Entanglement and Magic Correlations Generated by Discrete Beam-Splitters

Abstract

Beam-splitters are basic and instrumental tools not only in the study of foundational issues in quantum mechanics, but also in various applications of quantum information processing. In the continuous-variable scenario involving quantum optical states and Gaussian quantum information, interference phenomena are widely investigated and characterized via beam-splitters. In this work, within the framework of stabilizer quantum computation in finite quantum systems, entanglement and magic correlations generated by discrete beam-splitters are explored. Two types of magic correlations are distinguished: mutual magic (analogous to quantum mutual information) and non-local magic. Explicit formulas for these correlations are derived in the qubit scenario where the beam-splitter is implemented by the controlled-NOT gate, with the $H$-type magic states playing a particularly prominent role as input states. Extending to prime-dimensional qudit systems, it is shown that fiducial states of mutually unbiased bases also play a remarkable role. Basic properties of these magic correlations are revealed and illustrated through some typical examples.