Chained Bell Inequalities

1989 ◽  
pp. 27-36
Author(s):  
Samuel L. Braunstein ◽  
Carlton M. Caves
Keyword(s):  
Bell Inequalities

scholarly journals Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

2021 ◽  
Vol 7 (7) ◽  
pp. eabc3847
Author(s):  
Armin Tavakoli ◽  
Máté Farkas ◽  
Denis Rosset ◽  
Jean-Daniel Bancal ◽  
Jedrzej Kaniewski
Keyword(s):  
Quantum Key Distribution ◽  
Random Number ◽  
Random Number Generation ◽  
Bell Inequalities ◽  
Extremal Point ◽  
Optimal Rate ◽  
Quantum Nonlocality ◽  
Space Structures ◽  
Mutually Unbiased Bases ◽  
Practical Relevance

Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by (i) introducing families of Bell inequalities that are maximally violated by d-dimensional MUBs and SICs, respectively, (ii) proving device-independent certification of natural operational notions of MUBs and SICs, and (iii) using MUBs and SICs to develop optimal-rate and nearly optimal-rate protocols for device-independent quantum key distribution and device-independent quantum random number generation, respectively. Moreover, we also present the first example of an extremal point of the quantum set of correlations that admits physically inequivalent quantum realizations. Our results elaborately demonstrate the foundational and practical relevance of the two most important discrete Hilbert space structures to the field of quantum nonlocality.

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.

Bell inequalities for entangled qubits: Quantitative tests of quantum character and nonlocality on quantum computers

2020 ◽  
Author(s):  
David Z Wang ◽  
Aidan Q Gauthier ◽  
Ashley E Siegmund ◽  
Katharine Clarke Hunt
Keyword(s):  
Bell Inequalities ◽  
Bell States ◽  
Quantum Computers

This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM’s publicly accessible quantum computers. Violations of the 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.

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 A nonlocal game for witnessing quantum networks

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Ming-Xing Luo
Keyword(s):  
Computational Complexity ◽  
Main Idea ◽  
Bell Inequalities ◽  
Theoretical Computer Science ◽  
Graph Representation ◽  
Necessary Condition ◽  
Quantum Networks ◽  
Theoretical Computer ◽  
Sufficient And Necessary Condition ◽  
Unified Method

Abstract Nonlocal game as a witness of the nonlocality of entanglement is of fundamental importance in various fields. The well-known nonlocal games or equivalent linear Bell inequalities are only useful for Bell networks consisting of single entanglement. Our goal in this paper is to propose a unified method for constructing cooperating games in network scenarios. We propose an efficient method to construct multipartite nonlocal games from any graphs. The main idea is the graph representation of entanglement-based quantum networks. We further specify these graphic games with quantum advantages by providing a simple sufficient and necessary condition. The graphic games imply a linear Bell testing of the nonlocality of general quantum networks consisting of EPR states. It also allows generating new instances going beyond CHSH game. These results have interesting applications in quantum networks, Bell theory, computational complexity, and theoretical computer science.

scholarly journals What If Quantum Theory Violates All Mathematics?

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 598-602
Author(s):  
Elemér Elad Rosinger
Keyword(s):  
Mathematical Logic ◽  
Quantum Theory ◽  
Bell Inequalities ◽  
List Type ◽  
Elementary Argument ◽  
And Mathematics

Abstract It is shown by using a rather elementary argument in Mathematical Logic that if indeed, quantum theory does violate the famous Bell Inequalities, then quantum theory must inevitably also violate all valid mathematical statements, and in particular, such basic algebraic relations like 0 = 0, 1 = 1, 2 = 2, 3 = 3, … and so on … An interest in that result is due to the following three alternatives which it imposes upon both Physics and Mathematics: Quantum Theory is inconsistent. Quantum Theory together with Mathematics are inconsistent. Mathematics is inconsistent. In this regard one should recall that, up until now, it is not known whether Mathematics is indeed consistent.

The classification of two-particle spin states and generalized Bell inequalities

2001 ◽  
Vol 281 (5-6) ◽  
pp. 278-288 ◽  
Author(s):  
V.A. Andreev ◽  
V.I. Man'ko
Keyword(s):  
Bell Inequalities ◽  
Spin States ◽  
Particle Spin
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