Covariance, correlation and entanglement

20 00 Covariance , Correlation and Entanglement

Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based upon covariance. This works for two-and three-component systems but produces ambiguities for multicomponent systems of composite diemnsion. Its relationship to angu...

Separability and entanglement of quantum states based on covariance matrices

Covariance and Correlation Class 7 , 18 . 05

Estimation under unknown correlation: covariance intersection revisited

This paper addresses the problem of obtaining a consistent estimate (or upper bound) of the covariance matrix when combining two quantities with unknown correlation. The combination is defined linearly with two gains. When the gains are chosen a priori, a family of consistent estimates is presented in the paper. The member in this family having minimal trace is said to be “family-optimal”. When...

Moving Average Models for Volatility and Correlation, and Covariance Matrices

The volatilities and correlations of the returns on a set of assets, risk factors or interest rates are summarized in a covariance matrix. This matrix lies at the heart of risk and return analysis. It contains all the information necessary to estimate the volatility of a portfolio, to simulate correlated values for its risk factors, to diversify investments and to obtain efficient portfolios th...