Quantum Imaginarity-Mixedness Trade-off: Characterizing Maximally Imaginary Mixed States
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913328976101376 |
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| author | Chen, Bin Fei, Shao-Ming |
| author_facet | Chen, Bin Fei, Shao-Ming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16279 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Imaginarity-Mixedness Trade-off: Characterizing Maximally Imaginary Mixed States Chen, Bin Fei, Shao-Ming Quantum Physics 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. |
| title | Quantum Imaginarity-Mixedness Trade-off: Characterizing Maximally Imaginary Mixed States |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.16279 |