No-go theorems for photon state transformations in quantum linear optics

TL;DR

This paper establishes fundamental limitations on photon state transformations in linear optical systems, identifying conserved quantities and proving the impossibility of certain entanglement and state redistribution tasks.

Contribution

It introduces a necessary condition for photon state transformations, derives a conserved quantity, and presents three general no-go theorems in linear quantum optics.

Findings

Impossible to deterministically redistribute photons between modes.

Cannot generate perfect Bell states in heralded schemes with separable inputs.

Restrictions on converting GHZ to W entangled states.

Abstract

We give a necessary condition for photon state transformations in linear optical setups preserving the total number of photons. From an analysis of the algebra describing the quantum evolution, we find a conserved quantity that appears in all allowed optical transformations. We comment some examples and numerical applications, with example code, and give three general no-go results. These include (i) the impossibility of deterministic transformations which redistribute the photons from one to two different modes, (ii) a proof that it is impossible to generate a perfect Bell state in heralded schemes with a separable input for any number of ancillary photons and modes and a fixed herald and (iii) a restriction for the conversion between different types of entanglement (converting GHZ to W states).