Infinite-Dimensional Programmable Quantum Processors

TL;DR

This paper extends the concept of programmable quantum processors to infinite-dimensional systems with energy constraints, providing bounds on resources needed for implementing Gaussian channels and unitaries.

Contribution

It generalizes finite-dimensional programmable quantum processors to infinite dimensions, establishing bounds for energy-limited channels and analyzing Gaussian channels.

Findings

Derived upper and lower bounds on program dimension for energy-constrained channels

Analyzed resource requirements for Gaussian and Gaussian unitary channels

Introduced an information-theoretic approach for infinite-dimensional processor bounds

Abstract

A universal programmable quantum processor uses program quantum states to apply an arbitrary quantum channel to an input state. We generalize the concept of a finite-dimensional programmable quantum processor to infinite dimension assuming an energy constraint on the input and output of the target quantum channels. By proving reductions to and from finite-dimensional processors, we obtain upper and lower bounds on the program dimension required to approximately implement energy-limited quantum channels. In particular, we consider the implementation of Gaussian channels. Due to their practical relevance, we investigate the resource requirements for gauge-covariant Gaussian channels. Additionally, we give upper and lower bounds on the program dimension of a processor implementing all Gaussian unitary channels. These lower bounds rely on a direct information-theoretic argument, based on the generalization from finite to infinite dimension of a certain replication lemma for unitaries.