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Quantum State Preparation Representation Quantum Simulation Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations

Relative volume of comparable pairs under semigroup majorization

arXiv
Authors: Fabio Deelan Cunden, Jakub Czartowski, Giovanni Gramegna, A. de Oliveira Junior

Year

2024

Paper ID

37449

Status

Preprint

Abstract Read

~2 min

Abstract Words

108

Citations

N/A

Abstract

Any semigroup mathcal{S} of stochastic matrices induces a semigroup majorization relation prec^{mathcal{S}} on the set Δn-1 of probability n-vectors. Pick X,Y at random in Δn-1: what is the probability that X and Y are comparable under prec^{mathcal{S}}? We review recent asymptotic $n→infty$ results and conjectures in the case of majorization relation when $mathcal{S}$ is the set of doubly stochastic matrices, discuss natural generalisations, and prove a new asymptotic result in the case of majorization, and new exact finite-n formulae in the case of UT-majorization relation, i.e. when mathcal{S} is the set of upper-triangular stochastic matrices.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • Any semigroup mathcalS of stochastic matrices induces a semigroup majorization relation prec^mathcalS on the set Δn-1 of probability n-vectors.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2410.23196 [2] arXiv https://arxiv.org/abs/2410.23196 [3] Publisher https://arxiv.org/abs/2410.23196

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