Quantifying Superpositions Between Quantum Evolutions

TL;DR

This paper develops a resource theory framework to quantify and utilize superpositions between quantum evolutions, revealing their role in enabling non-classical quantum phenomena and tasks.

Contribution

It introduces a novel resource theoretic approach to quantify superpositions in quantum evolutions and explores their potential for quantum information processing.

Findings

Identifies maximally resourceful quantum evolutions.

Shows superpositions enable implementation of arbitrary quantum operations.

Links superpositions to non-classical behaviors like a-causality and indefinite causal order.

Abstract

Quantum mechanics allows coherent superposition between different states of matter. This quality is responsible for major non-classical phenomena that occur in quantum systems. Beyond states, coherent superpositions are also possible between quantum evolutions. We characterize such superpositions here. A resource theoretic framework is developed to quantify superposition present in an arbitrary quantum evolution. In addition to characterization, the framework considers superposition as a quantum resource. This resource can be exploited to perform certain quantum tasks that are otherwise impossible. We identify maximally resourceful evolutions and demonstrate how these could enable one to implement arbitrary quantum operations and super-operations. We also discuss the roles of superposition to exhibit non-classical behaviors present in evolutions, for example, a-causality, temporal Bell correlations, and indefinite temporal and causal orders.