Entanglement and Magic Correlations Generated by Discrete Beam‐Splitters

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 ‐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.