[Paper Review] Device-independent quantum key distribution secure against adversaries with no long-term quantum memory

Stefano Pironio, Lluís Masanes+2 more|arXiv (Cornell University)|Nov 6, 2012

Quantum Information and Cryptography45 references20 citations

TL;DR

This paper presents a device-independent quantum key distribution (DIQKD) protocol that achieves security against adversaries without long-term quantum memory, using arbitrary Bell inequalities and maintaining high noise tolerance and efficiency. The key contribution is a security proof that enables practical, fully device-independent QKD under realistic assumptions about current quantum memory limitations.

ABSTRACT

Device-Independent Quantum Key Distribution (DIQKD) is a formalism that supersedes traditional quantum key distribution, as its security does not rely on any detailed modelling of the internal working of the devices. This strong form of security is possible only using devices producing correlations that violate a Bell inequality. Full security proofs of DIQKD have been recently reported, but they tolerate zero or small amounts of noise and are restricted to protocols based on specific Bell inequalities. Here, we provide a security proof of DIQKD that is both more efficient and noise resistant, and also more general as it applies to protocols based on arbitrary Bell inequalities and can be adapted to cover supra-quantum eavesdroppers limited by the no-signalling principle only. It requires, however, the extra assumption that the adversary does not have a long-term quantum memory, a condition that is not a limitation at present since the best existing quantum memories have very short coherence times.

Motivation & Objective

• To develop a device-independent quantum key distribution protocol that does not rely on trusted devices or detailed modeling of hardware.
• To address the limitations of prior DIQKD proofs that require memoryless devices or tolerate only negligible noise.
• To extend security to arbitrary Bell inequalities and non-signaling eavesdroppers, while maintaining high efficiency and noise resilience.
• To make the security assumption realistic by requiring only that the adversary lacks long-term quantum memory—feasible with current technology.
• To provide a framework that enables practical, fully device-independent QKD with strong security guarantees under minimal assumptions.

Proposed method

• The protocol uses two devices per party (Alice and Bob), eliminating the need for memoryless or independent devices.
• It relies on the violation of an arbitrary Bell inequality to certify nonlocal correlations and intrinsic randomness.
• A key step involves a two-universal random function to perform privacy amplification, ensuring the final key is nearly uniform and secure.
• The security proof uses a hybrid approach combining a high-probability event (G) and a small error term to bound the trace distance between the actual and ideal key distributions.
• The proof leverages Lemma 4 to bound the statistical distance using the guessing probability of the adversary’s information, leading to a trace distance bound of $ 2^{(1-n^{1/2})/2} + 6 ext{exp}(-m n^{-3/4} eta_0^{-2}) + 2( ho_A ho_B)^{-|{ m E}|} $.
• The framework is extended to supra-quantum eavesdroppers limited only by the no-signaling principle, demonstrating broader applicability.

Experimental results

Research questions

• RQ1 Can a DIQKD protocol be secure using only two devices per party, without assuming memoryless or independent devices?
• RQ2 Can the security proof be generalized to arbitrary Bell inequalities, not just specific ones like CHSH or chained inequalities?
• RQ3 Does the protocol maintain high noise tolerance and efficiency comparable to protocols using multiple devices?
• RQ4 Can the proof be extended to non-signaling eavesdroppers, even when they can store quantum information?
• RQ5 Is the assumption that the adversary lacks long-term quantum memory a realistic and sufficient condition for security in practice?

Key findings

• The protocol achieves a trace distance between the actual and ideal key distribution bounded by $ 2^{(1-n^{1/2})/2} + 6 ext{exp}(-m n^{-3/4} eta_0^{-2}) + 2( ho_A ho_B)^{-|{ m E}|} $, ensuring high security for large key lengths.
• The security proof is noise-resistant and efficient, with key length scaling linearly with the number of measurements, matching performance of protocols using multiple devices.
• The framework applies to arbitrary Bell inequalities, making it more general than prior proofs restricted to specific inequalities.
• The proof remains valid for non-signaling eavesdroppers, demonstrating robustness beyond quantum theory.
• The assumption that the adversary lacks long-term quantum memory is realistic given current quantum memory coherence times, making the protocol practically viable.
• Privacy amplification is shown to be effective under the given assumptions, suggesting a path toward fully device-independent QKD with practical noise tolerance.