scholarly journals Violation of all two-party facet Bell inequalities by almost-quantum correlations

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Ravishankar Ramanathan
Keyword(s):  
Bell Inequalities ◽  
Quantum Correlations

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 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 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 correlations are weaved by the spinors of the Euclidean primitives

2018 ◽  
Vol 5 (5) ◽  
pp. 180526 ◽  
Author(s):  
Joy Christian
Keyword(s):  
Conformal Geometry ◽  
General Theorem ◽  
Three Dimensional ◽  
Physical Space ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Theoretical Physics ◽  
Strong Correlations ◽  
Algebraic Representation ◽  
Closed Set

The exceptional Lie group E 8 plays a prominent role in both mathematics and theoretical physics. It is the largest symmetry group associated with the most general possible normed division algebra, namely, that of the non-associative real octonions, which—thanks to their non-associativity—form the only possible closed set of spinors (or rotors) that can parallelize the 7-sphere. By contrast, here we show how a similar 7-sphere also arises naturally from the algebraic interplay of the graded Euclidean primitives, such as points, lines, planes and volumes, which characterize the three-dimensional conformal geometry of the ambient physical space, set within its eight-dimensional Clifford-algebraic representation. Remarkably, the resulting algebra remains associative, and allows us to understand the origins and strengths of all quantum correlations locally, in terms of the geometry of the compactified physical space, namely, that of a quaternionic 3-sphere, S 3 , with S 7 being its algebraic representation space. Every quantum correlation can thus be understood as a correlation among a set of points of this S 7 , computed using manifestly local spinors within S 3 , thereby extending the stringent bounds of ±2 set by Bell inequalities to the bounds of ± 2 2 on the strengths of all possible strong correlations, in the same quantitatively precise manner as that predicted within quantum mechanics. The resulting geometrical framework thus overcomes Bell’s theorem by producing a strictly deterministic and realistic framework that allows a locally causal understanding of all quantum correlations, without requiring either remote contextuality or backward causation. We demonstrate this by first proving a general theorem concerning the geometrical origins of the correlations predicted by arbitrarily entangled quantum states, and then reproducing the correlations predicted by the EPR-Bohm and the GHZ states. The raison d’être of strong correlations turns out to be the Möbius-like twists in the Hopf bundles of S 3 and S 7 .

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.

Multipartite quantum correlations in the extended J1–J2 Heisenberg model

2017 ◽  
Vol 31 (28) ◽  
pp. 1750206
Author(s):  
J. Batle ◽  
O. Tarawneh ◽  
Koji Nagata ◽  
Tadao Nakamura ◽  
S. Abdalla ◽  
...  
Keyword(s):  
Heisenberg Model ◽  
Nearest Neighbors ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Multipartite Entanglement ◽  
Spin Interaction ◽  
Zero Temperature ◽  
Quantum Annealing

Multipartite entanglement and the maximum violation of Bell inequalities are studied in finite clusters of spins in an extended J1–J2 Heisenberg model at zero temperature. The ensuing highly frustrated states will unveil a rich structure for different values of the corresponding spin–spin interaction strengths. The interplay between nearest-neighbors, next-nearest neighbors and further couplings will be explored using multipartite correlations. The model is relevant to certain quantum annealing computation architectures where an all-to-all connectivity is considered.

scholarly journals Quantum Bounds on Detector Efficiencies for Violating Bell Inequalities Using Semidefinite Programming

Cryptography ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 2
Author(s):  
Alexander Sauer ◽  
Gernot Alber
Keyword(s):  
Quantum Information ◽  
Quantum Key Distribution ◽  
Quantum Information Processing ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Quantum Nonlocality ◽  
Semidefinite Programs ◽  
Dark Counts ◽  
Optimal Inequality ◽  
Detector Model

Loophole-free violations of Bell inequalities are crucial for fundamental tests of quantum nonlocality. They are also important for future applications in quantum information processing, such as device-independent quantum key distribution. Based on a detector model which includes detector inefficiencies and dark counts, we estimate the minimal requirements on detectors needed for performing loophole-free bipartite and tripartite Bell tests. Our numerical investigation is based on a hierarchy of semidefinite programs for characterizing possible quantum correlations. We find that for bipartite setups with two measurement choices and our detector model, the optimal inequality for a Bell test is equivalent to the Clauser–Horne inequality.

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 Quantum violations in the Instrumental scenario and their relations to the Bell scenario

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 186 ◽  
Author(s):  
Thomas Van Himbeeck ◽  
Jonatan Bohr Brask ◽  
Stefano Pironio ◽  
Ravishankar Ramanathan ◽  
Ana Belén Sainz ◽  
...  
Keyword(s):  
Opposite Direction ◽  
Causal Structure ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Causal Models ◽  
Classical Quantum ◽  
Bell Nonlocality ◽  
Causal Structures

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.

Sign in / Sign up

Export Citation Format

Share Document