—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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Rate-limited Quantum-to-Classical Optimal Transport: A Lossy Source Coding Perspective
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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- Award ID(s):
- 2007878
- NSF-PAR ID:
- 10466993
- Publisher / Repository:
- IEEE
- Date Published:
- Page Range / eLocation ID:
- 1925 to 1930
- Format(s):
- Medium: X
- Location:
- Taipei, Taiwan
- Sponsoring Org:
- National Science Foundation
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