Robustness of raw quantum tomography

TL;DR

This paper investigates how non-ideal data acquisition impacts quantum state tomography, demonstrating robustness even with incomplete or approximate data, and clarifying the effects of noise and finite measurement resolution.

Contribution

It provides a detailed analysis of the effects of noise and finite measurement resolution on quantum tomography, showing robustness and clarifying the role of normalization constants.

Findings

Quantum tomography is robust under incomplete data.

Finite measurement effects only alter normalization, not the reconstruction.

Results extend to discrete measurement meshes.

Abstract

We scrutinize the effects of non-ideal data acquisition on the homodyne tomograms of photon quantum states. The presence of a weight function, schematizing the effects of the finite thickness of the probing beam or equivalently noise, only affects the state reconstruction procedure by a normalization constant. The results are extended to a discrete mesh and show that quantum tomography is robust under incomplete and approximate knowledge of tomograms.