Coherent states engineering with linear optics: Possible and impossible tasks

TL;DR

This paper characterizes the transformations of coherent states achievable with linear optics, establishing a correspondence with single photon states, and discusses the limitations in manipulating entangled coherent states.

Contribution

It introduces a linear map framework for designing linear optical schemes with coherent states and explores the boundaries of what is possible with linear optics.

Findings

Linear transformations of coherent states are characterized by a specific linear map.

A correspondence between coherent state transformations and single photon state transformations is established.

Limitations in manipulating entangled coherent states with linear optics are discussed.

Abstract

The general transformation of the product of coherent states $\prod_{i=1}^N|\alpha_i>$ to the output state $\prod_{i=1}^M|\beta_i>$ ($N=M$ or $N\neq M$), which is realizable with linear optical circuit, is characterized with a linear map from the vector $(\alpha^{\ast}_1,...,\alpha^{\ast}_N)$ to $(\beta^{\ast}_1,...,\beta^{\ast}_M)$. A correspondence between the transformations of a product of coherent states and those of a single photon state is established with such linear maps. It is convenient to apply this linear transformation method to design any linear optical scheme working with coherent states. The examples include message encoding and quantum database searching. The limitation of manipulating entangled coherent states with linear optics is also discussed.