Entanglement Embezzlement from Diffusive Hydrodynamics
Abstract
Entanglement embezzlement asks how much entanglement can be borrowed from a many-body state by local operations and classical communication while returning that state with a small error. We uncover a conservation-law mechanism that redistributes the dominant probability mass of the Schmidt spectrum in the logarithmic Schmidt-rank coordinate and thereby controls this operational resource. For typical random pure states at fixed U(1) charge, we prove a finite-error conversion law: away from half filling, the charge bias converts O(√L) charge fluctuations into O(√L) borrowable entanglement, whereas particle--hole symmetry at half filling removes this contribution entirely. We then show how the resource develops dynamically in charge-conserving random circuits. Combining hydrodynamic analysis with large-scale replica tensor-network calculations, we find that diffusion broadens the operationally relevant distribution in the logarithmic Schmidt-rank coordinate on the scale t1/4 and increases the amount of entanglement that can be borrowed. Charge transport therefore continues to reorganize the entanglement spectrum and activate embezzlement after the leading volume-law entropy has saturated.
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BibTeX
@misc{zhang2026entanglement,
title = {{Entanglement Embezzlement from Diffusive Hydrodynamics}},
author = {Shi-Xin Zhang and Shuo Liu and Yu-Qin Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26362},
eprint = {2609.26362},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26362},
}
RIS
TY - UNPB
TI - Entanglement Embezzlement from Diffusive Hydrodynamics
AU - Shi-Xin Zhang
AU - Shuo Liu
AU - Yu-Qin Chen
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26362
UR - https://arxiv.org/abs/2609.26362
AB - Entanglement embezzlement asks how much entanglement can be borrowed from a many-body state by local operations and classical communication while returning that state with a small error. We uncover a conservation-law mechanism that redistributes the dominant probability mass of the Schmidt spectrum in the logarithmic Schmidt-rank coordinate and thereby controls this operational resource. For typical random pure states at fixed U(1) charge, we prove a finite-error conversion law: away from half filling, the charge bias converts O(√L) charge fluctuations into O(√L) borrowable entanglement, whereas particle--hole symmetry at half filling removes this contribution entirely. We then show how the resource develops dynamically in charge-conserving random circuits. Combining hydrodynamic analysis with large-scale replica tensor-network calculations, we find that diffusion broadens the operationally relevant distribution in the logarithmic Schmidt-rank coordinate on the scale t^1/4 and increases the amount of entanglement that can be borrowed. Charge transport therefore continues to reorganize the entanglement spectrum and activate embezzlement after the leading volume-law entropy has saturated.
ER -