Conditional quantum state engineering at beam splitter arrays

TL;DR

This paper explores a method for engineering quantum states using beam splitter arrays and conditional measurements, enabling the generation and measurement of complex states like Schrödinger-cat states.

Contribution

It introduces a framework for conditional quantum state manipulation at beam splitter arrays, including a detailed description of the non-unitary transformation operators involved.

Findings

Derived the overall non-unitary transformation operator for beam splitter arrays.

Showed how to generate and measure Schrödinger-cat-like states.

Provided a mathematical description of state transformations using s-ordered operator products.

Abstract

The generation of arbitrary single-mode quantum states from the vacuum by alternate coherent displacement and photon adding as well as the measurement of the overlap of a signal with an arbitrarily chosen quantum state are studied. With regard to implementations, the transformation of the quantum state of a traveling optical field at an array of beam splitters is considered, using conditional measurement. Allowing for arbitrary quantum states of both the input reference modes and the output reference modes on which the measurements are performed, the setup is described within the concept of two-port non-unitary transformation, and the overall non-unitary transformation operator is derived. It is shown to be a product of operators, where each operator is assigned to one of the beam splitters and can be expressed in terms of an s-ordered operator product, with s being determined by the beam splitter transmittance or reflectance. As an example we discuss the generation of and overlap measurement with Schroedinger-cat-like states.