Rate-Distortion Theory for Mixed States
- URL: http://arxiv.org/abs/2208.11698v3
- Date: Thu, 20 Jun 2024 17:15:14 GMT
- Title: Rate-Distortion Theory for Mixed States
- Authors: Zahra Baghali Khanian, Kohdai Kuroiwa, Debbie Leung,
- Abstract summary: Rate-distortion theory studies the trade-off between the compression rate and the per-copy error.
We derive the rate-distortion function of mixed-state compression.
- Score: 3.2771631221674333
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This paper is concerned with quantum data compression of asymptotically many independent and identically distributed copies of ensembles of mixed quantum states. The encoder has access to a side information system. The figure of merit is per-copy or local error criterion. Rate-distortion theory studies the trade-off between the compression rate and the per-copy error. The optimal trade-off can be characterized by the rate-distortion function, which is the best rate given a certain distortion. In this paper, we derive the rate-distortion function of mixed-state compression. The rate-distortion functions in the entanglement-assisted and unassisted scenarios are in terms of a single-letter mutual information quantity and the regularized entanglement of purification, respectively. For the general setting where the consumption of both communication and entanglement are considered, we present the full qubit-entanglement rate region. Our compression scheme covers both blind and visible compression models (and other models in between) depending on the structure of the side information system.
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