Moderate deviation expansion for fully quantum tasks
- URL: http://arxiv.org/abs/2112.07167v1
- Date: Tue, 14 Dec 2021 05:15:22 GMT
- Title: Moderate deviation expansion for fully quantum tasks
- Authors: Navneeth Ramakrishnan and Marco Tomamichel and Mario Berta
- Abstract summary: The moderate deviation regime is concerned with the finite block length trade-off between communication cost and error for information processing tasks.
We find exact characterisations of these trade-offs for a variety of fully quantum communication tasks.
- Score: 20.30365614522286
- License: http://creativecommons.org/licenses/by-sa/4.0/
- Abstract: The moderate deviation regime is concerned with the finite block length
trade-off between communication cost and error for information processing tasks
in the asymptotic regime, where the communication cost approaches a
capacity-like quantity and the error vanishes at the same time. We find exact
characterisations of these trade-offs for a variety of fully quantum
communication tasks, including quantum source coding, quantum state splitting,
entanglement-assisted quantum channel coding, and entanglement-assisted quantum
channel simulation. The main technical tool we derive is a tight relation
between the partially smoothed max-information and the hypothesis testing
relative entropy. This allows us to obtain the expansion of the partially
smoothed max-information for i.i.d. states in the moderate deviation regime.
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