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Laser Physics Letters

Estimation for geometric imaginarity measure of superposition states

Chengyang Zhang, Zhihua Guo, Cao Huai-xin

Published Nov 1, 2025• 3 citations
Publisher

Abstract

Abstract Quantum imaginarity plays a crucial role in quantum information theory and represents one of the most distinctive features of quantum mechanics. In this paper, we derive a lower bound for the imaginarity of the superposition composed of two orthogonal states based on the geometric imaginarity measure. We further generalize the result to the superposition of n orthogonal states and establish a lower bound. These findings provide a more precise estimation of the imaginarity of superposition states.

DOI
10.1088/1612-202x/ae18ac

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Abstract Quantum imaginarity plays a crucial role in quantum information theory and represents one of the most distinctive features of quantum mechanics. In this paper, we derive a lower bound for the imaginarity of the superposition composed of two orthogonal states based on the geometric imaginarity measure. We further generalize the result to the superposition of n orthogonal states and establish a lower bound. These findings provide a more precise estimation of the imaginarity of superposition states.
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Abstract Quantum coherence is a fundamental resource in quantum information science and one of the most distinctive features of quantum mechanics. In this paper, we derive a tight upper bound for the coherence of the superposition composed of two orthogonal states using ℓ 1 -norm coherence measure, demonstrating that our upper bound is tighter than the one presented by Yue et al (2017 Sci. Rep. 7 4006). Furthermore, we extend the result to the superposition of n orthogonal states and establish the optimal upper bound for its coherence. Our results provide a more accurate estimate of the coherence of the superposition state.
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Complex numbers play an indispensable role in quantum mechanics and quantum information, as validated by both theoretical analysis and experimental verification. Since quantum information processing inherently relies on quantum channels, the resource theory for quantum channels is equally fundamental to that for quantum states. In this paper, we propose two frameworks for quantifying the imaginarity of Gaussian channels. The first framework regards all real superchannels as free superchannels. Within this setting, we introduce two concrete imaginarity measures for Gaussian channels: I_s^GC based on existing imaginarity measures of Gaussian states, and I_d^GC derived directly from the intrinsic parameters of Gaussian channels, which enjoys high computational simplicity. The second framework adopts only a proper subset of real superchannels as free superchannels. Under this framework, we put forward another imaginarity measure I_c^GC , which is fully determined by the inherent parameters of Gaussian channels and features continuity as well as tractable computation. As a practical application, we employ I_c^GC to investigate the dynamical behavior of Quantum Brownian Motion Gaussian channels throughout the entire evolutionary process.
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.