  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.
