◽  
Alexandre Nolin ◽  
Jérémie Roland ◽  
Gabriel Senno
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Communication Complexity ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Local Distribution ◽  
Classical Communication ◽  
Quantum Communication Complexity ◽  
Complexity Lower Bounds ◽  
Quantum Distributions

The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say that a Bell inequality is normalized if its absolute value does not exceed 1 for any classical (i.e. local) distribution. Upper and (almost) tight lower bounds have been given for the quantum violation of these Bell inequalities in terms of number of outputs of the distribution, number of inputs, and the dimension of the shared quantum states. In this work, we revisit normalized Bell inequalities together with another family: inefficiency-resistant Bell inequalities. To be inefficiency-resistant, the Bell value must not exceed 1 for any local distribution, including those that can abort. This makes the Bell inequality resistant to the detection loophole, while a normalized Bell inequality is resistant to general local noise. Both these families of Bell inequalities are closely related to communication complexity lower bounds. We show how to derive large violations from any gap between classical and quantum communication complexity, provided the lower bound on classical communication is proven using these lower bound techniques. This leads to inefficiency-resistant violations that can be exponential in the size of the inputs. Finally, we study resistance to noise and inefficiency for these Bell inequalities.

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.

A qutrit quantum key distribution protocol using Bell inequalities with larger violation capabilities

2015 ◽  
Vol 15 (15&16) ◽  
pp. 1295-1306
Author(s):  
Zoe Amblard ◽  
Francois Arnault
Keyword(s):  
Quantum Key Distribution ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Key Distribution ◽  
Trojan Horse ◽  
Noise Resistance ◽  
The One ◽  
Trojan Horse Attack ◽  
Quantum Key Distribution Protocol

The Ekert quantum key distribution protocol [1] uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The 3DEB protocol [2] uses instead pairs of entangled qutrits to achieve better noise resistance than the Ekert protocol. It performs checks based on a Bell inequality for qutrits named CHSH-3 and found in [3, 4]. In this paper, we present a new protocol, which also uses pairs of entangled qutrits, but gaining advantage of a Bell inequality which achieves better noise resistance than the one used in 3DEB. The latter inequality is called here hCHSH-3 and was discovered in [5]. For each party, the hCHSH-3 inequality involves four observables already used in CHSH-3 but also two products of observables which do not commute. We explain how the parties can measure the observables corresponding to these products and thus are able to check the violation of hCHSH-3. In the presence of noise, this violation guarantees the security against a local Trojan horse attack. We also designed a version of our protocol which is secure against individual attacks.

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