The uncertainty principle determines the non-locality of quantum mechanics

Abstract

Two central concepts of quantum mechanics are Heisenberg's uncertainty principle, and a subtle form of non-locality that Einstein famously called ``spooky action at a distance''. These two fundamental features have thus far been distinct concepts. Here we show that they are inextricably and quantitatively linked. Quantum mechanics cannot be more non-local with measurements that respect the uncertainty principle. In fact, the link between uncertainty and non-locality holds for all physical theories.More specifically, the degree of non-locality of any theory is determined by two factors -- the strength of the uncertainty principle, and the strength of a property called ``steering'', which determines which states can be prepared at one location given a measurement at another.

28 pages, 6 figures

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Cited by in corpus (62)

• Semi-device-independent security of one-way quantum key distribution
• Simple explanation of the quantum violation of a fundamental inequality
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• Fine-grained lower limit of entropic uncertainty in the presence of quantum memory
• Macroscopically local correlations can violate information causality
• Rényi entropy uncertainty relation for successive projective measurements
• Nonlocality of a single photon: paths to an EPR-steering experiment
• Uncertainty relation in Schwarzschild spacetime
• Entanglement and superposition are equivalent concepts in any physical theory
• What is nonclassical about uncertainty relations?
• Variance-based uncertainty relations for incompatible observables
• Detecting mixedness of qutrit systems using the uncertainty relation
• Multi-observable Uncertainty Relations in Product Form of Variances
• Experimental observation of impossible-to-beat quantum advantage on a hybrid photonic system
• Entropic uncertainty relations from equiangular tight frames and their applications
• Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness
• Maximum nonlocality and minimum uncertainty using magic states
• Experimental investigation of multi-observable uncertainty relations
• Tighter Einstein-Podolsky-Rosen steering inequality based on the sum uncertainty relation
• Quantum Bell Inequalities from Macroscopic Locality
• Incompatibility of observables, channels and instruments in information theories
• Consequences and applications of the completeness of Hardy's nonlocality
• A unified view on Hardy's paradox and the CHSH inequality
• Multiplicative Bell Inequalities
• Quantum contextuality from a simple principle?
• Nonlinear Schrödinger equations and generalized Heisenberg uncertainty principle violating the principle of estimation independence
• Experimental Test of Nonlocality Limits from Relativistic Independence
• Uncertainty relation between detection probability and energy fluctuations
• Uncertainty relations for quantum measurements from generalized equiangular tight frames
• Uncertainty regions of observables and state-independent uncertainty relations
• Uncertainty relations based on Wigner-Yanase skew information
• Entangled Rendezvous: A Possible Application of Bell Non-Locality For Mobile Agents on Networks
• Uncertainty limits of the information exchange between a quantum system and an external meter
• Connection between Measurement Disturbance Relation and Multipartite Quantum Correlation
• Single-particle entanglement gives rise to truly nonlocal effects like single-particle steering
• Maximum quantum nonlocality between systems that never interacted
• The Operational Choi-Jamiolkowski Isomorphism
• Estimation independence as an axiom for quantum uncertainty
• Experimental investigation of the relation between measurement uncertainties and non-local quantum correlations
• Wigner-Yanase skew information-based uncertainty relations for quantum channels
• Relating entropies of quantum channels
• Physical interpretation of nonlocal quantum correlation through local description of subsystems
• Beyond the Projection Postulate and Back: Quantum Theories with Generalised State-Update Rules
• Effects of spatial nonlocality versus nonlocal causality for bound electrons in external fields
• Strength of the nonlocality of two-qubit entangled state and its applications
• Optimal CHSH values for regular polygon theories in generalized probabilistic theories
• Uncertainty Relations and Indistinguishable Particles
• Stronger sum uncertainty relations for non-Hermitian operators
• Uncertainty relations based on the $\rho$-absolute variance for quantum channels
• Cyclic measurements and simplified quantum state tomography
• Probability density functions of quantum mechanical observable uncertainties
• Hardy's Paradox and Measurement-disturbance Relations
• On the Meaning of Localization in Non-Local Quantum Field Theory and On the Limits of a Space-Time Description and the Physical Meaning of Phase Space in a Nonlocal Continuum
• Quantum Uncertainty Dynamics
• NPA Hierarchy and Extremal Criterion in the Simplest Bell Scenario
• Multi-observable Uncertainty Equality based on the sum of standard deviations in the qubit system
• Uncertainty-disturbance relations and applications
• Computational Perspectives on Bell Inequalities and Many-body Quantum Correlations
• Epistemic uncertainty from an averaged Hamilton-Jacobi formalism
• Detection of the genuine non-locality of any three-qubit state
• The thermodynamics of readout devices and semiclassical gravity
• Confidence uncertainty: position and momentum can be jointly determined with a guaranteed probability