Finite-Key Analysis of Quantum Key Distribution with Characterized Devices Using Entropy Accumulation

TL;DR

This paper extends the Entropy Accumulation Theorem to device-dependent quantum key distribution, providing new tools and algorithms that improve finite-key rates for practical QKD protocols.

Contribution

It introduces methods to apply EAT in device-dependent QKD, enhancing finite-size key rates with optimized entropy techniques and new construction algorithms.

Findings

Improved finite-key rates for device-dependent QKD protocols.

Application of EAT to various practical QKD setups including BB84 and high-dimensional protocols.

Demonstrated benefits of direct Rènyi entropy optimization over traditional methods.

Abstract

The Entropy Accumulation Theorem (EAT) was introduced to significantly improve the finite-size rates for device-independent quantum information processing tasks such as device-independent quantum key distribution (QKD). A natural question would be whether it also improves the rates for device-dependent QKD. In this work, we provide an affirmative answer to this question. We present new tools for applying the EAT in the device-dependent setting. We present sufficient conditions for the Markov chain conditions to hold as well as general algorithms for constructing the needed min-tradeoff function. Utilizing Dupuis' recent privacy amplification without smoothing result, we improve the key rate by optimizing the sandwiched R\'{e}nyi entropy directly rather than considering the traditional smooth min-entropy. We exemplify these new tools by considering several examples including the BB84 protocol with the qubit-based version and with a realistic parametric downconversion source, the six-state four-state protocol and a high-dimensional analog of the BB84 protocol.