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

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 coherence-induced state ordering under Markovian channels

Long-Mei Yang, Bin Chen, Shao-Ming Fei +1 more

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

Dynamics of coherence-induced state ordering under Markovian channels

Yang, L., Chen, B., Fei, S. +1 more

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 l1 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 l1 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.

Jan 1, 20185 citations

The Geometry of Quantum Coherence for Two Qubit $X$ States

Yaokun Wang, Lian-He Shao, Yu-Ran Zhang

We plot the geometry of several distance-based quantifiers of coherence for Bell-diagonal states. We find that along with both $l_{1}$ norm and relative entropy of coherence changes continuously from zero to one, their surfaces move from the separable regions to the entangled regions. Based on this fact, it is more illuminating to use an intuitive geometry to explain quantum states with nonzero coherence can be used for entanglement creation, rather than the other way around. We find the necessary and sufficient conditions that quantum discord of Bell-diagonal states equal to its relative entropy of coherence and depict the surfaces of the equality. We give surfaces of relative entropy of coherence for $X$ states. We show the surfaces of dynamics of relative entropy of coherence for Bell-diagonal states under local nondissipative channels and find that all coherence under local nondissipative channels decrease.We plot the geometry of several distance-based quantifiers of coherence for Bell-diagonal states. We find that along with both $l_{1}$ norm and relative entropy of coherence changes continuously from zero to one, their surfaces move from the separable regions to the entangled regions. Based on this fact, it is more illuminating to use an intuitive geometry to explain quantum states with nonzero coherence can be used for entanglement creation, rather than the other way around. We find the necessary and sufficient conditions that quantum discord of Bell-diagonal states equal to its relative entropy of coherence and depict the surfaces of the equality. We give surfaces of relative entropy of coherence for $X$ states. We show the surfaces of dynamics of relative entropy of coherence for Bell-diagonal states under local nondissipative channels and find that all coherence under local nondissipative channels decrease.

arXiv:1703.02440Mar 7, 20170 citations

Dynamics of skew information-based quantum coherence under correlated noisy channels

Guoyou Wang, You-neng Guo, Zhi‐Hong Deng

In this paper, we study analytically the skew information-based coherence, and compare its dynamics with that of the l1 norm of coherence for two-qubit Bell-diagonal states under the influence of correlated Pauli channels, such as correlated dephase, depolarizing and classical noisy channels, respectively. The similar as well as different features between the skew information-based coherence and l1 norm of coherence are discussed. In addition, the physical mechanism of preserving quantum coherence based on memory coefficient of correlated channels and non-Markovian memory effect is also expounded.In this paper, we study analytically the skew information-based coherence, and compare its dynamics with that of the l1 norm of coherence for two-qubit Bell-diagonal states under the influence of correlated Pauli channels, such as correlated dephase, depolarizing and classical noisy channels, respectively. The similar as well as different features between the skew information-based coherence and l1 norm of coherence are discussed. In addition, the physical mechanism of preserving quantum coherence based on memory coefficient of correlated channels and non-Markovian memory effect is also expounded.

Journal of Modern OpticsApr 26, 20223 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

We plot the geometry of several distance-based quantifiers of coherence for Bell-diagonal states. We find that along with both

l_{1}

norm and relative entropy of coherence changes continuously from zero to one, their surfaces move from the separable regions to the entangled regions. Based on this fact, it is more illuminating to use an intuitive geometry to explain quantum states with nonzero coherence can be used for entanglement creation, rather than the other way around. We find the necessary and sufficient conditions that quantum discord of Bell-diagonal states equal to its relative entropy of coherence and depict the surfaces of the equality. We give surfaces of relative entropy of coherence for

X

states. We show the surfaces of dynamics of relative entropy of coherence for Bell-diagonal states under local nondissipative channels and find that all coherence under local nondissipative channels decrease.