Quantum state tomography with informationally complete POVMs generated in the time domain

TL;DR

This paper introduces a method for quantum state tomography using time-domain POVMs generated dynamically, enabling state reconstruction with limited measurements on qubits and qutrits.

Contribution

It presents a novel framework for generating informationally complete POVMs in the time domain, expanding quantum tomography capabilities with fewer initial measurements.

Findings

Feasible quantum state tomography with limited measurements.

Demonstrated on qubits and qutrits.

Applicable to certain dynamical maps.

Abstract

The article establishes a framework for dynamic generation of informationally complete POVMs in quantum state tomography. Assuming that the evolution of a quantum system is given by a dynamical map in the Kraus representation, one can switch to the Heisenberg picture and define the measurements in the time domain. Consequently, starting with an incomplete set of positive operators, one can obtain sufficient information for quantum state reconstruction by multiple measurements. The framework has been demonstrated on qubits and qutrits. For some types of dynamical maps, it suffices to initially have one measurement operator. The results demonstrate that quantum state tomography is feasible even with limited measurement potential.