Quantifying the coherence of pure quantum states
In recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an explicit characterization of the closest incoherent state to a given pure state under the trace distance measure of coherence, and we affirm a recent conjecture that the ℓ1 measure of coherence of a pure state is never smaller than its relative entropy of coherence. We then use our result to show that the states maximizing the trace distance of coherence are exactly the maximally coherent states, and we derive a new inequality relating the negativity and distillable entanglement of pure states.
- Official publication from Physical Review A
- Preprint from arXiv:1601.06269 [quant-ph]
- Local preprint [pdf]
- J. Chen, S. Grogan, N. Johnston, C.-K. Li, and S. Plosker. Quantifying the coherence of pure quantum states. Physical Review A, 94:042313, 2016.
- MATLAB code for computing the trace distance of coherence of a pure state via the method given in this paper, and also via the (slower) naive method of semidefinite programming
- QETLAB function for computing the trace distance of coherence (works with both pure and mixed states, and automatically chooses the fastest possible algorithm)