Limits to multipartite entanglement generation with bosons and fermions

TL;DR

This paper introduces a unifying framework for understanding the limits of multipartite entanglement generation via interference of bosons and fermions, revealing bounds on the complexity and dimensionality of achievable entangled states.

Contribution

It provides a comprehensive theoretical framework that characterizes the states producible by many-particle interference and establishes fundamental bounds on their entanglement complexity.

Findings

Bosons can generate more entangled states than fermions at lower success probabilities.

Derived upper bounds on the generalized Schmidt number of generated states.

Established limits on the dimensionality of the manifold of entangled states.

Abstract

Many-photon interference in linear-optics setups can be exploited to generate and detect multipartite entanglement. Without recurring to any inter-particle interaction, many entangled states have been created experimentally, and a panoply of theoretical schemes for the generation of various classes of entangled states is available. Here, we present a unifying framework that accommodates the present experiments and theoretical protocols for the creation of multiparticle entanglement via interference. A general representation of the states that can be created is provided for bosons and fermions, for any particle number, and for any dimensionality of the entangled degree of freedom. Using the framework, we derive an upper bound on the generalized Schmidt number of the states that can be generated, and we establish bounds on the dimensionality of the manifold of these states. We show that - at the expense of a smaller success probability - more states can be created with bosons than with fermions, and give an intuitive interpretation of the state representation and of the established bounds in terms of superimposed many-particle paths.