Tomography on Continuous Variable Quantum States

TL;DR

This paper explores quantum state tomography techniques for continuous variable systems, emphasizing phase space representations and the importance of data post-processing for accurate state reconstruction and entanglement analysis.

Contribution

It introduces a simplified approach to phase space quantum states and highlights the necessity of semi-definite programming for precise state estimation in multi-mode systems.

Findings

Back-projection method introduces errors due to cutoff frequency.

Semi-definite programming improves state estimation accuracy.

Entanglement features can be analyzed after state reconstruction.

Abstract

In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike most texts of Quantum information in which the Wigner function for a single mode is often more used, in this text the multi-modes state Wigner function is also approached. Our numerical investigations indicate that the reconstructed method using back-projection add some error due the choice of cutoff frequency, therefore it is necessary to use data post-processing, like the semi-definite programs, which provides sufficient conditions correctly estimate the state. Once the information about the state is recovered, important features such as entanglement can also be investigated.