Joint quasiprobability distribution on the measurement outcomes of MUB-driven operators

• URL: http://arxiv.org/abs/2101.08109v1
• Date: Wed, 20 Jan 2021 13:10:26 GMT
• Title: Joint quasiprobability distribution on the measurement outcomes of MUB-driven operators
• Authors: H S Smitha Rao, Swarnamala Sirsi and Karthik Bharath
• Abstract summary: Method is based on a complete set of orthonormal commuting operators related to Mutually Unbiased Bases. We geometrically characterise the set of states for which the quasiprobability distribution is non-negative. The set is an $(n2-1)$-dimensional convex polytope with $n+1$ as the only pure states, $nn+1$ number of higher dimensional faces, and $n3(n+1)/2$ edges.
• Score: 2.9005223064604078
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a method to define quasiprobability distributions for general spin-$j$ systems of dimension $n=2j+1$, where $n$ is a prime or power of prime. The method is based on a complete set of orthonormal commuting operators related to Mutually Unbiased Bases which enable (i) a parameterisation of the density matrix and (ii) construction of measurement operators that can be physically realised. As a result we geometrically characterise the set of states for which the quasiprobability distribution is non-negative, and can be viewed as a joint distribution of classical random variables assuming values in a finite set of outcomes. The set is an $(n^2-1)$-dimensional convex polytope with $n+1$ vertices as the only pure states, $n^{n+1}$ number of higher dimensional faces, and $n^3(n+1)/2$ edges.

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