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A Conditional Quantum Kac-Bernstein Theorem
Abstract
We establish a conditional quantum Kac-Bernstein theorem for mixing of two independent, finite-mode bosonic inputs with quantum memories. We characterize exactly when the outputs are conditionally independent given both memories. Each input then decomposes into orthogonal memory sectors sharing a common Gaussian state on the physical system and a bosonic memory factor, up to sector-dependent physical displacements. In particular, triviality of the common bosonic factor implies separability of the inputs, as occurs whenever either memory has finite-dimensional support.
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BibTeX
@misc{hosseini2026conditional,
title = {{A Conditional Quantum Kac-Bernstein Theorem}},
author = {Hesam Hosseini and Jinpei Zhao and Masahito Hayashi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04363},
eprint = {2611.04363},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04363},
}
RIS
TY - UNPB
TI - A Conditional Quantum Kac-Bernstein Theorem
AU - Hesam Hosseini
AU - Jinpei Zhao
AU - Masahito Hayashi
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04363
UR - https://arxiv.org/abs/2611.04363
AB - We establish a conditional quantum Kac-Bernstein theorem for mixing of two independent, finite-mode bosonic inputs with quantum memories. We characterize exactly when the outputs are conditionally independent given both memories. Each input then decomposes into orthogonal memory sectors sharing a common Gaussian state on the physical system and a bosonic memory factor, up to sector-dependent physical displacements. In particular, triviality of the common bosonic factor implies separability of the inputs, as occurs whenever either memory has finite-dimensional support.
ER -