Measuring Measurement: Theory and Practice
A. Feito, J.S. Lundeen, H. Coldenstrodt-Ronge, J. Eisert, M.B. Plenio, and I.A. Walmsley

TL;DR
This paper discusses the formalism and practical challenges of quantum detector tomography, focusing on photon detectors, and demonstrates how to fully characterize these detectors with minimal assumptions.
Contribution
It provides a comprehensive overview of quantum detector tomography formalism and applies it to photon detectors, highlighting its general applicability and practical considerations.
Findings
Successfully characterizes photon detectors with minimal assumptions
Identifies experimental and theoretical challenges in quantum tomography
Demonstrates the formalism's broad applicability to various detectors
Abstract
Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well specified assumptions. The formalism is completely general and can be applied to a wide range of detectors
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