# Photodetector figures of merit in terms of POVMs

## TL;DR

This paper develops a framework to characterize photodetectors using POVMs, linking classical and quantum figures of merit, and proposing a universal, model-independent comparison method based on measurement operators.

## Contribution

It introduces a comprehensive approach to define photodetector figures of merit via POVMs, enabling standardized, platform-independent comparisons across different detector types.

## Key findings

- Defined classical and quantum figures of merit in terms of POVMs
- Proposed a conjecture on trade-offs between classical and quantum figures
- Suggested POVMs as a universal platform for photodetector comparison

## Abstract

A photodetector may be characterized by various figures of merit such as response time, bandwidth, dark count rate, efficiency, wavelength resolution, and photon-number resolution. On the other hand, quantum theory says that any measurement device is fully described by its POVM, which stands for Positive-Operator-Valued Measure, and which generalizes the textbook notion of the eigenstates of the appropriate hermitian operator (the "observable") as measurement outcomes. Here we show how to define a multitude of photodetector figures of merit in terms of a given POVM. We distinguish classical and quantum figures of merit and issue a conjecture regarding trade-off relations between them. We discuss the relationship between POVM elements and photodetector clicks, and how models of photodetectors may be tested by measuring either POVM elements or figures of merit. Finally, the POVM is advertised as a platform-independent way of comparing different types of photodetectors, since any such POVM refers to the Hilbert space of the incoming light, and not to any Hilbert space internal to the detector.