One-Shot State Preparations using Local Operations and Limited Correlated Resources

IQC Seminar - Ian George, UIUC

As quantum networks approach real life implementation, a theoretical understanding of their limitations becomes practically important. In this talk, I will discuss recent works with my collaborators where we characterize the ability to prepare a target quantum state over simple networks using local operations (LO) and limited correlated resources in the one-shot setting. We will begin with the determination of the minimal amount of shared randomness necessary for the generation of multipartite quantum states using LO and shared randomness (LOSR), thereby generalizing previous asymptotic results. We will also consider analogues that use shared entanglement instead of shared randomness and show these results have undesired behaviour. Motivated by this, we will determine simple optimization programs for the error of one-shot transformations between pure states under LOSR, which will allow us to consider one-shot catalytic state transformations under LO. Finally, rather than viewing the limitations of pure state transformations with LOSR as necessarily bad, we will discuss the construction and security of a cryptographic protocol that makes use of these limitations. 

Based on arXiv:2301.04301, arXiv:2301.04735, and work in preparation