Coherence measure: Logarithmic coherence number

Abstract

We introduce a measure of coherence, which is extended from the coherence rank via the standard convex roof construction, we call it the logarithmic coherence number. This approach is parallel to the Schmidt measure in entanglement theory, We study some interesting properties of the logarithmic coherence number, and show that this quantifier can be considered as a proper coherence measure. We also find that the logarithmic coherence number can be calculated exactly for a large class of states. We give the relationship between coherence and entanglement in bipartite system, and our results are generalized to multipartite setting. Finally, we find that the creation of entanglement with bipartite incoherent operations is bounded by the logarithmic coherence number of the initial system during the process.

arXiv comment7 pages. Comments are welcome!

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Cited by in corpus (15)

• Quantum Discord for multiqubit Systems
• Efficient estimation of multipartite quantum coherence
• Epsilon-smooth measure of coherence
• Wave-particle duality employing quantum coherence in superposition with non-orthogonal pointers
• Average skew information-based coherence and its typicality for random quantum states
• Skew information-based coherence generating power of quantum channels
• Tomographic Witnessing and Holographic Quantifying of Coherence
• Coherence-mixedness trade-offs
• Common Coherence Witnesses and Common Coherent States
• Witnessing quantum coherence with prior knowledge of observables
• Noncommutative coherence and quantum phase estimation algorithm
• Analytic Formulas for Quantum Discord of Special Families of N-Qubit States
• The tightness of multipartite coherence from spectrum estimation
• Closed expressions for one-qubit states of convex roof coherence measures
• Simplest non-additive measures of quantum resources