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

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).

18 pages. Comments welcome!

References in corpus (6)

• Resource-efficient linear optical quantum computation
• Strong Violations of Bell-type Inequalities for Path-Entangled Number States
• Efficient Quantum Network Communication using Optimized Entanglement-Swapping Trees
• General linear-optical quantum state generation scheme: Applications to maximally path-entangled states
• Which multiphoton states are related via linear optics?
• QOptCraft: A Python package for the design and study of linear optical quantum systems

Cited by in corpus (6)

• Multiphoton, multimode state classification for nonlinear optical circuits
• Complexity of quantum tomography from genuine non-Gaussian entanglement
• Observation of Lie algebraic invariants in Quantum Linear Optics
• Multipartite entanglement classes of a multiport beam-splitter
• Rigorous no-go theorems for heralded linear-optical state generation tasks
• The symplectic rank of non-Gaussian quantum states