Optimized Tomography of Continuous Variable Systems Using Excitation Counting

TL;DR

This paper introduces an optimized quantum tomography method for continuous variable systems using excitation counting and displacement operations, significantly reducing measurement settings and improving robustness.

Contribution

It develops a systematic optimization procedure for excitation counting-based tomography, enhancing efficiency and robustness over traditional methods.

Findings

Reduced measurement settings compared to Husimi or Wigner function methods

Demonstrated order of magnitude error reduction with optimized settings

Bound on reconstruction error involving condition number of sensing map

Abstract

We propose a systematic procedure to optimize quantum state tomography protocols for continuous variable systems based on excitation counting preceded by a displacement operation. Compared with conventional tomography based on Husimi or Wigner function measurement, the excitation counting approach can significantly reduce the number of measurement settings. We investigate both informational completeness and robustness, and provide a bound of reconstruction error involving the condition number of the sensing map. We also identify the measurement settings that optimize this error bound, and demonstrate that the improved reconstruction robustness can lead to an order of magnitude reduction of estimation error with given resources. This optimization procedure is general and can incorporate prior information of the unknown state to further simplify the protocol.