Quantum Chernoff divergence in advantage distillation for quantum key distribution and device-independent quantum key distribution

Abstract

Device-independent quantum key distribution (DIQKD) aims to mitigate adversarial exploitation of imperfections in quantum devices, by providing an approach for secret key distillation with modest security assumptions. Advantage distillation, a two-way communication procedure in error correction, has proven effective in raising noise tolerances in both device-dependent and device-independent QKD. Previously, device-independent security proofs against IID collective attacks were developed for an advantage distillation protocol known as the repetition-code protocol, based on security conditions involving the fidelity between some states in the protocol. However, there exists a gap between the sufficient and necessary security conditions, which hinders the calculation of tight noise-tolerance bounds based on the fidelity. We close this gap by presenting an alternative proof structure that replaces the fidelity with the quantum Chernoff divergence, a distinguishability measure that arises in symmetric hypothesis testing. Working in the IID collective attacks model, we derive matching sufficient and necessary conditions for the repetition-code protocol to be secure (up to a natural conjecture regarding the latter case) in terms of the quantum Chernoff divergence, hence indicating that this serves as the relevant quantity of interest for this protocol. Furthermore, using this security condition we obtain some improvements over previous results on the noise tolerance thresholds for DIQKD. Our results provide insight into a fundamental question in quantum information theory regarding the circumstances under which DIQKD is possible.

Close to published version

References in corpus (31)

• Bell nonlocality
• Distillation of secret key and entanglement from quantum states
• Device-independent quantum key distribution secure against collective attacks
• The Quantum Chernoff Bound
• Full-field implementation of a perfect eavesdropper on a quantum cryptography system
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• Asymptotic Error Rates in Quantum Hypothesis Testing
• Phase-Remapping Attack in Practical Quantum Key Distribution Systems
• Properties of Classical and Quantum Jensen-Shannon Divergence
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Risk analysis of Trojan-horse attacks on practical quantum key distribution systems
• Device-Independent Quantum Key Distribution with Random Key Basis
• Key distillation from quantum channels using two-way communication protocols
• Advantage distillation for device-independent quantum key distribution
• Noisy pre-processing facilitating a photonic realisation of device-independent quantum key distribution
• Device-independent quantum key distribution with asymmetric CHSH inequalities
• Device-independent quantum key distribution with random postselection
• Numerical Calculations of Finite Key Rate for General Quantum Key Distribution Protocols
• Bell nonlocality is not sufficient for the security of standard device-independent quantum key distribution protocols
• Device-independent quantum key distribution from generalized CHSH inequalities
• Improved DIQKD protocols with finite-size analysis
• Device-independent lower bounds on the conditional von Neumann entropy
• On the security and degradability of Gaussian channels
• Quantum Online Memory Checking
• Quantum state discrimination bounds for finite sample size
• Symmetric extension in two-way quantum key distribution
• Pretty good measures in quantum information theory
• Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints
• Randomness in post-selected events
• Numerical evidence for bound secrecy from two-way post-processing in quantum key distribution
• Fidelity Bounds for Device-Independent Advantage Distillation