—In this work, we address the lossy quantum-classical
(QC) source coding problem, where the task is to compress the
classical information about a quantum source, obtained after
performing a measurement, below the Shannon entropy of the
measurement outcomes, while incurring a bounded reconstruction error. We propose a new formulation, namely, "rate-channel
theory", for the lossy QC source coding problem based on the
notion of a backward (posterior) channel. We employ a singleletter posterior channel to capture the reconstruction error in
place of the single-letter distortion observable. The formulation
requires the reconstruction of the compressed quantum source to
satisfy a block error constraint as opposed to the average singleletter distortion criterion in the rate-distortion setting. We also
develop an analogous formulation for the classical variant with
respect to a corresponding posterior channel. Furthermore, we
characterize the asymptotic performance limit of the lossy QC
and classical source coding problems in terms of single-letter
quantum mutual information and mutual information quantities
of the given posterior channel, respectively. We provide examples
for the above formulations.
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Faithful Simulation of Distributed Quantum Measurements with Applications in Distributed Rate-Distortion Theory
We investigate faithful simulation of distributed quantum measurements as an extension of Winter's measurement compression theorem. We characterize a set of communication and common randomness rates needed to provide faithful simulation of distributed measurements. To achieve this, we introduce binning and mutual packing lemma for distributed quantum measurements. These techniques can be viewed as the quantum counterpart of their classical analogues. Finally, using these results, we develop a distributed quantum-to-classical rate distortion theory and characterize a rate region analogous to Berger-Tung's in terms of single-letter quantum mutual information quantities.
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- NSF-PAR ID:
- 10123062
- Date Published:
- Journal Name:
- IEEE International Symposium on Information Theory
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
