Bipartite and tripartite steering by a nonlinear medium in a cavity

Abstract

Nonlocal quantum correlations are important for potential applications in quantum optics and quantum information. Multipartite quantum correlations are relevant to access to high-dimensional systems such as qudits. There are also different proposals for the generation of quantum steering based on nonlinear systems and cavities. Here, we consider the Hamiltonian of a triple photon parametric down-conversion process to investigate the regions where bipartite and tripartite steering are generated. In this model, three beams interact with a nonlinear medium inside a cavity through the process of parametric down-conversion, creating three output fields. The positive P representation is used to analyze this system and steady-state solutions are obtained. We calculated the intracavity fluctuation spectra to analyze steering in the frequency domain and used different criteria to certify this quantum correlation. We certified bipartite steering for the three output fields from the cavity. In the case of full tripartite two-way steering inseparability, it is also present for all the bipartitions under consideration. Our results show regimes where bipartite and tripartite steering is certified for this model.

Monogamy of quantum correlations shared in a cavity-freeoptomechanical system

“…An in-depth study of this property by using CKW-monogamy inequalities to govern the entanglement distribution between three qubits, was carried out by Coofman-Kundu-Wotters (CKW) [24], and had been generalized by Osborne and Verstraete [35]. The monogamy inequality for sharing entanglement has been proven for all Gaussian states [36] and many quantum measures proposed as quantifiers of bipartite correlations in CKW-monogamy, namely (Gaussian) Contangle [8], Gaussian steering [37], and Gaussian the Gaussian Rényi-2(GR2) [6], have also been used to demonstrate the monogamy property or to quantify tripartite correlations [22,[38][39][40][41][42][43]. In [39], monogamy of entanglement has been studied in a cavity-free optomechanical system consisting of two optical modes stemming from interaction between the laser beam and an actuator mirror, as well as one mechanically mode, by quantifying bipartite entanglement using Gaussian contangle and the tripartite entanglement by exploiting residual Gaussian Contangle.…”