title: Schur Complement Inequalities for Covariance Matrices and Monogamy of Quantum Correlations.
abstract: We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This allows us to prove general results on the monogamy of entanglement and steering quantifiers in continuous variable systems with an arbitrary number of modes per party. A powerful hierarchical relation for correlation measures based on the log-determinant of covariance matrices is further established for all Gaussian states, which has no counterpart among quantities based on the conventional von Neumann entropy.
authors.affiliation: Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain.
authors.forename: Ludovico
authors.initials: L
authors.lastname: Lami
authors.affiliation: Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain.
authors.forename: Christoph
authors.initials: C
authors.lastname: Hirche
authors.affiliation: Centre for the Mathematical and Theoretical Physics of Quantum Non-Equilibrium Systems, School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Gerardo
authors.initials: G
authors.lastname: Adesso
authors.affiliation: Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain.|ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, ES-08010 Barcelona, Spain.
authors.forename: Andreas
authors.initials: A
authors.lastname: Winter