Coherence and imaginarity of quantum states

• URL: http://arxiv.org/abs/2404.06210v1
• Date: Tue, 9 Apr 2024 10:58:27 GMT
• Title: Coherence and imaginarity of quantum states
• Authors: Jianwei Xu,
• Abstract summary: In BCP framework, a quantum state is called incoherent if it is diagonal in the fixed orthonormal basis. We show that any coherence measure $C$ in BCP framework has the property $C(rho )-C($Re$rho )geq 0$ if $C$ is in quantifying under state complex conjugation. We also establish some similar results for bosonic Gaussian states.
• Score: 0.32634122554914
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\rho $ has nonzero imaginary part, then $\rho $ 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 $C(\rho )-C($Re$\rho )\geq 0$ if $C$ is invariant under state complex conjugation, i.e., $C(\rho )=C(\rho ^{\ast })$, here $\rho ^{\ast }$ is the conjugate of $\rho ,$ Re$\rho $ is the real part of $\rho .$ If $C$ does not satisfy $C(\rho )=C(\rho ^{\ast }),$ we can define a new coherence measure $C^{\prime }(\rho )=\frac{1}{2}[C(\rho )+C(\rho ^{\ast })]$ such that $C^{\prime }(\rho )=C^{\prime }(\rho ^{\ast }).$ We also establish some similar results for bosonic Gaussian states.

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