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We consider the rate-limited quantum-to-classical optimal transport in terms of output-constrained rate-distortion coding for discrete quantum measurement systems with limited classical common randomness. The main coding theorem provides the achievable rate region of a lossy measurement source coding for an exact construction of the destination distribution (or the equivalent quantum state) while maintaining a threshold of distortion from the source state according to a generally defined distortion observable. The constraint on the output space fixes the output distribution to an i.i.d. predefined probability mass function. Therefore, this problem can also be viewed as information-constrained optimal transport which finds the optimal cost of transporting the source quantum state to the destination state via an entanglement-breaking channel with limited communication rate and common randomness.
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A New Formulation of Lossy Quantum-Classical and Classical Source Coding based on a Posterior Channel
—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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- PAR ID:
- 10466975
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 978-1-6654-7554-9
- Page Range / eLocation ID:
- 743 to 748
- Format(s):
- Medium: X
- Location:
- Taipei, Taiwan
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ISIT54713.2023.10206859
