Schur Complement Inequalities for Covariance Matrices and Monogamy of Quantum Correlations
نویسندگان
چکیده
منابع مشابه
Schur Complement Inequalities for Covariance Matrices and Monogamy of Quantum Correlations.
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 ...
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Let H = ( H11 H12 H∗ 12 H22 ) be an n×n positive semidefinite matrix, where H11 is k×k with 1 ≤ k < n. The generalized Schur complement of H11 in H is defined as S(H) = H22 −H∗ 12H † 11H12, where H 11 is the Moore-Penrose generalized inverse of H11. It has the extremal characterizations S(H) = max { W : H − ( 0k 0 0 W ) ≥ 0,W is (n− k)× (n− k) Hermitian } and S(H) = min {[Z|In−k]H[Z|In−k] : Z i...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2016
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.117.220502