Moderate Deviation Analysis for Quantum State Transfer

Quantum state transfer involves two parties who use pre-shared entanglement and noiseless communication in order to transfer parts of a quantum state. In this work, we quantity the communication cost of one-shot state splitting in terms of the partially smoothed max-information. We then give an analysis of state splitting in the moderate deviation regime, where the error in the protocol goes sub-exponentially fast to zero as a function of the number of i.i.d. copies. The main technical tool we derive is a tight relation between the partially smoothed max-information and the hypothesis testing relative entropy, which allows us to obtain the expansion of the partially smoothed max-information for i.i.d. states in the moderate deviation regime. This then also establishes the moderate deviation analysis for other variants of state transfer such as state merging and source coding.