Full Realization Scheme of the Tensor Product Space of N Distinguishable Photons in Two States

TL;DR

This paper demonstrates that a non-unitary interferometer is necessary to fully realize the tensor product space of N distinguishable photons in two states, advancing quantum control capabilities.

Contribution

It introduces a non-unitary interferometer design to achieve complete realization of the tensor product space for multiple photons in two states.

Findings

A non-unitary process is required for full realization.

Design of a non-unitary interferometer for two photons.

Extension to N photons in two states.

Abstract

The ability to control and hence to realize a given number of photons is of major interest from a fundamental point of view, e.g. Bell inequalities, photons bunching. In recent years this interest has grown by the so-called the "Second Quantum Revolution" where such an ability is needed for quantum computers, etc. In this paper, we show that such a realization can not be done by a unitary process. Therefore, a non-unitary interferometer is given to build a full realization of the tensor product space for two photons at two states. Finally, by modifying the previous interferometer, the full tonsorial product space of N photons in two states is shown.