Quantifying Superposition

TL;DR

This paper introduces measures to quantify superposition in quantum states, relating them to entanglement measures and providing operational interpretations, with applications demonstrated through interferometry models.

Contribution

It develops new superposition measures based on entanglement concepts and operational interpretations, expanding the understanding of quantum superposition quantification.

Findings

Superposition measures can be derived from entanglement measures.

Operational interpretation of superposition in interferometry.

Superposition measures behave under specific quantum channels.

Abstract

Measures are introduced to quantify the degree of superposition in mixed states with respect to orthogonal decompositions of the Hilbert space of a quantum system. These superposition measures can be regarded as analogues to entanglement measures, but can also be put in a more direct relation to the latter. By a second quantization of the system it is possible to induce superposition measures from entanglement measures. We consider the measures induced from relative entropy of entanglement and entanglement of formation. We furthermore introduce a class of measures with an operational interpretation in terms of interferometry. We consider the superposition measures under the action of subspace preserving and local subspace preserving channels. The theory is illustrated with models of an atom undergoing a relaxation process in a Mach-Zehnder interferometer.