Quantum time-flip beats adaptive metrology: Asymptotic benefit, activation, and unsimulability

• URL: http://arxiv.org/abs/2609.01175v1
• Date: Tue, 01 Sep 2026 12:50:51 GMT
• Title: Quantum time-flip beats adaptive metrology: Asymptotic benefit, activation, and unsimulability
• Abstract summary: We show that quantum operations with indefinite time direction, specifically, time-flip (TF)-assisted strategies, can overcome this equivalence.<n>We rigorously demonstrate that TF-assisted protocols can achieve quantum Fisher information (QFI) strictly exceeding the value attainable by parallel, adaptive, and causal-superposition strategies.<n>We identify a class of Pauli noise channels for which ITDM Heisenberg achieves scaling, while all parallel, adaptive, and causal-superposition strategies remain restricted to standard scaling.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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