Dynamics of coherence-induced state ordering under Markovian channels

We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels: amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qubit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l 1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α -entropies, while the bit flit channel does change for some special cases.We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels: amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qubit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l 1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α -entropies, while the bit flit channel does change for some special cases.

arXiv:1805.03898Frontiers of PhysicsMay 8, 201810 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

Dynamics of Cohering and Decohering Power under Markovian Channels*

Ming-Ming 明明 Chen 陈, Yu 宇 Luo 罗, Lian-He 连合 Shao 邵 +1 more

Abstract In this paper, we investigate the cohering and decohering power of the one-qubit Markovian channels with respect to coherence measures based on the l 1 - norm, the Rényi α - relative entropy and the Tsallis α - relative entropy of coherence, respectively. The amplitude damping channel, phase damping channel, depolarizing channel, and flip channels are analytically calculated. It shows that the decohering power of the amplitude damping channel on the x , y , and z basis is equal to each other. The same phenomenon can be seen for the phase damping channel and the flip channels. The cohering power for the phase damping channel and the flip channels on the x , y basis also equals to that on the z basis. However, the cohering and decohering power of the depolarizing channel is independent to the reference basises. And the cohering power of the amplitude damping channel on the x , y basis is different to that on the z basis.Abstract In this paper, we investigate the cohering and decohering power of the one-qubit Markovian channels with respect to coherence measures based on the l 1 - norm, the Rényi α - relative entropy and the Tsallis α - relative entropy of coherence, respectively. The amplitude damping channel, phase damping channel, depolarizing channel, and flip channels are analytically calculated. It shows that the decohering power of the amplitude damping channel on the x , y , and z basis is equal to each other. The same phenomenon can be seen for the phase damping channel and the flip channels. The cohering power for the phase damping channel and the flip channels on the x , y basis also equals to that on the z basis. However, the cohering and decohering power of the depolarizing channel is independent to the reference basises. And the cohering power of the amplitude damping channel on the x , y basis is different to that on the z basis.

arXiv:1612.05355Communications in Theoretical PhysicsNov 1, 20172 citations

Dynamics of Quantum Coherence in Bell-Diagonal States under Markovian Channels*

Yao-Kun 耀坤 Wang 王, Shao-Ming 少明 Fei 费, Zhi-Xi 志玺 Wang 王

Abstract We study the curves of coherence for the Bell-diagonal states including l 1 -norm of coherence and relative entropy of coherence under the Markovian channels in the first subsystem once. For a special Bell-diagonal state under bit-phase ip channel, we find frozen coherence under l 1 norm occurs, but relative entropy of coherence decrease. It illustrates that the occurrence of frozen coherence depends on the type of the measure of coherence. Also, we study the coherence evolution of Bell-diagonal states under Markovian channels in the first subsystem n times and find that coherence under depolarizing channel decreases initially then increases for small n and tends to zero for large n. The dynamics of coherence of the Bell-diagonal state under two independent same type local Markovian channels is discussed.Abstract We study the curves of coherence for the Bell-diagonal states including l 1 -norm of coherence and relative entropy of coherence under the Markovian channels in the first subsystem once. For a special Bell-diagonal state under bit-phase ip channel, we find frozen coherence under l 1 norm occurs, but relative entropy of coherence decrease. It illustrates that the occurrence of frozen coherence depends on the type of the measure of coherence. Also, we study the coherence evolution of Bell-diagonal states under Markovian channels in the first subsystem n times and find that coherence under depolarizing channel decreases initially then increases for small n and tends to zero for large n. The dynamics of coherence of the Bell-diagonal state under two independent same type local Markovian channels is discussed.

arXiv:1902.02962Communications in Theoretical PhysicsMay 1, 201910 citations

Dynamics of quantum coherence in Bell-diagonal states under Markovian channels

Wang, Y., Fei, S., Wang, Z.

Jan 1, 20191 citation

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.