Abstract This paper studies the order relations among various quantum coherence measures in a single-qubit system. Ten representative coherence measures are selected from three categories: distance-based, fidelity-based, and relative entropy-based measures. The analytical expressions for the coherence values are derived in the Bloch sphere representation of the single-qubit state, and the order relations within the same category and across categories are systematically analyzed. The study shows that coherence measures within the same category generally maintain consistent order relations in the single-qubit system. However, there is typically no fixed order relation between fidelity-based coherence measures (represented by geometric coherence) and relative entropy-based coherence measures (represented by α -affinity coherence measures). Yet, in pure single-qubit states and certain restricted sets of mixed states, these two types of coherence measures exhibit the same order relation. The results indicate that the order relations between coherence measures depend not only on their construction but also on the quantum state space structure and the constraints on parameters.Abstract This paper studies the order relations among various quantum coherence measures in a single-qubit system. Ten representative coherence measures are selected from three categories: distance-based, fidelity-based, and relative entropy-based measures. The analytical expressions for the coherence values are derived in the Bloch sphere representation of the single-qubit state, and the order relations within the same category and across categories are systematically analyzed. The study shows that coherence measures within the same category generally maintain consistent order relations in the single-qubit system. However, there is typically no fixed order relation between fidelity-based coherence measures (represented by geometric coherence) and relative entropy-based coherence measures (represented by α -affinity coherence measures). Yet, in pure single-qubit states and certain restricted sets of mixed states, these two types of coherence measures exhibit the same order relation. The results indicate that the order relations between coherence measures depend not only on their construction but also on the quantum state space structure and the constraints on parameters.

Laser Physics LettersJun 1, 20260 citations

Ordering states with entanglement measures

S. Virmani, Martin Bodo Plenio

arXiv:quant-ph/9911119Physics Letters AApr 1, 200096 citations

Sufficient Conditions of the Same State Order Induced by Coherence*

Fu-Gang Zhang, Yongming Li

Abstract In this paper, we study coherence-induced state ordering with Tsallis relative entropy of coherence, relative entropy of coherence and l 1 norm of coherence, and give the sufficient conditions of the same state order induced by above coherence measures. First, we show that the above measures give the same ordering for single-qubit states in some special cases. Second, we consider some special states in a d -dimensional quantum system. We show that the above measures generate the same ordering for these special states. Finally, we discuss dynamics of coherence-induced state ordering under Markovian channels. We find amplitude damping channel changes the coherence-induced ordering even though for single-qubit states with fixed mixedness.Abstract In this paper, we study coherence-induced state ordering with Tsallis relative entropy of coherence, relative entropy of coherence and l 1 norm of coherence, and give the sufficient conditions of the same state order induced by above coherence measures. First, we show that the above measures give the same ordering for single-qubit states in some special cases. Second, we consider some special states in a d -dimensional quantum system. We show that the above measures generate the same ordering for these special states. Finally, we discuss dynamics of coherence-induced state ordering under Markovian channels. We find amplitude damping channel changes the coherence-induced ordering even though for single-qubit states with fixed mixedness.

Communications in Theoretical PhysicsAug 1, 20182 citations

Coherent-induced state ordering with fixed mixedness

Fu-Gang Zhang, Yongming Li

In this paper, we study coherence-induced state ordering with Tsallis relative entropy of coherence, relative entropy of coherence and $l_{1}$ norm of coherence. Firstly, we show that these measures give the same ordering for single-qubit states with a fixed mixedness or a fixed length along the direction $σ_{z}$ . Secondly, we consider some special cases of high dimensional states, we show that these measures generate the same ordering for the set of high dimensional pure states if any two states of the set satisfy majorization relation. Moreover, these three measures generate the same ordering for all $X$ states with a fixed mixedness. Finally, we discuss dynamics of coherence-induced state ordering under Markovian channels. We find phase damping channel don't change the coherence-induced state ordering for some single-qubit states with fixed mixedness, instead amplitude damping channel change the coherence-induced ordering even though for single-qubit states with fixed mixedness.In this paper, we study coherence-induced state ordering with Tsallis relative entropy of coherence, relative entropy of coherence and $l_{1}$ norm of coherence. Firstly, we show that these measures give the same ordering for single-qubit states with a fixed mixedness or a fixed length along the direction $σ_{z}$. Secondly, we consider some special cases of high dimensional states, we show that these measures generate the same ordering for the set of high dimensional pure states if any two states of the set satisfy majorization relation. Moreover, these three measures generate the same ordering for all $X$ states with a fixed mixedness. Finally, we discuss dynamics of coherence-induced state ordering under Markovian channels. We find phase damping channel don't change the coherence-induced state ordering for some single-qubit states with fixed mixedness, instead amplitude damping channel change the coherence-induced ordering even though for single-qubit states with fixed mixedness.

arXiv:1704.02244Apr 7, 20172 citations

In this paper, we study coherence-induced state ordering with Tsallis relative entropy of coherence, relative entropy of coherence and

l_{1}

norm of coherence. Firstly, we show that these measures give the same ordering for single-qubit states with a fixed mixedness or a fixed length along the direction

σ_{z}

. Secondly, we consider some special cases of high dimensional states, we show that these measures generate the same ordering for the set of high dimensional pure states if any two states of the set satisfy majorization relation. Moreover, these three measures generate the same ordering for all

X

states with a fixed mixedness. Finally, we discuss dynamics of coherence-induced state ordering under Markovian channels. We find phase damping channel don't change the coherence-induced state ordering for some single-qubit states with fixed mixedness, instead amplitude damping channel change the coherence-induced ordering even though for single-qubit states with fixed mixedness.