Generic aspects of the resource theory of quantum coherence

Abstract

The class of incoherent operations induces a pre-order on the set of quantum pure states, defined by the possibility of converting one state into the other by transformations within the class. We prove that if two $n$-dimensional pure states are chosen independently according to the natural uniform distribution, then the probability that they are comparable vanishes as $n\to \infty$. We also study the maximal success probability of incoherent conversions and find an explicit formula for its large-$n$ asymptotic distribution. Our analysis is based on the observation that the extreme values (largest and smallest components) of a random point uniformly sampled from the unit simplex are distributed asymptotically as certain explicit homogeneous Markov chains.

12 pages, 4 figures

References in corpus (3)

• Aspects of generic entanglement
• Quantifying Superposition
• Performance of Dense Coding and Teleportation for Random States --Augmentation via Pre-processing

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