Quantum Steering and Entanglement in a Tritter: Hierarchy under Loss
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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.