Bosonic Quantum Conditional Mutual Information and Bose-Einstein Condensation
Abstract
This article aims to introduce the bosonic asymmetric quantum conditional mutual information (QCMI), IB(A; B|C), as a rigorously defined information-theoretic quantity for continuous-variable (bosonic) systems. After defining IB(A; B|C) through quantum instruments on infinite-dimensional Fock spaces, we prove that Bose-Einstein condensation (BEC) induces a logarithmic divergence $ I_{B}(A; B|C) \geq α\log_2 (N_{0}^C+1)$, which further establishes IB(A; B|C) as a quantum-information order parameter for BEC with power-law scaling near the critical point. We provide the complete five-step proof of this result, connecting measurement back-action, off-diagonal long-range order, and Jensen's inequality. In the condensed phase, the effective causal propagation velocity is set by the Bogoliubov sound speed cs in the long-wavelength limit, and vanishes continuously at the superfluid--Mott-insulator transition. Applications to composite bosons, the BEC--BCS crossover, and a quantum-gas-microscope measurement protocol are presented. Finally, we demonstrate how the reduced bosonic QCMI serves as a finite-size scaling probe analogous to the Binder cumulant.
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BibTeX
@misc{ghosh2026bosonic,
title = {{Bosonic Quantum Conditional Mutual Information and Bose-Einstein Condensation}},
author = {Anupam Ghosh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16626},
eprint = {2610.16626},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16626},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Bosonic Quantum Conditional Mutual Information and Bose-Einstein Condensation
AU - Anupam Ghosh
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16626
UR - https://arxiv.org/abs/2610.16626
AB - This article aims to introduce the bosonic asymmetric quantum conditional mutual information (QCMI), I_B(A; B|C), as a rigorously defined information-theoretic quantity for continuous-variable (bosonic) systems. After defining I_B(A; B|C) through quantum instruments on infinite-dimensional Fock spaces, we prove that Bose-Einstein condensation (BEC) induces a logarithmic divergence $ I_{B}(A; B|C) \geq α\log_2 (N_{0}^C+1)$, which further establishes I_B(A; B|C) as a quantum-information order parameter for BEC with power-law scaling near the critical point. We provide the complete five-step proof of this result, connecting measurement back-action, off-diagonal long-range order, and Jensen's inequality. In the condensed phase, the effective causal propagation velocity is set by the Bogoliubov sound speed c_s in the long-wavelength limit, and vanishes continuously at the superfluid--Mott-insulator transition. Applications to composite bosons, the BEC--BCS crossover, and a quantum-gas-microscope measurement protocol are presented. Finally, we demonstrate how the reduced bosonic QCMI serves as a finite-size scaling probe analogous to the Binder cumulant.
ER -