The Link between Entropic Uncertainty and Nonlocality

Abstract

Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such that their outcomes cannot both be predicted. On the other hand, nonlocal correlations of measurement outcomes at different locations cannot be explained by classical physics, but appear in the presence of entanglement. Here, we show that these two fundamental quantum effects are quantitatively related. Namely, we provide an entropic uncertainty relation for the outcomes of two binary measurements, where the lower bound on the uncertainty is quantified in terms of the maximum Clauser-Horne-Shimony-Holt value that can be achieved with these measurements. We discuss applications of this uncertainty relation in quantum cryptography, in particular, to certify quantum sources using untrusted devices.

Completely revised manuscript; extended result to uncertainty relations in terms of smooth entropies

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• A Monogamy-of-Entanglement Game With Applications to Device-Independent Quantum Cryptography
• Self-testing of binary observables based on commutation
• Security of two-way quantum key distribution
• Device-Independent Quantum Key Distribution with Random Key Basis
• Certifying the building blocks of quantum computers from Bell's theorem
• Device-independent quantum key distribution with single-photon sources
• Device-Independent Quantum Key Distribution with Local Bell Test
• Security of device-independent quantum key distribution protocols: a review
• Entropic uncertainty from effective anti-commutators
• Entropic uncertainty relations under the relativistic motion
• Device-independent two-party cryptography secure against sequential attacks
• Quantum to Classical Randomness Extractors
• Maximum nonlocality and minimum uncertainty using magic states
• Self-testing with finite statistics enabling the certification of a quantum network link
• A geometric formulation of uncertainty principle
• Entropic measures of joint uncertainty: effects of lack of majorization
• Bounds on semi-device-independent quantum random number expansion capabilities
• Optimal joint measurements of complementary observables by a single trapped ion
• Measurement uncertainty from no-signaling and non-locality
• Entropy bounds for device-independent quantum key distribution with local Bell test
• Interplay of Quantum Resources in Nonlocality Tests
• Towards secure communication using intra-particle entanglement
• Single-qubit measurement of Heisenberg uncertainty lower bounds for three incompatible observables