Mutually disjoint, maximally commuting set of physical observables for optimum state determination

TL;DR

This paper develops a method to construct a set of maximally commuting, physically realizable observables from Mutually Unbiased Bases for spin systems, optimizing quantum state determination.

Contribution

It introduces a general procedure to create orthonormal, maximally commuting operators from MUBs applicable to various spin systems and finite-dimensional quantum states.

Findings

Constructed operators are physically implementable and maximally commuting.

Method applies to spin-1, spin-3/2, spin-2, and higher-dimensional systems.

Framework extends to arbitrary finite-dimensional density matrices.

Abstract

We consider the state determination problem using Mutually Unbiased Bases(MUBs). For spin-1, spin-3/2 and spin-2 systems, analogous to Pauli operators of spin-1/2 system, which are experimentally implementable and correspond to the optimum measurement in characterizing the density matrix, we describe a procedure to construct an orthonormal set of operators from MUBs. The constructed operators are maximally commuting, can be physically realized, and correspond to physical observables. The method of construction is general enough to allow for extensions to higher-dimensional spin systems and arbitrary density matrices in finite dimensions for which MUBs are known to exist.