Abstract:

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.

Authors:

• Jianxin Chen
• Shane Grogan
• Nathaniel Johnston
• Chi-Kwong Li
• Sarah Plosker

Download:

• Official publication from Physical Review A
• Preprint from arXiv:1601.06269 [quant-ph]
• Local preprint [pdf]
• Talk slides: version 1, version 2, version 3 [ppt]

Cite as:

• 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.

Supplementary material:

• 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)
• The modified trace distance of coherence is constant on most pure states – a later publication that investigates a closely-related modification of the trace distance of coherence