Generic aspects of the resource theory of quantum coherence

• URL: http://arxiv.org/abs/2010.06533v3
• Date: Thu, 1 Jul 2021 06:18:27 GMT
• Title: Generic aspects of the resource theory of quantum coherence
• Authors: Fabio Deelan Cunden, Paolo Facchi, Giuseppe Florio, Giovanni Gramegna
• Abstract summary: 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 as $nrightarrowinfty$. We also study the maximal success probability of incoherent conversions and find an explicit formula for its large-$n$ distribution.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $n\rightarrow\infty$. 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.

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