PreprintCC BY 4.0arXiv
Optimality of the Petz-Fuchs Smoothed State
Abstract
Quantum state smoothing is an estimation technique that uses past and future measurement information obtained from a continuous-in-time measurement record to reconstruct the state of an open quantum system. Recently, there has been a new approach to quantum state smoothing based on quantum retrodiction known as the Petz-Fuchs smoothed state. Here I prove that this Petz-Fuchs smoothed state majorizes all other smoothed states that only depend on the filtered state (the operator conditioned on the past measurement record) and the retrofiltered effect (the operator describing the future measurement record). To do this, I characterize the set of all possible smoothed states satisfying this condition.
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BibTeX
@misc{laverick2026optimality,
title = {{Optimality of the Petz-Fuchs Smoothed State}},
author = {Kiarn T. Laverick},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41311},
eprint = {2610.41311},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41311},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimality of the Petz-Fuchs Smoothed State
AU - Kiarn T. Laverick
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41311
UR - https://arxiv.org/abs/2610.41311
AB - Quantum state smoothing is an estimation technique that uses past and future measurement information obtained from a continuous-in-time measurement record to reconstruct the state of an open quantum system. Recently, there has been a new approach to quantum state smoothing based on quantum retrodiction known as the Petz-Fuchs smoothed state. Here I prove that this Petz-Fuchs smoothed state majorizes all other smoothed states that only depend on the filtered state (the operator conditioned on the past measurement record) and the retrofiltered effect (the operator describing the future measurement record). To do this, I characterize the set of all possible smoothed states satisfying this condition.
ER -