The impossibility of non-signaling privacy amplification

Abstract

Barrett, Hardy, and Kent have shown in 2005 that protocols for quantum key agreement exist the security of which can be proven under the assumption that quantum or relativity theory is correct. More precisely, this is based on the non-local behavior of certain quantum systems, combined with the non-signaling postulate from relativity. An advantage is that the resulting security is independent of what (quantum) systems the legitimate parties' devices operate on: they do not have to be trusted. Unfortunately, the protocol proposed by Barrett et al. cannot tolerate any errors caused by noise in the quantum channel. Furthermore, even in the error-free case it is inefficient: its communication complexity is Theta(1/epsilon) when forcing the attacker's information below epsilon, even if only a single key bit is generated. Potentially, the problem can be solved by privacy amplification of relativistic - or non-signaling - secrecy. We show, however, that such privacy amplification is impossible with respect to the most important form of non-local behavior, and application of arbitrary hash functions.

24 pages, 2 figures

References in corpus (4)

• Device-independent security of quantum cryptography against collective attacks
• Is Entanglement Monogamous?
• Efficient quantum key distribution secure against no-signalling eavesdroppers
• Secrecy extraction from no-signalling correlations

Cited by in corpus (16)

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• Limits of privacy amplification against non-signalling memory attacks
• Parallel Device-Independent Quantum Key Distribution
• Necessary detection efficiencies for secure quantum key distribution and bound randomness
• de Finetti reductions for correlations
• Information-based measure of nonlocality
• A Rigorous Analysis of the Clauser-Horne-Shimony-Holt Inequality Experiment When Trials Need Not Be Independent
• Towards the Impossibility of Non-Signalling Privacy Amplification from Time-Like Ordering Constraints
• Limitations on device independent key secure against non signaling adversary via the squashed non-locality
• Optimal measurements for nonlocal correlations
• Quantifying the randomness of copies of noisy Popescu-Rohrlich correlations
• Signaling between time steps does not allow for nonlocality beyond hidden nonlocality
• Monogamy relations for relativistically causal correlations
• Stronger Attacks on Causality-Based Key Agreement
• Device-independent quantum key distribution
• De Finetti Theorems for Quantum Conditional Probability Distributions with Symmetry