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arXiv · 2404.16279

Quantum Imaginarity-Mixedness Trade-off: Characterizing Maximally Imaginary Mixed States

Bin Chen·Shao-Ming Fei
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Abstract

We investigate the trade-off relations between imaginarity and mixedness in arbitrary $d$-dimensional quantum systems. For given mixedness, a quantum state with maximum imaginarity is defined to be a "maximally imaginary mixed state" (MIMS). By using the $l_{1}$ norm of imaginarity and the normalized linear entropy, we conclusively identify the MIMSs for both qubit and qutrit systems. For high-dimensional quantum systems, we present a comprehensive class of MIMSs, which also gives rise to complementarity relations between the $1$-norm of imaginarity and the $1$-norm of mixedness, as well as between the relative entropy of imaginarity and the von Neumann entropy. Furthermore, we examine the evolution of the trade-off relation for single-qubit states under four specific Markovian channels: bit flip channel, phase damping channel, depolarizing channel and amplitude damping channel.

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Bin Chen, Shao-Ming Fei. 2024-04-25. Quantum Imaginarity-Mixedness Trade-off: Characterizing Maximally Imaginary Mixed States. https://arxiv.org/abs/2404.16279

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