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

A Note on Geometric Imaginarity

Tiantian Xia, Jianwei Xu, Ming‐Jing Zhao

International Journal of Theoretical PhysicsDec 21, 20243 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.