# Proper error bars for self-calibrating quantum tomography

## TL;DR

This paper develops a method for accurately estimating quantum states and measurement device parameters simultaneously, providing reliable error regions, with applications to quantum cryptography and satellite-based quantum key distribution.

## Contribution

It introduces a joint estimation framework for self-calibrating quantum tomography using optimal error regions, improving uncertainty quantification.

## Key findings

- Successfully applied to BB84 measurement scenario
- Reconstructed quantum state and device parameters simultaneously
- Demonstrated relevance for satellite-based quantum key distribution

## Abstract

Self-calibrating quantum state tomography aims at reconstructing the unknown quantum state and certain properties of the measurement devices from the same data. Since the estimates of the state and device parameters come from the same data, one should employ a joint estimation scheme, including the construction and reporting of joint state-device error regions to quantify uncertainty. We explain how to do this naturally within the framework of optimal error regions. As an illustrative example, we apply our procedure to the double-crosshair measurement of the BB84 scenario in quantum cryptography and so reconstruct the state and estimate the detection efficiencies simultaneously and reliably. We also discuss the practical situation of a satellite-based quantum key distribution scheme, for which self-calibration and proper treatment of the data are necessities.