Unifying parameter estimation and the Deutsch-Jozsa algorithm for continuous variables

TL;DR

This paper unifies quantum parameter estimation and the Deutsch-Jozsa algorithm in continuous variable systems, showing how a single procedure can implement both tasks with optimal and probabilistic outcomes, without entanglement.

Contribution

It introduces a general two-parameter procedure that seamlessly combines parameter estimation and the Deutsch-Jozsa algorithm for continuous variables.

Findings

Achieves Heisenberg-limited parameter estimation.

Provides a probabilistic implementation of the Deutsch-Jozsa algorithm.

Demonstrates a unified framework without entanglement.

Abstract

We reveal a close relationship between quantum metrology and the Deutsch-Jozsa algorithm on continuous variable quantum systems. We develop a general procedure, characterized by two parameters, that unifies parameter estimation and the Deutsch-Jozsa algorithm. Depending on which parameter we keep constant, the procedure implements either the parameter estimation protocol or the Deutsch-Jozsa algorithm. The parameter estimation part of the procedure attains the Heisenberg limit and is therefore optimal. Due to the use of approximate normalizable continuous variable eigenstates the Deutsch-Jozsa algorithm is probabilistic. The procedure estimates a value of an unknown parameter and solves the Deutsch-Jozsa problem without the use of any entanglement.