Entanglement and Quantum Logical Gates. Part I.

Abstract

We introduce the notion of proper unitary connective-gate and we prove that entanglement cannot be characterized by such gates. We consider then a larger class of gates (called pseudo-unitary gates), which contains both the unitary and the anti-unitary quan- tum operations. By using a mixed language (a proper extension of the standard quantum computational language), we show how a logical characterization of entanglement is pos- sible in the framework of a mixed semantics, which generalizes both the unitary and the pseudo-unitary quantum computational semantics.