Efficient certification of time-reversal symmetry requires entanglement
Abstract
Time-reversal symmetry is a fundamental principle of physics describing the invariance of physical laws under reversal of the direction of time. We formulate a Bell-inequality-like test of this antiunitary symmetry using only forward access and trusted quantum operations: entanglement converts temporal input--output relations into measurable spatial exchange symmetry. For n-qubit unitary dynamics, we prove that reliably distinguishing the time-reversal-symmetric circular ensembles from Haar-random dynamics requires Ω(min{2n/2,2n−e}) queries for any classically adaptive protocol. Here, e=min{es,em} with es and em representing the probe and measurement logarithmic entanglement negativities, respectively. Maximally entangled probes and SWAP measurements reduce this cost to a constant number of queries. Furthermore, we develop a time-reversal symmetry test for arbitrary fixed, compatible probes and measurements, relate its query complexity to their logarithmic negativities, and match the lower-bound scaling in the high-entanglement regime by optimizing the probe and measurement. Our results establish a quantitative connection between entanglement and time-reversal symmetry, bridging two central concepts in quantum information science and fundamental physics.
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BibTeX
@misc{liu2026efficient,
title = {{Efficient certification of time-reversal symmetry requires entanglement}},
author = {Zhenhuan Liu and Zhenyu Du and Yifan Tang and Zi-Wen Liu and Jens Eisert and Ingo Roth},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01555},
eprint = {2610.01555},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01555},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Efficient certification of time-reversal symmetry requires entanglement
AU - Zhenhuan Liu
AU - Zhenyu Du
AU - Yifan Tang
AU - Zi-Wen Liu
AU - Jens Eisert
AU - Ingo Roth
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01555
UR - https://arxiv.org/abs/2610.01555
AB - Time-reversal symmetry is a fundamental principle of physics describing the invariance of physical laws under reversal of the direction of time. We formulate a Bell-inequality-like test of this antiunitary symmetry using only forward access and trusted quantum operations: entanglement converts temporal input--output relations into measurable spatial exchange symmetry. For n-qubit unitary dynamics, we prove that reliably distinguishing the time-reversal-symmetric circular ensembles from Haar-random dynamics requires Ω(min{2^n/2,2^n−e}) queries for any classically adaptive protocol. Here, e=min{e_s,e_m} with e_s and e_m representing the probe and measurement logarithmic entanglement negativities, respectively. Maximally entangled probes and SWAP measurements reduce this cost to a constant number of queries. Furthermore, we develop a time-reversal symmetry test for arbitrary fixed, compatible probes and measurements, relate its query complexity to their logarithmic negativities, and match the lower-bound scaling in the high-entanglement regime by optimizing the probe and measurement. Our results establish a quantitative connection between entanglement and time-reversal symmetry, bridging two central concepts in quantum information science and fundamental physics.
ER -