Phase estimation of time-bin qudits by time-resolved single-photon counting

TL;DR

This paper develops a quantum state tomography method for time-bin qudits in fiber optics, accounting for detector noise, and analyzes how fiber length and detector jitter affect state reconstruction quality.

Contribution

It introduces a POVM-based framework for QST of time-bin qudits considering realistic detector noise, with detailed numerical analysis of performance dependencies.

Findings

State fidelity decreases with longer fiber lengths.

Detector jitter significantly impacts phase reconstruction accuracy.

Optimal parameters depend on fiber length and detector characteristics.

Abstract

We present a comprehensive framework for quantum state tomography (QST) of time-bin qudits sent through a fiber. Starting from basic assumptions, we define a positive-operator valued measure (POVM) which is then applied to the quantum state reconstruction problem. A realistic scenario is considered where the time uncertainty of the detector is treated as a source of experimental noise. The performance of the quantum tomography framework is examined through a series of numerical simulations conducted for different parameters describing the apparatus. The quality of state recovery, quantified by the notion of minimum fidelity, is depicted on graphs for a range of fiber lengths. Special attention is paid to relative phase reconstruction for qubits and qutrits. The results present relevant interdependence between the fiber length and the detector jitter.