aiqbench analysis
This research advances the resource theory of imaginarity by deriving exact attenuation theorems for single-qubit states under real quantum noise channels and establishing quantitative links between photon loss and residual imaginarity in photonic dual-rail encodings. By distinguishing operational de-imaginary power from reference-state loss, the study provides rigorous benchmarks for preserving quantum coherence in noisy environments, which is critical for fault-tolerant quantum computation architectures.
Quantification of the Resource Theory of Imaginarity Revisited
arXiv:2603.13980v2 Announce Type: replace Abstract: 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 $\Omega_{++}=|+\rangle\langle+|\otimes|+\rangle\langle+|$ 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.
Abstract: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 $\Omega_{++}=|+\rangle\langle+|\otimes|+\rangle\langle+|$ 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.
Quantum Physics (quant-ph); Information Theory (cs.IT); Mathematical Physics (math-ph); Optimization and Control (math.OC); Quantum Algebra (math.QA)
arXiv:2603.13980 [quant-ph]
(or arXiv:2603.13980v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2603.13980 Focus to learn more arXiv-issued DOI via DataCite
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