• Accepted Paper

Quantum-Fisher-information-based imaginarity quantifiers under covariant real operations

Xuzheng Lu, Zhihua Guo, Huaixin Cao, and Yajing Fan

Phys. Rev. A - Accepted 13 November, 2026

DOI: https://doi.org/10.1103/gcvh-hjzz

Abstract

Imaginarity is indispensable in quantum mechanics and plays a key role in various quantum information processing tasks. We introduce a family of quantum-Fisher-information-based imaginarity quantifiers through a concrete channel-estimation task. A probe state () is sent through a quantum channel ({m,p}), where (m) is a fixed calibration parameter and (p) is the unknown parameter to be estimated. The quantity ({m,p}()) is the quantum Fisher information of the output family and therefore determines the corresponding quantum Cram'er-Rao bound. Real input states carry no information about (p), whereas the transpose-antisymmetric, or imaginary, part of a state provides the signal. We prove faithfulness and convexity and establish monotonicity under real channels covariant with the full encoding family. In arbitrary finite dimension, we derive the exact maximum of (_{m,p}) and identify its pure-state maximizers. For qubits, the encoding admits a random-Pauli implementation, and we obtain a closed formula, a complementarity relation for three mutually unbiased bases, and ordering results. We finally use selected noise channels and a damped Jaynes-Cummings model to illustrate losses and temporary revivals of estimation sensitivity.

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