The l1 Norm of Coherence of Assistance

Abstract

We introduce and study the l1 norm of coherence of assistance both theoretically and operationally. We first provide an upper bound for the l1 norm of coherence of assistance and show a necessary and sufficient condition for the saturation of the upper bound. For two and three dimensional quantum states, the analytical expression of the l1 norm of coherence of assistance is given. Operationally, the mixed quantum coherence can always be increased with the help of another party' s local measurement and one way classical communication since the l1 norm of coherence of assistance, as well as the relative entropy of coherence of assistance, is shown to be strictly larger than the original coherence. The relation between the l1 norm of coherence of assistance and entanglement is revealed. Finally, a comparison between the l1 norm of coherence of assistance and the relative entropy of coherence of assistance is made.

References in corpus (4)

• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• Entanglement of Multipartite Schmidt-correlated States
• Coherence of assistance and regularized coherence of assistance
• Assisted coherence distillation of certain mixed states

Cited by in corpus (5)

• Average skew information-based coherence and its typicality for random quantum states
• Based-nonequilibrium-environment non-Markovianity, quantum Fisher information and quantum coherence
• Geometry of skew information-based quantum coherence
• Coherence of assistance and assisted maximally coherent states
• Coherence Concurrence for X States