10 papers
Dimension-Free Polylogarithmic Quantum Shadow Tomography from Sequential Pretty-Good Measurements
Fernando Granha Jeronimo, Qizhao Huang, Lenny Liu
\textit{Shadow tomography} is a fundamental problem in quantum information theory. Given multiple copies of an unknown -dimensional quantum state and a known collection of o…
Optimal Quantum de Finetti Theorems via Argmax Rounding
Fernando Granha Jeronimo, Pei Wu, Haochen Xu
We prove optimal finite quantum de Finetti upper bounds. Given a bosonic state , there is a probability measure on the unit sphere such…
An Optimal Analysis of the Product Test
Jacob Beckey, Fernando Granha Jeronimo, Pei Wu
Product testing, i.e., deciding whether a pure multipartite quantum state is fully unentangled across a specified tensor decomposition, serves as a bridge between quantum property…
Optimal Proximity Gap for Folded Reed--Solomon Codes via Subspace Designs
Fernando Granha Jeronimo, Lenny Liu, Pranav Rajpal
A collection of sets satisfies a -proximity gap with respect to some property if for every set in the collection, either (i) all members of the set are -close…
The Collapse of Unentangled Stoquastic Merlin-Arthur Proof Systems
William Gay, Fernando Granha Jeronimo
Entanglement and interference are among the most fundamental properties of quantum mechanics. In this work, we investigate the role and power of interference in the context of dete…
Probabilistic Guarantees to Explicit Constructions: Local Properties of Linear Codes
Fernando Granha Jeronimo, Nikhil Shagrithaya
We present a general framework for derandomizing random linear codes with respect to a broad class of properties, known as local properties, which encompass several standard notion…