Coherence and imaginarity of quantum states
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912183739219968 |
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| author | Xu, Jianwei |
| author_facet | Xu, Jianwei |
| contents | Baumgratz, Cramer and Plenio established a rigorous framework (BCP framework) for quantifying the coherence of quantum states [\href{http://dx.doi.org/10.1103/PhysRevLett.113.140401}{Phys. Rev. Lett. 113, 140401 (2014)}]. In BCP framework, a quantum state is called incoherent if it is diagonal in the fixed orthonormal basis, and a coherence measure should satisfy some conditions. For a fixed orthonormal basis, if a quantum state $ρ$ has nonzero imaginary part, then $ρ$ must be coherent. How to quantitatively characterize this fact? In this work, we show that any coherence measure $C$ in BCP framework has the property $C(ρ)-C($Re$ρ)\geq 0$ if $C$ is invariant under state complex conjugation, i.e., $C(ρ)=C(ρ^{\ast })$, here $ρ^{\ast }$ is the conjugate of $ρ,$ Re$ρ$ is the real part of $ρ.$ If $C$ does not satisfy $C(ρ)=C(ρ^{\ast }),$ we can define a new coherence measure $C^{\prime }(ρ)=\frac{1}{2}[C(ρ)+C(ρ^{\ast })]$ such that $C^{\prime }(ρ)=C^{\prime }(ρ^{\ast }).$ We also establish some similar results for bosonic Gaussian states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coherence and imaginarity of quantum states Xu, Jianwei Quantum Physics Mathematical Physics Baumgratz, Cramer and Plenio established a rigorous framework (BCP framework) for quantifying the coherence of quantum states [\href{http://dx.doi.org/10.1103/PhysRevLett.113.140401}{Phys. Rev. Lett. 113, 140401 (2014)}]. In BCP framework, a quantum state is called incoherent if it is diagonal in the fixed orthonormal basis, and a coherence measure should satisfy some conditions. For a fixed orthonormal basis, if a quantum state $ρ$ has nonzero imaginary part, then $ρ$ must be coherent. How to quantitatively characterize this fact? In this work, we show that any coherence measure $C$ in BCP framework has the property $C(ρ)-C($Re$ρ)\geq 0$ if $C$ is invariant under state complex conjugation, i.e., $C(ρ)=C(ρ^{\ast })$, here $ρ^{\ast }$ is the conjugate of $ρ,$ Re$ρ$ is the real part of $ρ.$ If $C$ does not satisfy $C(ρ)=C(ρ^{\ast }),$ we can define a new coherence measure $C^{\prime }(ρ)=\frac{1}{2}[C(ρ)+C(ρ^{\ast })]$ such that $C^{\prime }(ρ)=C^{\prime }(ρ^{\ast }).$ We also establish some similar results for bosonic Gaussian states. |
| title | Coherence and imaginarity of quantum states |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2404.06210 |