Quantum covariant bit threads
Abstract
Entanglement entropy plays a central role in holography. The quantum extremal surface (QES) formula is the standard tool in settings where both dynamics and bulk quantum corrections are important, such as in black hole evaporation. We derive and explore QES-equivalent prescriptions --- quantum covariant bit threads --- that formulate holographic entanglement entropy in terms of minimal or maximal bulk flows rather than extremal surfaces. Like classical covariant bit threads, our prescriptions come in two types: (typically) spacelike V-flows, and timelike U-flows. To account for bulk quantum corrections, the flow lines can start and end at points in the bulk, with the distribution of endpoints controlled by bulk entanglement entropies. In our bit thread language, the QES is a quantum bottleneck to the flow, with some threads passing through it (accounting for the area term in the generalized entropy) and others jumping across it (accounting for the entropy term). Our prescriptions provide a complementary perspective to the QES formula and offer new insights on important phenomena such as black hole evaporation, islands, and baby universes.
Related
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BibTeX
@misc{headrick2026quantum,
title = {{Quantum covariant bit threads}},
author = {Matthew Headrick and Sreeman Reddy Kasireddy and Andrew Rolph},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03929},
eprint = {2610.03929},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03929},
}
RIS
TY - UNPB
TI - Quantum covariant bit threads
AU - Matthew Headrick
AU - Sreeman Reddy Kasireddy
AU - Andrew Rolph
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03929
UR - https://arxiv.org/abs/2610.03929
AB - Entanglement entropy plays a central role in holography. The quantum extremal surface (QES) formula is the standard tool in settings where both dynamics and bulk quantum corrections are important, such as in black hole evaporation. We derive and explore QES-equivalent prescriptions --- quantum covariant bit threads --- that formulate holographic entanglement entropy in terms of minimal or maximal bulk flows rather than extremal surfaces. Like classical covariant bit threads, our prescriptions come in two types: (typically) spacelike V-flows, and timelike U-flows. To account for bulk quantum corrections, the flow lines can start and end at points in the bulk, with the distribution of endpoints controlled by bulk entanglement entropies. In our bit thread language, the QES is a quantum bottleneck to the flow, with some threads passing through it (accounting for the area term in the generalized entropy) and others jumping across it (accounting for the entropy term). Our prescriptions provide a complementary perspective to the QES formula and offer new insights on important phenomena such as black hole evaporation, islands, and baby universes.
ER -