Deterministic Gaussian conversion protocols for non-Gaussian single-mode resources

TL;DR

This paper investigates deterministic Gaussian protocols for converting non-Gaussian states in continuous-variable quantum systems, revealing new equivalences and improved generation schemes for specific states through systematic numerical analysis.

Contribution

It introduces systematic numerical methods to analyze approximate state conversions, demonstrating new equivalences and enhanced protocols for generating non-Gaussian states.

Findings

Cat and binomial states are approximately equivalent at finite energy.

Enhanced schemes for generating cat states from photon-added/subtracted squeezed states.

Conversions of trisqueezed to cubic-phase states with improved performance.

Abstract

In the context of quantum technologies over continuous variables, Gaussian states and operations are typically regarded as freely available, as they are relatively easily accessible experimentally. In contrast, the generation of non-Gaussian states, as well as the implementation of non-Gaussian operations, pose significant challenges. This divide has motivated the introduction of resource theories of non-Gaussianity. As for any resource theory, it is of practical relevance to identify free conversion protocols between resources, namely Gaussian conversion protocols between non-Gaussian states. Via systematic numerical investigations, we address the approximate conversion between experimentally relevant single-mode non-Gaussian states via arbitrary deterministic one-to-one mode Gaussian maps. First, we show that cat and binomial states are approximately equivalent for finite energy, while this equivalence was previously known only in the infinite-energy limit. Then we consider the generation of cat states from photon-added and photon-subtracted squeezed states, improving over known schemes by introducing additional squeezing operations. The numerical tools that we develop also allow to devise conversions of trisqueezed into cubic-phase states beyond previously reported performances. Finally, we identify various other conversions which instead are not viable.