Monogamy of nonlocal quantum correlations

Abstract

We describe a new technique for obtaining Tsirelson bounds, or upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signaling, we obtain a Tsirelson bound by maximizing over all no-signaling probability distributions. This maximization can be cast as a linear program. 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 CHSH 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.

This is the submitted version. The refereed version, which contains an additional result about strong parallel repetition and corrects some typos, is available on my personal web site at http://bentoner.com/papers/monogamyrs.pdf [PDF]

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• General properties of Nonsignaling Theories
• Quantum Communication between N partners and Bell's inequalities
• Local Hidden Variable Theories for Quantum States
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• Monogamy of Bell's inequality violations in non-signaling theories
• Correlation complementarity yields Bell monogamy relations
• Three-observer Bell inequality violation on a two-qubit entangled state
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• Security of device-independent quantum key distribution protocols: a review
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• Nonlocality and entanglement in qubit systems
• Detecting faked continuous variable entanglement using one-sided device-independent entanglement witnesses
• Tripartite quantum state violating the hidden influence constraints
• Laws of Nature as Constraints
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• Volume monogamy of quantum steering ellipsoids for multi-qubit systems
• Multipartite Entanglement Measure and Complete Monogamy Relation
• Understanding nature from experimental observations: a theory independent test for gravitational decoherence
• Observation of nonlocality sharing via not-so-weak measurements
• Nonlocality is transitive
• Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture
• Quantum Proofs
• Elemental and tight monogamy relations in nonsignalling theories
• Quantifying multipartite nonlocality via the size of the resource
• Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement
• Quantum correlations as probes of chaos and ergodicity
• Shareability of Quantum Steering and its Relation with Entanglement
• Distribution of entanglement and correlations in all finite dimensions
• Full multipartite steering inseparability, genuine multipartite steering and monogamy for continuous variable systems
• Finite de Finetti theorem for conditional probability distributions describing physical theories
• Spectrum conditions for symmetric extendible states
• Strong monogamies of no-signaling violations for bipartite correlation Bell inequalities
• Theoretical description and experimental simulation of quantum entanglement near open time-like curves via pseudo-density operators
• Exponentially many entanglement and correlation constraints for multipartite quantum states
• Nonlocality and Entanglement for Symmetric States
• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Activation of monogamy in non-locality using local contextuality
• Conditions for monogamy of quantum correlations in multipartite systems
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• Conclusive Identification of Quantum Channels via Monogamy of Quantum Correlations
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• Nonclassicality of local bipartite correlations
• Bell monogamy relations in arbitrary qubit networks
• Non-monogamy of spatio-temporal correlations and the black hole information loss paradox
• Forbidden regimes in the distribution of bipartite quantum correlations due to multiparty entanglement
• Trade-offs in multi-party Bell inequality violations in qubit networks
• On the separation of correlation-assisted sum capacities of multiple access channels
• Complementarity of genuine multipartite non-locality
• A Toy Model of the Information Paradox in Empty Space
• Complete monogamy of the multipartite quantum mutual information
• Entangled games are hard to approximate
• Lower bounds on violation of monogamy inequality for quantum correlation measures
• Device independent security of quantum key distribution from monogamy-of-entanglement games
• A Survey of Physical Principles Attempting to Define Quantum Mechanics
• Information complementarity in multipartite quantum states and security in cryptography
• Exclusion principle for nonlocal advantage of quantum coherence
• Monogamy relations of all quantum correlation measures for multipartite quantum systems
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Tighter constraints of multiqubit entanglement in terms of Rényi-$\alpha$ entropy
• Distribution of Bell inequality violation vs. multiparty quantum correlation measures
• Unmasking the Polygamous Nature of Quantum Nonlocality
• Monogamy relations for nonclassical correlations of multi-qubit states
• Verification of Bell Nonlocality by Violating Quantum Monogamy Relations
• Trade-off relations of l_1-norm coherence for multipartite systems
• Connection between Measurement Disturbance Relation and Multipartite Quantum Correlation
• Quantum guessing games with posterior information
• Distribution of Mutual Information in Multipartite States
• Partial-Norm of Entanglement: Entanglement Monotones That are not Monogamous
• Hierarchical axioms for quantum mechanics
• Oracularization and Two-Prover One-Round Interactive Proofs against Nonlocal Strategies
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
• Heralded Channel Holevo Superadditivity Bounds from Entanglement Monogamy
• No Strong Parallel Repetition with Entangled and Non-signaling Provers
• Simple and tight monogamy relations for a class of Bell inequalities
• Tighter parameterized monogamy relations
• General tradeoff relations of quantum nonlocality in the Clauser-Horne-Shimony-Holt scenario
• Sufficient condition for nonexistence of symmetric extension of qudits using Bell inequalities
• Restrictions on shareability of classical correlations for random multipartite quantum states
• Monogamy of Nonlocal Games
• Genuine monogamy relations in no-signaling theories - a geometric approach
• Relaxed uncertainty relations and information processing
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• A No-go theorem for device-independent security in relativistic causal theories
• Tsirelson's Bound and the Quantum Monogamy Bound from Global Determinism
• Dimensionality Distinguishers
• Polynomial-Space Approximation of No-Signaling Provers
• Quantum Zeno Effect on Genuine Tripartite Nonlocality and Entanglement in Quantum Dissipative System
• Monogamy inequalities for entanglement using continuous variable measurements
• The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy
• Quantum Entanglement in Time
• Communication strength of correlations violating monogamy relations
• Tighter monogamy and polygamy relations using Rényi-$\alpha$ entropy