Optimal reconstruction of states in qutrits system

TL;DR

This paper presents an optimal and experimentally feasible scheme for quantum state tomography in multi-qutrit systems, minimizing the number of operations needed for accurate state reconstruction.

Contribution

It introduces a minimal-operation scheme for qutrit state tomography based on mutually unbiased measurements, including decomposition into basic unitary operations and complexity minimization.

Findings

Optimal scheme reduces the number of conditional operations

Decomposition into single- and two-qutrit unitaries is feasible

Physical complexity varies with different MUB structures

Abstract

Based on mutually unbiased measurements, an optimal tomographic scheme for the multiqutrit states is presented explicitly. Because the reconstruction process of states based on mutually unbiased states is free of information waste, we refer to our scheme as the optimal scheme. By optimal we mean that the number of the required conditional operations reaches the minimum in this tomographic scheme for the states of qutrit systems. Special attention will be paid to how those different mutually unbiased measurements are realized; that is, how to decompose each transformation that connects each mutually unbiased basis with the standard computational basis. It is found that all those transformations can be decomposed into several basic implementable single- and two-qutrit unitary operations. For the three-qutrit system, there exist five different mutually unbiased-bases structures with different entanglement properties, so we introduce the concept of physical complexity to minimize the number of nonlocal operations needed over the five different structures. This scheme is helpful for experimental scientists to realize the most economical reconstruction of quantum states in qutrit systems.