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The Entropy Accumulation Theorem (EAT) was introduced to significantlyimprove the finite-size rates for device-independent quantum informationprocessing tasks such as device-independent quantum key distribution (QKD). Anatural question would be whether it also improves the rates fordevice-dependent QKD. In this work, we provide an affirmative answer to thisquestion. We present new tools for applying the EAT in the device-dependentsetting. We present sufficient conditions for the Markov chain conditions tohold as well as general algorithms for constructing the needed min-tradeofffunction. Utilizing Dupuis' recent privacy amplification without smoothingresult, we improve the key rate by optimizing the sandwiched R\'{e}nyi entropydirectly rather than considering the traditional smooth min-entropy. Weexemplify these new tools by considering several examples including the BB84protocol with the qubit-based version and with a realistic parametricdownconversion source, the six-state four-state protocol and a high-dimensionalanalog of the BB84 protocol.

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