Moderate Deviation Analysis for Quantum State Transfer

Authors

Image provided by Navneeth Ramakrishnan
Navneeth
Ramakrishnan
Imperial College London
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Marco
Tomamichel
National University of Singapore
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Mario
Berta
Imperial College London

Abstract

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 quantify 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.

Paper Manuscript