This work studies the decay of three imaginarity measures, namely the $l_1$ -norm-based imaginarity, the robustness of imaginarity, and the relative-entropy-based imaginarity, under typical noise channels. For arbitrary single-qubit pure states subject to real quantum channels, we prove an exact attenuation theorem: the $l_1$ -norm-based imaginarity and the robustness exhibit identical attenuation governed by a common channel-dependent factor, whereas the relative-entropy-based imaginarity additionally depends on the input-state orientation relative to the reference basis. We extend the investigation to two-qubit entangled and dual-rail states, establishing a quantitative link between photon-loss probability and residual imaginarity for photonic dual-rail encodings. For separable two-qubit states, we define a real-operation resource preorder and show that $Ω_{++}=|+\rangle\langle+|\otimes|+\rangle\langle+|$ is operationally maximal. We further distinguish operational de-imaginary power from reference-state imaginarity loss. For several real two-qubit channels we derive exact operational de-imaginary powers, while for other channels we provide analytic reference-state losses serving as benchmarks and rigorous lower bounds.This work studies the decay of three imaginarity measures, namely the $l_1$-norm-based imaginarity, the robustness of imaginarity, and the relative-entropy-based imaginarity, under typical noise channels. For arbitrary single-qubit pure states subject to real quantum channels, we prove an exact attenuation theorem: the $l_1$-norm-based imaginarity and the robustness exhibit identical attenuation governed by a common channel-dependent factor, whereas the relative-entropy-based imaginarity additionally depends on the input-state orientation relative to the reference basis. We extend the investigation to two-qubit entangled and dual-rail states, establishing a quantitative link between photon-loss probability and residual imaginarity for photonic dual-rail encodings. For separable two-qubit states, we define a real-operation resource preorder and show that $Ω_{++}=|+\rangle\langle+|\otimes|+\rangle\langle+|$ is operationally maximal. We further distinguish operational de-imaginary power from reference-state imaginarity loss. For several real two-qubit channels we derive exact operational de-imaginary powers, while for other channels we provide analytic reference-state losses serving as benchmarks and rigorous lower bounds.

quant-pharXiv:2603.13980Journal of Physics A Mathematical and TheoreticalMar 17, 20260 citations

Quantum imaginarity measure sensitivity to deimaginarizing maps

Peng-Fei Wang, Xu-Zheng Lu, Zhihua Guo +1 more

Abstract In this paper, we introduce a measure of quantum imaginarity based on the deimaginarization strength exerted by a class of quantum operations on quantum states, and derive an upper bound for this measure. For the qubit scenario, we establish a tight upper bound on the sum of imaginarity measures with respect to three mutually unbiased bases. Finally, we investigate the decay behavior of quantum imaginarity for maximally imaginary states under the action of the bit-flip, phase-damping, and amplitude-damping channels.Abstract In this paper, we introduce a measure of quantum imaginarity based on the deimaginarization strength exerted by a class of quantum operations on quantum states, and derive an upper bound for this measure. For the qubit scenario, we establish a tight upper bound on the sum of imaginarity measures with respect to three mutually unbiased bases. Finally, we investigate the decay behavior of quantum imaginarity for maximally imaginary states under the action of the bit-flip, phase-damping, and amplitude-damping channels.

Laser Physics LettersApr 30, 20260 citations

This work studies the decay of three imaginarity measures, namely the

l_1

-norm-based imaginarity, the robustness of imaginarity, and the relative-entropy-based imaginarity, under typical noise channels. For arbitrary single-qubit pure states subject to real quantum channels, we prove an exact attenuation theorem: the

l_1

-norm-based imaginarity and the robustness exhibit identical attenuation governed by a common channel-dependent factor, whereas the relative-entropy-based imaginarity additionally depends on the input-state orientation relative to the reference basis. We extend the investigation to two-qubit entangled and dual-rail states, establishing a quantitative link between photon-loss probability and residual imaginarity for photonic dual-rail encodings. For separable two-qubit states, we define a real-operation resource preorder and show that

Ω_{++}=|+\rangle\langle+|\otimes|+\rangle\langle+|

is operationally maximal. We further distinguish operational de-imaginary power from reference-state imaginarity loss. For several real two-qubit channels we derive exact operational de-imaginary powers, while for other channels we provide analytic reference-state losses serving as benchmarks and rigorous lower bounds.