Optimal quantum state reconstruction for cold trapped ions

TL;DR

This paper presents an optimal quantum state tomography method for multi-qubit systems using trapped ions, leveraging mutually unbiased measurements and analyzing their physical complexity for efficient implementation.

Contribution

It introduces a physically feasible optimal tomography protocol for trapped ion qubits based on mutually unbiased measurements and evaluates their complexity.

Findings

The protocol achieves optimal state reconstruction accuracy.

Mutually unbiased measurements are feasible with current ion trap technology.

Physical complexity analysis guides efficient implementation.

Abstract

We study the physical implementation of an optimal tomographic reconstruction scheme for the case of determining the state of a multi-qubit system, where trapped ions are used for defining qubits. The protocol is based on the use of mutually unbiased measurements and on the physical information described in H. H\"{a}ffner \emph{et. al} [Nature \textbf{438}, 643-646 (2005)]. We introduce the concept of physical complexity for different types of unbiased measurements and analyze their generation in terms of one and two qubit gates for trapped ions.