We establish a rigorous framework that identifies imaginarity as a fundamental resource inherent in quantum coherence. By means of a geometric decomposition, we partition coherence into distinct imaginarity and residual components, thereby revealing a universal hierarchical relationship among these resources. For bipartite systems, this decomposition provides explicit bounds on the extent to which nonlocal correlations and imaginarity limit local coherence generation. Furthermore, we devise an explicit operational protocol that converts imaginarity into usable coherence, demonstrating the direct interconvertibility of these resources under physically admissible operations. The dynamical evolution under diagonal Hamiltonians is fully characterized, showing that while total coherence is conserved, imaginarity and residual coherence exhibit complementary oscillations. Our results provide a rigorous geometric and operational characterization of imaginarity as a fundamental constituent of quantum coherence, offering concrete insights for resource management in distributed quantum technologies. The geometric framework and theoretical bounds established herein are fully general, while the explicit conversion protocol and dynamical analysis serve as a compelling proof-of-principle demonstration in qubit systems.We establish a rigorous framework that identifies imaginarity as a fundamental resource inherent in quantum coherence. By means of a geometric decomposition, we partition coherence into distinct imaginarity and residual components, thereby revealing a universal hierarchical relationship among these resources. For bipartite systems, this decomposition provides explicit bounds on the extent to which nonlocal correlations and imaginarity limit local coherence generation. Furthermore, we devise an explicit operational protocol that converts imaginarity into usable coherence, demonstrating the direct interconvertibility of these resources under physically admissible operations. The dynamical evolution under diagonal Hamiltonians is fully characterized, showing that while total coherence is conserved, imaginarity and residual coherence exhibit complementary oscillations. Our results provide a rigorous geometric and operational characterization of imaginarity as a fundamental constituent of quantum coherence, offering concrete insights for resource management in distributed quantum technologies. The geometric framework and theoretical bounds established herein are fully general, while the explicit conversion protocol and dynamical analysis serve as a compelling proof-of-principle demonstration in qubit systems.

quant-pharXiv:2607.14435Physical Review AJul 17, 20260 citations

Quantification of the Resource Theory of Imaginarity Revisited

Yue Han, Naihong Hu

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

Erasing imaginarity: Selective imaginarity-breaking channels and non-selective imaginarity-breaking channels

Yuhang Xie, Yanjun Chu, Chenyang Cui

Physics Letters AMar 11, 20261 citation

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.