Quantifying nonlocality as a resource for device-independent quantum key distribution

Abstract

We introduce, for any bipartite Bell scenario, a measure that quantifies both the amount of nonlocality and the efficiency in device-independent quantum key distribution of a set of measurement outcomes probabilities. It is a proper measure of nonlocality as it vanishes when this set is Bell local and does not increase under the allowed transformations of the nonlocality resource theory. This device-independent key rate $R$ is defined by optimizing over a class of protocols, to generate the raw keys, in which each legitimate party does not use just one preselected measurement but randomly chooses at each round one among all the measurements at its disposal. A common and secret key can certainly be established when $R$ is positive but not when it is zero. For any continuous proper measure of nonlocality $N$, $R$ is tightly lower bounded by a nondecreasing function of $N$ that vanishes when $N$ does. There can thus be a threshold value for the amount of nonlocality as quantified by $N$ above which a secret key is surely achievable. A readily computable measure with such a threshold exists for two two-outcome measurements per legitimate party.

References in corpus (32)

• Quantum entanglement
• Quantum Cryptography
• Quantum cryptography: Public key distribution and coin tossing
• Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
• Bell nonlocality
• Quantifying Entanglement
• Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long Distances
• Device-independent security of quantum cryptography against collective attacks
• Random Numbers Certified by Bell's Theorem
• No Signalling and Quantum Key Distribution
• Distillation of secret key and entanglement from quantum states
• Entanglement monotones
• Monogamy of entanglement and other correlations
• Device-independent quantum key distribution secure against collective attacks
• Fully device independent quantum key distribution
• Secure device-independent quantum key distribution with causally independent measurement devices
• Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
• Lower and upper bounds on the secret key rate for QKD protocols using one--way classical communication
• All Entangled Quantum States Are Nonlocal
• Memory Attacks on Device-Independent Quantum Cryptography
• Maximal violation of the I3322 inequality using infinite dimensional quantum systems
• On nonlocality as a resource theory and nonlocality measures
• Distilling Non-Locality
• Entropy accumulation with improved second-order term
• A framework for quantum-secure device-independent randomness expansion
• Device independent quantum key distribution secure against coherent attacks with memoryless measurement devices
• Device-independent randomness generation from several Bell estimators
• Certifying Quantum Randomness by Probability Estimation
• Monogamy inequality for any local quantum resource and entanglement
• A Limit on Non-Locality Distillation
• Internal entanglement and external correlations of any form limit each other
• Measure-independent anomaly of nonlocality

Cited by in corpus (3)

• Effect of source statistics on utilizing photon entanglement in quantum key distribution
• Quantum nonlocality in extended theories of gravity
• Resource theory of dephasing estimation in multiqubit systems