[Paper Review] Device-independent quantum key distribution

Esther Hänggi|arXiv (Cornell University)|Dec 17, 2010

Quantum Information and Cryptography17 citations

TL;DR

This paper establishes device-independent quantum key distribution (DIQKD) under two distinct frameworks: non-signalling adversaries and quantum-realizable correlations. It proves security using a generic proof framework that relies on non-signalling constraints and commutative measurements, demonstrating that secure key distillation is possible when these conditions are met, even without trust in device details or Hilbert space dimension.

ABSTRACT

In this thesis, we study two approaches to achieve device-independent quantum key distribution: in the first approach, the adversary can distribute any system to the honest parties that cannot be used to communicate between the three of them, i.e., it must be non-signalling. In the second approach, we limit the adversary to strategies which can be implemented using quantum physics. For both approaches, we show how device-independent quantum key distribution can be achieved when imposing an additional condition. In the non-signalling case this additional requirement is that communication is impossible between all pairwise subsystems of the honest parties, while, in the quantum case, we demand that measurements on different subsystems must commute. We give a generic security proof for device-independent quantum key distribution in these cases and apply it to an existing quantum key distribution protocol, thus proving its security even in this setting. We also show that, without any additional such restriction there always exists a successful joint attack by a non-signalling adversary.

Motivation & Objective

• To achieve device-independent quantum key distribution without relying on device trust.
• To prove security under non-signalling adversaries who cannot communicate between subsystems.
• To establish security under quantum-realizable correlations with commuting measurements.
• To show that additional constraints are necessary to prevent collective attacks by non-signalling adversaries.
• To provide a generic security proof applicable to explicit QKD protocols under minimal assumptions.

Proposed method

• Proposes a device-independent QKD framework based on observable measurement statistics rather than device specifications.
• Introduces two models: non-signalling adversaries (weaker constraints) and quantum-realizable correlations (stronger physical constraints).
• Imposes two key conditions: no communication between subsystems and commutative measurements on different subsystems.
• Develops a generic security proof using convex optimization and min-entropy analysis to bound eavesdropper's knowledge.
• Applies the proof to a concrete QKD protocol, showing it remains secure under the stated assumptions.
• Uses de Finetti-type theorems and duality in convex optimization to analyze the security of key distillation.

Experimental results

Research questions

• RQ1 Can device-independent QKD be achieved without trusting the physical devices used?
• RQ2 What additional constraints are necessary to prevent non-signalling adversaries from breaking QKD protocols?
• RQ3 How does the security of QKD change when only the observed correlations are trusted, not the underlying quantum devices?
• RQ4 Can a generic security proof be constructed that applies to multiple QKD protocols under minimal assumptions?
• RQ5 What role do non-signalling and commutativity constraints play in ensuring secure key generation?

Key findings

• Security in device-independent QKD is achievable when non-signalling constraints and commutative measurements are imposed.
• Without additional constraints, non-signalling adversaries can mount collective attacks on multiple systems simultaneously.
• The proposed framework enables a generic security proof for QKD protocols based solely on observed correlations.
• The security proof relies on convex optimization and min-entropy techniques to bound the adversary's information.
• The results show that device-independent security is possible even without knowledge of the Hilbert space dimension or device details.
• The framework demonstrates that causality and non-communication constraints are sufficient to guarantee secure key distillation.