Maximally Non-Local and Monogamous Quantum Correlations

Abstract

We introduce a version of the chained Bell inequality for an arbitrary number of measurement outcomes, and use it to give a simple proof that the maximally entangled state of two d dimensional quantum systems has no local component. That is, if we write its quantum correlations as a mixture of local correlations and general (not necessarily quantum) correlations, the coefficient of the local correlations must be zero. This suggests an experimental programme to obtain as good an upper bound as possible on the fraction of local states, and provides a lower bound on the amount of classical communication needed to simulate a maximally entangled state in dxd dimensions. We also prove that the quantum correlations violating the inequality are monogamous among non-signalling correlations, and hence can be used for quantum key distribution secure against post-quantum (but non-signalling) eavesdroppers.

5 pages, no figures

References in corpus (1)

• The Communication Cost of Simulating Bell Correlations

Cited by in corpus (131)

• Quantum entanglement
• Bell nonlocality
• Device-independent quantum key distribution secure against collective attacks
• Bounding the set of quantum correlations
• The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
• Free randomness can be amplified
• Entanglement Certification $-$ From Theory to Experiment
• Private Randomness Expansion With Untrusted Devices
• Certified randomness in quantum physics
• No extension of quantum theory can have improved predictive power
• Measurements in two bases are sufficient for certifying high-dimensional entanglement
• Kochen-Specker Contextuality
• Memory Attacks on Device-Independent Quantum Cryptography
• Are general quantum correlations monogamous?
• The contextual fraction as a measure of contextuality
• Semi-device-independent framework based on natural physical assumptions
• Maximal violation of the CGLMP inequality for infinite dimensional states
• Using complete measurement statistics for optimal device-independent randomness evaluation
• Hidden variable models for quantum theory cannot have any local part
• Quantum Tagging: Authenticating Location via Quantum Information and Relativistic Signalling Constraints
• Limits on non-local correlations from the structure of the local state space
• Bell inequalities tailored to maximally entangled states
• Monogamy of Correlations vs. Monogamy of Entanglement
• Family of Bell-like inequalities as device-independent witnesses for entanglement depth
• A system's wave function is uniquely determined by its underlying physical state
• Unconditionally secure device-independent quantum key distribution with only two devices
• Towards device-independent information processing on general quantum networks
• Fully nonlocal quantum correlations
• Genuine multipartite nonlocality is intrinsic to quantum networks
• Simple Hardy-like proof of quantum contextuality
• Fully nonlocal, monogamous, and random genuinely multipartite quantum correlations
• Experimental fully contextual correlations
• Causal hierarchy of multipartite Bell nonlocality
• Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems
• Full security of quantum key distribution from no-signaling constraints
• Bell tests with min-entropy sources
• Quantum Tasks in Minkowski Space
• Limits of privacy amplification against non-signalling memory attacks
• A framework for the study of symmetric full-correlation Bell-like inequalities
• Computing secure key rates for quantum key distribution with untrusted devices
• Maximal quantum randomness in Bell tests
• Exploring the limits of quantum nonlocality with entangled photons
• On the local and non-local content of bipartite qubit and qutrit correlations
• Device-Independent Relativistic Quantum Bit Commitment
• Multipartite fully-nonlocal quantum states
• The local content of all pure two-qubit states
• Elemental and tight monogamy relations in nonsignalling theories
• Work fluctuations and entanglement in quantum batteries
• An experimental test of all theories with predictive power beyond quantum theory
• Multipartite quantum nonlocality under local decoherence
• Violations of locality and free choice are equivalent resources in Bell experiments
• Stronger steerability criterion for more uncertain continuous variable systems
• Simulation of partial entanglement with nonsignaling resources
• Chained Bell Inequality Experiment with High-Efficiency Measurements
• Bell scenarios with communication
• Quantifying non-classical and beyond-quantum correlations in the unified operator formalism
• 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
• Any Physical Theory of Nature Must Be Boundlessly Multipartite Nonlocal
• Bell inequalities for three systems and arbitrarily many measurement outcomes
• Quantifying Unknown Quantum Entanglement via a Hybrid Quantum-Classical Machine Learning Framework
• Can observed randomness be certified to be fully intrinsic?
• Nonlocality and Entanglement for Symmetric States
• Classical Cost of Transmitting a Qubit
• de Finetti reductions for correlations
• Various quantum nonlocality tests with a simple 2-photon entanglement source
• Self-testing of multipartite GHZ states of arbitrary local dimension with arbitrary number of measurements per party
• Monotones in General Resource Theories
• Activation of monogamy in non-locality using local contextuality
• Graph-theoretic strengths of contextuality
• Detecting nonlocality of noisy multipartite states with the CHSH inequality
• Higher dimensional communication complexity problems: classical protocols vs quantum ones based on Bell's Theorem or prepare-transmit-measure schemes
• Minimum detection efficiency for a loophole-free violation of the Braunstein-Caves chained Bell inequalities
• Bell inequalities tailored to the Greenberger-Horne-Zeilinger states of arbitrary local dimension
• Bell scenarios in which nonlocality and entanglement are inversely related
• Boosting device-independent cryptography with tripartite nonlocality
• Geometric Decompositions of Bell Polytopes with Practical Applications
• Quantum correlations on the no-signaling boundary: self-testing and more
• Non-signaling Causal Hierarchy of General Multisource Networks
• Device and semi-device independent random numbers based on non-inequality paradox
• The non-locality of n noisy Popescu-Rohrlich boxes
• A tight Tsirelson inequality for infinitely many outcomes
• Robust certification of arbitrary outcome quantum measurements from temporal correlations
• Quantum Information Processing with Adversarial Devices
• The future of secure communications: device independence in quantum key distribution
• Overcoming Noise Limitations in QKD with Quantum Privacy Amplification
• The local content of bipartite qubit correlations
• Equivalence between face nonsignaling correlations, full nonlocality, all-versus-nothing proofs, and pseudotelepathy
• Two Copies of the Einstein-Podolsky-Rosen State of Light Lead to Refutation of EPR Ideas
• Anomalies of weight-based coherence measure and mixed maximally coherent states
• Measurable criteria of generalized non-locality under the correlation symmetry
• Measurement-device-independent quantification of irreducible high-dimensional entanglement
• An impossibility theorem for Parameter Independent hidden variable theories
• Distance-based resource quantification for sets of quantum measurements
• Test to separate quantum theory from non-signaling theories
• Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing
• Secure positioning and non-local correlations
• Continuous-variable supraquantum nonlocality
• Maximal Non-Classicality in Multi-Setting Bell Inequalities
• Corrected Bell and Noncontextuality Inequalities for Realistic Experiments
• Geometric chained inequalities for higher-dimensional systems
• Quantum non-locality, causality and mistrustful cryptography
• Deriving Bell's nonlocality from nonlocality at detection
• Unmasking the Polygamous Nature of Quantum Nonlocality
• Extending quantum mechanics entails extending special relativity
• On optimal entanglement assisted one-shot classical communication
• Self-testing quantum systems of arbitrary local dimension with minimal number of measurements
• The minimal communication cost for simulating entangled qubits
• Bell Nonlocality in Classical Systems Coexisting with other System Types
• Simple and tight monogamy relations for a class of Bell inequalities
• Completely real? A critical note on the claims by Colbeck and Renner
• Necessary and Sufficient Condition for Randomness Certification from Incompatibility
• Relativistic Causality vs. No-Signaling as the limiting paradigm for correlations in physical theories
• Quantifying the randomness of copies of noisy Popescu-Rohrlich correlations
• Possibilistic and maximal indefinite causal order in the quantum switch
• Secure and Robust Transmission and Verification of Unknown Quantum States in Minkowski Space
• Bound on Bell Inequalities by Fraction of Determinism and Reverse Triangle Inequality
• Epistemic Boundaries and Quantum Uncertainty: What Local Observers Can (Not) Predict
• All genuinely entangled stabilizer subspaces are multipartite fully nonlocal
• Classical simulation of two spin-$S$ singlet state correlations involving spin measurements
• A counter-argument to "Hidden variable models for quantum theory cannot have any local part" arXiv:0801.2218
• Quantum Zeno Effect on Genuine Tripartite Nonlocality and Entanglement in Quantum Dissipative System
• Local correlations of mixed two-qubit states
• Trading symmetry for Hilbert-space dimension in Bell-inequality violation
• Comparing the cost of violating causal assumptions in Bell experiments: locality, free choice and arrow-of-time
• The Interplay between Quantum Contextuality and Wigner Negativity
• Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategies
• Hidden variable models for entanglements can or cannot have a local component?
• Nonlocality at detection and conservation of energy. Was Einstein looking for an "epistemic" interpretation, a "superdeterministic" one, or both?
• Local and Nonlocal Contents in N-qubit generalized GHZ states
• A Classification Program for Nonlocality Paradoxes of Three Qubits