Entanglement, loss, and quantumness: When balanced beam splitters are best

TL;DR

This paper proves that balanced beam splitters generate the most entanglement with the vacuum among all beam splitters, confirming a long-standing conjecture in quantum optics.

Contribution

It provides a rigorous proof of the conjecture that balanced beam splitters maximize entanglement generation, using properties of entanglement monotones and photon loss.

Findings

Balanced beam splitters produce the highest entanglement with vacuum.

The proof relies on monotonicity, convexity, and entropic properties of quantum states.

Results lead to new inequalities and confirm conjectures about quantumness evolution.

Abstract

The crux of quantum optics is using beam splitters to generate entanglement, including in pioneering experiments conducted by Hanbury-Brown and Twiss and Hong, Ou, and Mandel. This lies at the heart of what makes boson sampling hard to emulate by classical computers and is a vital component of quantum computation with light. Yet, despite overwhelming positive evidence, the conjecture that beam splitters with equal reflection and transmission probabilities generate the most entanglement for any state interfered with the vacuum has remained unproven for almost two decades [Asb\'oth et al., Phys. Rev. Lett. \textbf{94}, 173602 (2005)]. We prove this conjecture for ubiquitous entanglement monotones by uncovering monotonicity, convexity, and entropic properties of states undergoing photon loss. Because beam splitters are so fundamental, our results yield numerous corollaries for quantum optics, from inequalities for quasiprobability distributions to proofs of a recent conjecture for the evolution of a measure of quantumness through loss. One can now definitively state: the more balanced a beam splitter, the more entanglement it can generate with the vacuum.