We propose a family of coherence monotones, named the \emph{generalized coherence concurrence} (or coherence $k$ -concurrence), which has a close relation with the generalized entanglement concurrence. The coherence $k$ -concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than $k$ , and a state can be converted to a state with nonzero entanglement $k$ -concurrence via incoherent operations if and only if the state has nonzero coherence $k$ -concurrence. The generalized coherence concurrence can be considered as the entanglement-based coherence monotone.We propose a family of coherence monotones, named the \emph{generalized coherence concurrence} (or coherence $k$-concurrence), which has a close relation with the generalized entanglement concurrence. The coherence $k$-concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than $k$, and a state can be converted to a state with nonzero entanglement $k$-concurrence via incoherent operations if and only if the state has nonzero coherence $k$-concurrence. The generalized coherence concurrence can be considered as the entanglement-based coherence monotone.

Feb 20, 20170 citations

Generalized coherence concurrence and path distinguishability

Seungbeom Chin

Abstract We propose a new family of coherence monotones, named the generalized coherence concurrence (or coherence k -concurrence), which is an analogous concept to the generalized entanglement concurrence. The coherence k -concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than k , and a state can be converted to a state with nonzero entanglement k -concurrence via incoherent operations if and only if the state has nonzero coherence k -concurrence. We apply the coherence concurrence family to the problem of wave-particle duality in multi-path interference phenomena. We obtain a sharper equation for path distinguishability (which witnesses the duality) than the known one and show that the amount of each concurrence for the quanton state determines the number of slits which are identified unambiguously.Abstract We propose a new family of coherence monotones, named the generalized coherence concurrence (or coherence k -concurrence), which is an analogous concept to the generalized entanglement concurrence. The coherence k -concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than k , and a state can be converted to a state with nonzero entanglement k -concurrence via incoherent operations if and only if the state has nonzero coherence k -concurrence. We apply the coherence concurrence family to the problem of wave-particle duality in multi-path interference phenomena. We obtain a sharper equation for path distinguishability (which witnesses the duality) than the known one and show that the amount of each concurrence for the quanton state determines the number of slits which are identified unambiguously.

arXiv:1702.06061Journal of Physics A Mathematical and TheoreticalOct 3, 201719 citations

Quantum Coherence

José Tito Mendonça, Hugo Terças

Springer series on atomic, optical, and plasma physicsOct 8, 20120 citations

Quantum coherence of mixed states under noisy channels in noninertial frames

Tangrui Liao, Junhao Yang, Tinggui Zhang +1 more

We focus our attention on tripartite mixed states as initial states, and apply coherence concurrence to investigate quantum coherence properties in the background of a Schwarzschild black hole under phase damping, phase flip and bit flip channels, respectively. Several analytic complementary relationships based on coherence concurrence for tripartite subsystems are proposed. In the case of the bit flip channel, the behavior of the coherence concurrence is similar to the one of the phase damping channel, the accessible coherence concurrence always degrades as the Hawking acceleration rising, but sudden death never occurs, while the inaccessible coherence increases from zero monotonically. Interestingly, the coherence concurrence is decreasing at first and then increasing as the decay probability rising under phase flip channel. Unlike the case of tripartite pure states, the coherence concurrence of mixed state with X shape is equal to $l_1$ -norm of coherence.We focus our attention on tripartite mixed states as initial states, and apply coherence concurrence to investigate quantum coherence properties in the background of a Schwarzschild black hole under phase damping, phase flip and bit flip channels, respectively. Several analytic complementary relationships based on coherence concurrence for tripartite subsystems are proposed. In the case of the bit flip channel, the behavior of the coherence concurrence is similar to the one of the phase damping channel, the accessible coherence concurrence always degrades as the Hawking acceleration rising, but sudden death never occurs, while the inaccessible coherence increases from zero monotonically. Interestingly, the coherence concurrence is decreasing at first and then increasing as the decay probability rising under phase flip channel. Unlike the case of tripartite pure states, the coherence concurrence of mixed state with X shape is equal to $l_1$ -norm of coherence.

quant-pharXiv:2602.20785Feb 25, 20260 citations

Quantum coherence

Karen Southwell

Jan 1, 20080 citations

We propose a family of coherence monotones, named the \emph{generalized coherence concurrence} (or coherence

k

-concurrence), which has a close relation with the generalized entanglement concurrence. The coherence

k

-concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than

k

, and a state can be converted to a state with nonzero entanglement

k

-concurrence via incoherent operations if and only if the state has nonzero coherence

k

-concurrence. The generalized coherence concurrence can be considered as the entanglement-based coherence monotone.

l_1

-norm of coherence.