Security of quantum position-verification limits Hamiltonian simulation via holography

TL;DR

This paper explores the security limits of quantum position-verification using holographic models, revealing fundamental resource bounds for Hamiltonian simulation based on security assumptions.

Contribution

It establishes a novel connection between quantum position-verification security and Hamiltonian simulation resource requirements via holographic quantum error correcting codes.

Findings

Security of QPV linked to Hamiltonian simulation complexity

Lower bounds on resources for Hamiltonian simulation derived from QPV security assumptions

Holographic models used to analyze causality and security in quantum protocols

Abstract

We investigate the link between quantum position-verification (QPV) and holography established in [MPS19] using holographic quantum error correcting codes as toy models. By inserting the "temporal" scaling of the AdS metric by hand via the bulk Hamiltonian interaction strength, we recover a toy model with consistent causality structure. This leads to an interesting implication between two topics in quantum information: if position-based verification is secure against attacks with small entanglement then there are new fundamental lower bounds for resources required for one Hamiltonian to simulate another.