Quantum optical realization of arbitrary linear transformations allowing for loss and gain

TL;DR

This paper introduces a universal method for implementing arbitrary linear optical transformations, including loss and gain, expanding quantum optics capabilities beyond traditional unitary transformations.

Contribution

It provides a novel, step-by-step decomposition technique for nonunitary transformations, enabling practical realization of complex quantum optical networks with loss and gain.

Findings

Method handles arbitrary linear transformations including loss and gain.

Provides a decomposition approach similar to Reck's for nonunitary networks.

Enables implementation of POVMs and probabilistic quantum protocols.

Abstract

Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations that can involve loss and gain require a different approach. In this theory work, we present a universal method to deal with nonunitary networks. An input to the method is an arbitrary linear transformation matrix of optical modes that does not need to adhere to bosonic commutation relations. The method constructs a transformation that includes the network of interest and accounts for full quantum optical effects related to loss and gain. Furthermore, through a decomposition in terms of simple building blocks it provides a step-by-step implementation recipe, in a manner similar to the decomposition by Reck et al. [Reck et al., Phys. Rev. Lett. 73, 58 (1994)] but applicable to nonunitary transformations. Applications of the method include the implementation of positive-operator-valued measures and the design of probabilistic optical quantum information protocols.