Equalities and inequalities from entanglement, loss, and beam splitters

TL;DR

This paper explores fundamental inequalities and properties related to entanglement, nonclassicality, and state similarity in quantum optics, with implications for quantum information and system design.

Contribution

It extends key entanglement and nonclassicality properties to measures of state similarity and operator inequalities, proving new bounds and conjectures in quantum optics.

Findings

Monotonicity and convexity properties for quantum states with photon loss

Inequalities for creation and annihilation operators beyond Cauchy-Schwarz

Nonclassicality via quadrature coherence scale is uncertifiable beyond 50% loss

Abstract

Quantum optics bridges esoteric notions of entanglement and superposition with practical applications like metrology and communication. Throughout, there is an interplay between information theoretic concepts such as entropy and physical considerations such as quantum system design, noise, and loss. Therefore, a fundamental result at the heart of these fields has numerous ramifications in development of applications and advancing our understanding of quantum physics. Our recent proof for the entanglement properties of states interfering with the vacuum on a beam splitter led to monotonicity and convexity properties for quantum states undergoing photon loss [Lupu-Gladstein et al., arXiv:2411.03423 (2024)] by breathing life into a decades-old conjecture. In this work, we extend these fundamental properties to measures of similarity between states, provide inequalities for creation and annihilation operators beyond the Cauchy-Schwarz inequality, prove a conjecture [Hertz et al., PRA 110, 012408 (2024)] dictating that nonclassicality through the quadrature coherence scale is uncertifiable beyond a loss of 50%, and place constraints on quasiprobability distributions of all physical states. These ideas can now circulate afresh throughout quantum optics.