Quantum Steering and Entanglement in a Tritter: Hierarchy under Loss

TL;DR

This paper investigates the hierarchy of entanglement and EPR steering in a tripartite continuous-variable quantum state generated by a tritter, analyzing the effects of losses and establishing steering as a stricter form of entanglement.

Contribution

It provides a comprehensive analysis of entanglement and EPR steering in a tripartite state created with a tritter, highlighting the resilience of steering under losses and confirming its stricter nature compared to entanglement.

Findings

EPR steering remains more robust than entanglement under optical losses.

Steering is a stricter criterion than inseparability, forming a subset of entanglement.

Correlation strength depends only on the squeezing parameter, not on coherent amplitude.

Abstract

Multipartite entangled states of continuous variables are fundamental resources for scalable quantum information processing. We study the correlation hierarchy in a tripartite state engineered by mixing a two-mode squeezed vacuum with a coherent state on a tritter, a key linear optical element for multimode state generation. Using the covariance matrix formalism, we comprehensively analyze the entanglement and Einstein-Podolsky-Rosen (EPR) steering among the output modes. The strength of both correlations is governed solely by the squeezing parameter and is independent of the coherent amplitude. We further examine the impact of inevitable optical losses in various channel configurations. The results show that while losses degrade correlations, EPR steering remains monogamous and exhibits stricter resilience thresholds than entanglement. Our analysis, supported by parameter extension techniques, confirms that the steering condition is more stringent than the inseparability criterion, clearly demonstrating that steering forms a strict subset of entanglement. These results elucidate the correlation structure in a readily generated multimode state and offer practical insights for developing asymmetric quantum protocols, such as one-sided device-independent tasks, where EPR steering serves as a critical resource.