Quantum time-flip beats adaptive metrology: Asymptotic benefit, activation, and unsimulability
Abstract
In quantum metrology, adaptive and causal-superposition strategies are proven to be beneficial over parallel schemes for a finite number of channel uses, but their advantages disappear in the asymptotic limit. We show that quantum operations with indefinite time direction, specifically, time-flip (TF)-assisted strategies, referred to as indefinite time-directed metrology (ITDM), can overcome this asymptotic equivalence. Using semidefinite programming, we rigorously demonstrate that TF-assisted protocols can achieve quantum Fisher information (QFI) strictly exceeding the maximum value attainable by parallel, adaptive, and causal-superposition strategies, both for finite and asymptotically many channel uses. Moreover, we identify a class of Pauli noise channels for which ITDM achieves Heisenberg scaling, while all parallel, adaptive, and causal-superposition strategies remain restricted to standard scaling. We call this phenomenon as metrological activation. Interestingly, this activation can be used to exhibit that the quantum time-flip and transposition supermaps cannot be simulated by conventional quantum circuits or causal-superposition strategies using any finite number of channel queries, thereby establishing indefinite time direction as a genuine resource for quantum metrology.
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BibTeX
@misc{agrawal2026quantum,
title = {{Quantum time-flip beats adaptive metrology: Asymptotic benefit, activation, and unsimulability}},
author = {Gaurang Agrawal and Pritam Halder and Aditi Sen De},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01175},
eprint = {2609.01175},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01175},
}
RIS
TY - UNPB
TI - Quantum time-flip beats adaptive metrology: Asymptotic benefit, activation, and unsimulability
AU - Gaurang Agrawal
AU - Pritam Halder
AU - Aditi Sen De
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01175
UR - https://arxiv.org/abs/2609.01175
AB - In quantum metrology, adaptive and causal-superposition strategies are proven to be beneficial over parallel schemes for a finite number of channel uses, but their advantages disappear in the asymptotic limit. We show that quantum operations with indefinite time direction, specifically, time-flip (TF)-assisted strategies, referred to as indefinite time-directed metrology (ITDM), can overcome this asymptotic equivalence. Using semidefinite programming, we rigorously demonstrate that TF-assisted protocols can achieve quantum Fisher information (QFI) strictly exceeding the maximum value attainable by parallel, adaptive, and causal-superposition strategies, both for finite and asymptotically many channel uses. Moreover, we identify a class of Pauli noise channels for which ITDM achieves Heisenberg scaling, while all parallel, adaptive, and causal-superposition strategies remain restricted to standard scaling. We call this phenomenon as metrological activation. Interestingly, this activation can be used to exhibit that the quantum time-flip and transposition supermaps cannot be simulated by conventional quantum circuits or causal-superposition strategies using any finite number of channel queries, thereby establishing indefinite time direction as a genuine resource for quantum metrology.
ER -