A note concerning the modular valued von Neumann interaction operator

TL;DR

This paper introduces a modular valued operator for von Neumann interactions, explores its properties, compares it with standard modular values, and discusses potential applications in quantum computation, including an experimental implementation.

Contribution

It defines a new modular valued operator for von Neumann interactions, analyzes its properties, and suggests its utility in quantum computing with experimental insights.

Findings

Properties of the modular valued operator are characterized.

Comparison with standard modular values highlights differences.

Experimental implementation demonstrates practical feasibility.

Abstract

The modular valued operator $\widehat{V}_m$ of the von Neumann interaction operator for a projector is defined. The properties of $\widehat{V}_m$ are discussed and contrasted with those of the standard modular value of a projector. The associated notion of a faux qubit is introduced and its possible utility in quantum computation is noted. An experimental implementation of $\widehat{V}_m$ is also highlighted.