Quantum state tomography with time-continuous measurements: reconstruction with resource limitations

TL;DR

This paper demonstrates quantum state tomography using continuous measurements with limited resources, successfully reconstructing states of single and two-qubit systems with high fidelity and minimal measurement settings.

Contribution

It introduces a resource-efficient method for quantum state tomography using continuous measurements, applicable to multi-qubit systems with minimal measurement requirements.

Findings

Achieved state fidelities over 0.98 with few thousand measurements.

Demonstrated successful reconstruction for single, remote, and interacting qubits.

Analyzed control strategies and Fisher information to optimize tomography.

Abstract

We propose and analyze quantum state estimation (tomography) using continuous quantum measurements with resource limitations, allowing the global state of many qubits to be constructed from only measuring a few. We give a proof-of-principle investigation demonstrating successful tomographic reconstruction of an arbitrary initial quantum state for three different situations: single qubit, remote qubit, and two interacting qubits. The tomographic reconstruction utilizes only a continuous weak probe of a single qubit observable, a fixed coupling Hamiltonian, together with single-qubit controls. In the single qubit case, a combination of the continuous measurement of an observable and a Rabi oscillation is sufficient to find all three unknown qubit state components. For two interacting qubits, where only one observable of the first qubit is measured, the control Hamiltonian can be implemented to transfer all quantum information to the measured observable, via the qubit-qubit interaction and Rabi oscillation controls applied locally on each qubit. We discuss different sets of controls by analyzing the unitary dynamics and the Fisher information matrix of the estimation in the limit of weak measurement, and simulate tomographic results numerically. As a result, we obtained reconstructed state fidelities in excess of 0.98 with a few thousand measurement runs.