How to Project onto an Arbitrary Single-Photon Wavepacket

TL;DR

This paper develops methods for projecting onto arbitrary single-photon wavepackets using optimized POVMs, enabling high-efficiency, low-noise measurements crucial for quantum communication and super-resolution applications.

Contribution

It introduces a comprehensive quantum framework and practical prescriptions for high-fidelity, single-shot time-frequency measurements of single photons, advancing quantum detection technology.

Findings

Constructed ideal and realistic POVMs for arbitrary single-photon wavepackets

Achieved high-efficiency, low-noise projection techniques

Discussed fundamental limits and trade-offs in single-photon detection

Abstract

The time-frequency degree of freedom of the electromagnetic field is the final frontier for single-photon measurements. The temporal and spectral distribution a measurement retrodicts (that is, the state it projects onto) is determined by the detector's intrinsic resonance structure. In this paper, we construct ideal and more realistic positive operator-valued measures (POVMs) that project onto arbitrary single-photon wavepackets with high efficiency and low noise. We discuss applications to super-resolved measurements and quantum communication. In doing so we will give a fully quantum description of the entire photo detection process, give prescriptions for (in principle) performing single-shot Heisenberg-limited time-frequency measurements of single photons, and discuss fundamental limits and trade-offs inherent to single-photon detection.