Since the realization of high-quality microwave cavities coupled to quantum dots, one can envisage possibility investigate coherent interaction light and matter in semiconductor devices. Here we study a parallel double dot device operating as single-electron splitter interferometer, with each local photon cavity. We explore how correlation entanglement between two separated are generated by tra...

The Livingston determinant inequality involving the Maclaurin coefficients of a Carathéodory function are derived in a straightforward manner by use of the Riesz-Herglotz representation and the Schwarz inequality. The result is extended to the case of matrix-valued functions.

Some new refinements of the Schwarz inequality in inner product spaces are given. Applications for discrete and integral inequalities including the Heisenberg inequality for vectorvalued functions in Hilbert spaces are provided.