Bounding the set of quantum correlations

Abstract

We introduce a hierarchy of conditions necessarily satisfied by any distribution P(ab) representing the probabilities for two separate observers to obtain outcomes a and b when making local measurements on a shared quantum state. Each condition in this hierarchy is formulated as a semidefinite program. Our approach can be used to obtain upper-bounds on the quantum violation of an arbitrary Bell inequality. It yields, for instance, tight bounds for the violations of the Collins et al. inequalities.

5 pages, no figures. v2: minor modifications

References in corpus (7)

• Bell inequalities for arbitrarily high dimensional systems
• No Signalling and Quantum Key Distribution
• Quantum non-locality in two three-level systems
• Maximally Non-Local and Monogamous Quantum Correlations
• Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities
• Efficient quantum key distribution secure against no-signalling eavesdroppers
• Causality and Cirel'son bounds

Cited by in corpus (354)

• Bell nonlocality
• Advances in Quantum Cryptography
• Random Numbers Certified by Bell's Theorem
• Multidimensional quantum entanglement with large-scale integrated optics
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Non-locality and Communication Complexity
• Quantum Steering
• Secure device-independent quantum key distribution with causally independent measurement devices
• The uncertainty principle determines the non-locality of quantum mechanics
• Self-testing of quantum systems: a review
• Graph-Theoretic Approach to Quantum Correlations
• Testing the Hilbert space dimension
• Certified randomness in quantum physics
• Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and Complementarity (PLUS AN ERRATUM)
• Device-independent witnesses of genuine multipartite entanglement
• Quantum theory based on real numbers can be experimentally falsified
• A glance beyond the quantum model
• Local orthogonality as a multipartite principle for quantum correlations
• A strong no-go theorem on the Wigner's friend paradox
• Bell nonlocality in networks
• Monogamy of nonlocal quantum correlations
• Detection of entanglement in asymmetric quantum networks and multipartite quantum steering
• Kochen-Specker Contextuality
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Device-independent entanglement quantification and related applications
• Connes' embedding problem and Tsirelson's problem
• A Combinatorial Approach to Nonlocality and Contextuality
• Simple explanation of the quantum violation of a fundamental inequality
• Security of practical private randomness generation
• Detecting genuine multipartite quantum non-locality -- a simple approach and generalization to arbitrary dimension
• Maximal violation of the I3322 inequality using infinite dimensional quantum systems
• All noncontextuality inequalities for the n-cycle scenario
• Information-Theoretic Implications of Quantum Causal Structures
• Quantum Conference Key Agreement: A Review
• A lower bound on the dimension of a quantum system given measured data
• Large violation of Bell inequalities with low entanglement
• Generalized Probability Theories: What determines the structure of quantum theory?
• More Randomness from the Same Data
• Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
• More efficient Bell inequalities for Werner states
• Polynomial Bell inequalities
• Optimal randomness certification from one entangled bit
• Convergent relaxations of polynomial optimization problems with non-commuting variables
• Temporal quantum correlations and Leggett-Garg inequalities in multi-level systems
• Robust and versatile black-box certification of quantum devices
• Photonic verification of device-independent quantum key distribution against collective attacks
• Physical characterization of quantum devices from nonlocal correlations
• Non-locality distillation and post-quantum theories with trivial communication complexity
• Testing real quantum theory in an optical quantum network
• Recovering part of the quantum boundary from information causality
• Semi-device-independent framework based on natural physical assumptions
• Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
• Using complete measurement statistics for optimal device-independent randomness evaluation
• Evaluation of convex roof entanglement measures
• Security and Composability of Randomness Expansion from Bell Inequalities
• Bounding temporal quantum correlations
• Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing
• Bounding the set of finite dimensional quantum correlations
• Limits on non-local correlations from the structure of the local state space
• Bell inequalities tailored to maximally entangled states
• All the self-testings of the singlet for two binary measurements
• Quantum Bounds on Bell inequalities
• Self-testing protocols based on the chained Bell inequalities
• Family of Bell-like inequalities as device-independent witnesses for entanglement depth
• Device-independent parallel self-testing of two singlets
• Semi-device-independent bounds on entanglement
• Robust self testing of the 3-qubit $W$ state
• Unified Framework for Correlations in Terms of Local Quantum Observables
• Closed sets of non-local correlations
• Looking for symmetric Bell inequalities
• Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
• Nonlocality and conflicting interest games
• Characterising the correlations of prepare-and-measure quantum networks
• Machine learning non-local correlations
• Device-independent quantum key distribution with single-photon sources
• Device-independent tomography of multipartite quantum states
• Detection Loophole in Bell experiments: How post-selected local correlations can look non-local
• Semidefinite tests for quantum network topologies
• Security of device-independent quantum key distribution protocols: a review
• Self-testing through EPR-steering
• More non-locality with less entanglement
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• Reexamination of a multisetting Bell inequality for qudits
• Macroscopically local correlations can violate information causality
• Device-independent quantum key distribution with random postselection
• Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
• Bounds on Quantum Correlations in Bell Inequality Experiments
• Causal hierarchy of multipartite Bell nonlocality
• Tripartite quantum state violating the hidden influence constraints
• Device-independent point estimation from finite data and its application to device-independent property estimation
• Bounding the sets of classical and quantum correlations in networks
• Semidefinite programming relaxations for quantum correlations
• Device-independent quantum key distribution secure against adversaries with no long-term quantum memory
• Efficiency of higher dimensional Hilbert spaces for the violation of Bell inequalities
• Quantifying Bell non-locality with the trace distance
• Witnessing irreducible dimension
• Device-Independent Certification of a Nonprojective Qubit Measurement
• Identifying Nonconvexity in the Sets of Limited-Dimension Quantum Correlations
• A two-qubit Bell inequality for which POVM measurements are relevant
• Device-Independent Randomness Generation in the Presence of Weak Cross-Talk
• Device-Independent Quantum Key Distribution with Commuting Measurements
• Towards a realization of device-independent quantum key distribution
• Maximally nonlocal theories cannot be maximally random
• A framework for the study of symmetric full-correlation Bell-like inequalities
• A framework for quantum-secure device-independent randomness expansion
• Characterizing finite-dimensional quantum behavior
• A physical approach to Tsirelson's problem
• Maximal quantum randomness in Bell tests
• Device-Independent Secret Sharing and a Stronger Form of Bell Nonlocality
• Robustness of quantum randomness expansion protocols in the presence of noise
• Exploring the Local Orthogonality Principle
• Measurement-device-independent entanglement and randomness estimation in quantum networks
• Tsirelson's Problem
• Efficient device-independent entanglement detection for multipartite systems
• Generating high-order quantum exceptional points in synthetic dimensions
• The Smooth Entropy Formalism for von Neumann Algebras
• Characterization of quantum correlations with local dimension constraints and its device-independent applications
• Correlations in entanglement-assisted prepare-and-measure scenarios
• Maximum nonlocality in the (3,2,2) scenario
• Experimental nonlocality-based randomness generation with non-projective measurements
• A Genuine Multipartite Bell Inequality for Device-independent Conference Key Agreement
• Spatial versus Sequential Correlations for Random Access Coding
• How device-independent approaches change the meaning of physical theory
• Necessary and sufficient condition for contextuality from incompatibility
• Concentration phenomena in the geometry of Bell correlations
• Elemental and tight monogamy relations in nonsignalling theories
• Bounding sets of sequential quantum correlations and device-independent randomness certification
• Device-independent lower bounds on the conditional von Neumann entropy
• Information Causality and Extremal Tripartite Correlations
• Provably-secure quantum randomness expansion with uncharacterised homodyne detection
• Generalized Clauser-Horne-Shimony-Holt inequalities maximally violated by higher dimensional systems
• Qutrit witness from the Grothendieck constant of order four
• Quantum violations in the Instrumental scenario and their relations to the Bell scenario
• Closed sets of correlations: answers from the zoo
• Monotone Measures for Non-Local Correlations
• Quantum Bilinear Optimization
• Quantifying causal influences in the presence of a quantum common cause
• Optimization of device-independent witnesses of entanglement depth from two-body correlators
• Experimental multipartite entanglement and randomness certification of the W state in the quantum steering scenario
• Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems
• Bell inequalities violated using detectors of low efficiency
• Robust self-testing of steerable quantum assemblages and its applications on device-independent quantum certification
• Experimental robust self-testing of the state generated by a quantum network
• Bell scenarios with communication
• Quantum correlations are stronger than all nonsignaling correlations produced by n-outcome measurements
• Multigraph approach to quantum non-locality
• Covariance Bell inequalities
• Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise
• Randomness versus nonlocality in the Mermin-Bell experiment with three parties
• Semi-definite programming and quantum information
• Exponentially decreasing critical detection efficiency for any Bell inequality
• Maximally entangled mixed states for qubit-qutrit systems
• A weak form of self-testing
• Properties of dimension witnesses and their semi-definite programming relaxations
• Maximum nonlocality and minimum uncertainty using magic states
• Bell inequalities for three systems and arbitrarily many measurement outcomes
• Locality, detection efficiencies, and probability polytopes
• Extended nonlocal games and monogamy-of-entanglement games
• Postquantum common-cause channels: the resource theory of local operations and shared entanglement
• Entropy bounds for multiparty device-independent cryptography
• Geometry of the quantum set on no-signaling faces
• Coherence and contextuality in a Mach-Zehnder interferometer
• Device-Independent Quantum Key Distribution Based on the Mermin-Peres Magic Square Game
• A histories perspective on characterising quantum non-locality
• Randomness in post-selected events
• Quantum communication complexity beyond Bell nonlocality
• Does violation of a Bell inequality always imply quantum advantage in a communication complexity problem?
• Quantum Randomness Generation by Probability Estimation with Classical Side Information
• New Quantum Bounds for Inequalities involving Marginal Expectations
• Bell nonlocality with a single shot
• Nonlocality and Entanglement for Symmetric States
• Lower Bounding Ground-State Energies of Local Hamiltonians Through the Renormalization Group
• Bipartite post-quantum steering in generalised scenarios
• The Platonic solids and fundamental tests of quantum mechanics
• Designing Bell inequalities from a Tsirelson bound
• Macroscopic non-contextuality as a principle for Almost Quantum Correlations
• Bell Inequalities with Communication Assistance
• Device-Independent Bit Commitment based on the CHSH Inequality
• Quantum Bell Inequalities from Macroscopic Locality
• Quantum-Inspired Hierarchy for Rank-Constrained Optimization
• Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
• Are problems in Quantum Information Theory (un)decidable?
• A geometric comparison of entanglement and quantum nonlocality in discrete systems
• Bounding and simulating contextual correlations in quantum theory
• Experimental hierarchy of two-qubit quantum correlations without state tomography
• Device-independent quantification of measurement incompatibility
• The Magical Number Seven: An Unexpected Dimensional Threshold in Quantum Communication Complexity
• Device Independent Quantum Key Distribution with realistic single-photon source implementations
• Concavity of the quantum body for any given dimension
• Bounding the plausibility of physical theories in a device-independent setting via hypothesis testing
• Bell inequalities tailored to the Greenberger-Horne-Zeilinger states of arbitrary local dimension
• Device-Independent Quantum Key Distribution Based on Routed Bell Tests
• Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations
• Entanglement verification with detection-efficiency mismatch
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios
• Inflation: a Python library for classical and quantum causal compatibility
• Optimal violation of Leggett-Garg inequality for arbitrary spin and emergence of classicality through unsharp measurement
• Device-independent certification of tensor products of quantum states using single-copy self-testing protocols
• Cryptography in a Quantum World
• Bounding the amount of entanglement from witness operators
• Custom Bell inequalities from formal sums of squares
• Distilling Nonlocality in Quantum Correlations
• A convergent inflation hierarchy for quantum causal structures
• Device-independent bounds from Cabello's nonlocality argument
• Hierarchy of efficiently computable and faithful lower bounds to quantum discord
• Multipartite Nonlocality as a Resource and Quantum Correlations Having Indefinite Causal Order
• Proposed experiment to test fundamentally binary theories
• Simple conditions constraining the set of quantum correlations
• Information Causality without concatenation
• Maximal Violation of a Broad Class of Bell Inequalities and Its Implications on Self-Testing
• A paradox in bosonic energy computations via semidefinite programming relaxations
• Quantum Probability Estimation for Randomness with Quantum Side Information
• RepLAB: a computational/numerical approach to representation theory
• Almost quantum correlations and their refinements in a tripartite Bell scenario
• Non-Local Network Coding in Interference Channels
• Necessary and sufficient criterion for extremal quantum correlations in the simplest Bell scenario
• The future of secure communications: device independence in quantum key distribution
• The resource theory of nonclassicality of channel assemblages
• Avenues to generalising Bell inequalities
• Adaptive advantage in entanglement-assisted communications
• Certifying long-range quantum correlations through routed Bell tests
• Device-Independent Bounds on Detection Efficiency
• Three numerical approaches to find mutually unbiased bases using Bell inequalities
• Certified randomness in tight space
• Maximizing device-independent randomness from a Bell experiment by optimizing the measurement settings
• Optimal randomness generation from optical Bell experiments
• Nonlocality Distillation and Quantum Voids
• More non-locality in the three-qubit Greenberger-Horne-Zeilinger state
• Certificates of quantum many-body properties assisted by machine learning
• Entangled games are hard to approximate
• Naturally restricted subsets of nonsignaling correlations: typicality and convergence
• Proposals for ruling out the real quantum theories in an entanglement-swapping quantum network with causally independent sources
• Optimal and tight Bell inequalities for state-independent contextuality sets
• Probabilistic models on contextuality scenarios
• Experimental Test of Nonlocality Limits from Relativistic Independence
• A Survey of Physical Principles Attempting to Define Quantum Mechanics
• Authenticated teleportation with one-sided trust
• Generalizing optimal Bell inequalities
• Geometrical self-testing of partially entangled two-qubit states
• Semi-device-independently characterizing quantum temporal correlations
• Positive univariate trace polynomials
• Tight upper bound of the maximal quantum violation of Gisin's elegant Bell inequality and its application in randomness certification
• Connector tensor networks: a renormalization-type approach to quantum certification
• Prepare-and-measure scenarios with photon-number constraints
• Generalizations of Boxworld
• Quantifying the intrinsic randomness in sequential measurements
• Device-independent quantum key distribution based on measurement inputs
• Better Bell inequalities (passion at a distance)
• Local Orthogonality provides better upper bound for Hardy's nonlocality
• Cryptographic Quantum Bound on Nonlocality
• Entangled Rendezvous: A Possible Application of Bell Non-Locality For Mobile Agents on Networks
• Deciding the existence of perfect entangled strategies for nonlocal games
• SymDPoly: symmetry-adapted moment relaxations for noncommutative polynomial optimization
• Certifying steady-state properties of open quantum systems
• Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario
• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Interplay among entanglement, measurement incompatibility, and nonlocality
• Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks
• Semidefinite Programs at Finite Fermion Density
• Quantum realism and quantum surrealism
• Quantum Magic Rectangles: Characterization and Application to Certified Randomness Expansion
• Bell inequalities for nonlocality depth
• Information causality as a tool for bounding the set of quantum correlations
• Secure and robust randomness with sequential quantum measurements
• Self-testing tilted strategies for maximal loophole-free nonlocality
• Randomness versus Nonlocality in Multi-input and Multi-output Quantum Scenario
• Generalized measurements on qubits in quantum randomness certification and expansion
• Quantum sets of the multicolored-graph approach to contextuality
• Imprecision plateaus in quantum steering
• On characterising assemblages in Einstein-Podolsky-Rosen scenarios
• The relation between Hardy's non-locality and violation of Bell inequality
• Quantum Strategies for Rendezvous and Domination Tasks on Graphs with Mobile Agents
• Tsirelson Polytopes and Randomness Generation
• Bell non-locality using tensor networks and sparse recovery
• Variational Optimization for Quantum Problems using Deep Generative Networks
• Quantum Information Theory and Free Semialgebraic Geometry: One Wonderland Through Two Looking Glasses
• Macroscopic locality with equal bias reproduces with high fidelity a quantum distribution achieving the Tsirelson's bound
• Unique Games with Entangled Provers are Easy
• Quasi-polynomial time algorithms for free quantum games in bounded dimension
• Quantum correlations with a gap between the sequential and spatial cases
• Experimental Detection of Non-local Correlations using a Local Measurement-Based Hierarchy on an NMR Quantum Processor
• Testing microscopic discretization
• Fast semidefinite programming with feedforward neural networks
• Ex ante versus ex post equilibria in classical Bayesian games with a nonlocal resource
• Tsirelson bounds for quantum correlations with indefinite causal order
• Analytic Semi-device-independent Entanglement Quantification for Bipartite Quantum States
• Quantum value for a family of $I_{3322}$-like Bell functionals
• Extremal Tsirelson inequalities
• Computability limits non-local correlations
• Experimental demonstration of the violation of the temporal Peres-Mermin inequality using contextual temporal correlations and noninvasive measurements
• Multistage games and Bell scenarios with communication
• Classification of no-signaling correlations and the guess your neighbor's input game
• Monogamy of Nonlocal Games
• Optimal single-shot discrimination of optical modes
• Tight Bell inequalities from polytope slices
• Quantum Bell inequalities from Information Causality -- tight for Macroscopic Locality
• Complexity lower bounds for computing the approximately-commuting operator value of non-local games to high precision
• The quantum moment problem and bounds on entangled multi-prover games
• General tradeoff relations of quantum nonlocality in the Clauser-Horne-Shimony-Holt scenario
• Postquantum steering
• Cost of Locally Approximating High-Dimensional Ground States of Contextual Quantum Models
• Optimisation of time-ordered processes in the finite and asymptotic regime
• Error-free interconversion of nonlocal boxes
• Correlations, Bell Inequality Violation & Quantum Entanglement
• Device-independent secret key rates via a post-selected Bell inequality
• Hardy-type paradoxes for an arbitrary symmetric bipartite Bell scenario
• Device-independent certification of desirable properties with a confidence interval
• Quantum bounds for compiled XOR games and $d$-outcome CHSH games
• Practical parallel self-testing of Bell states via magic rectangles
• Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities
• Regularising data for practical randomness generation
• Quantum correlations cannot be reproduced with a finite number of measurements in any no-signaling theory
• Finding optimal Bell inequalities using the cone-projection technique
• Quantum bounds and device-independent security with rank-one qubit measurements
• Candidate entanglement invariants for two Dirac spinors
• Quantifying Multipartite Quantum Entanglement in a Semi-Device-Independent Manner
• Certifying Temporal Correlations
• Experimental self-testing of entangled states
• Device-independent Shannon entropy certification
• Mapping Phase Diagrams of Quantum Spin Systems through Semidefinite-Programming Relaxations
• Genuine multipartite entanglement is not necessary for standard device-independent conference key agreement
• Quantum Key Distribution with Imperfections: Recent Advances in Security Proofs
• Parallel remote state preparation for fully device-independent verifiable blind quantum computation
• SOS decomposition for general Bell inequalities in two qubits systems and its application to quantum randomness
• Low degree Lorentz invariant polynomials as potential entanglement invariants for multiple Dirac spinors
• Guarantees on the structure of experimental quantum networks
• A principle of quantumness
• Extended Nonlocal Games
• Quantum advantage for distributed computing without communication
• (Almost-)Quantum Bell Inequalities and Device-Independent Applications
• Signaling between time steps does not allow for nonlocality beyond hidden nonlocality
• Ruling Out Static Latent Homophily in Citation Networks
• Expanding bipartite Bell inequalities for maximum multi-partite randomness
• Partial ignorance communication tasks in quantum theory
• Quantum Optimal Control via Magnus Expansion and Non-Commutative Polynomial Optimization
• Tight and self-testing multipartite quantum Bell inequalities from the renormalization group
• Indefinite global time
• Interactive proofs with approximately commuting provers
• Testing Information Causality for General Quantum Communication Protocols
• Device-independent secure correlations in sequential quantum scenarios
• Entanglement Detection Beyond Local Bound with Coarse Calibrated measurements
• Quantitative and Optimal Device-Independent Lower Bounds on Detection Efficiency
• Trading symmetry for Hilbert-space dimension in Bell-inequality violation
• Computational Perspectives on Bell Inequalities and Many-body Quantum Correlations
• A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios
• Characterization of non-signaling correlations from mutual information
• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor
• Lossy-and-Constrained Extended Non-Local Games with Applications to Quantum Cryptography
• NPA Hierarchy and Extremal Criterion in the Simplest Bell Scenario
• Non-Locality Distillation is Impossible for Isotropic Quantum Systems
• Quantum description of reality is epistemically incomplete
• Device-independent quantum key distribution
• Platonic Bell inequalities for all dimensions
• The Interplay between Quantum Contextuality and Wigner Negativity