Security of quantum position-verification limits Hamiltonian simulation via holography

• Published in: The journal of high energy physics Vol. 2024; no. 8; pp. 152 - 40
• Main Authors: Apel, Harriet, Cubitt, Toby, Hayden, Patrick, Kohler, Tamara, Pérez-García, David
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2024; Springer Nature B.V; Springer Nature; SpringerOpen
• Subjects: AdS-CFT Correspondence; Causality; Classical and Quantum Gravitation; Codes; Computer science; Elementary Particles; Error analysis; Error correcting codes; Error correction; Error correction & detection; Hilbert space; Holography; Holography and Condensed Matter Physics (AdS/CMT); Lattice Models of Gravity; Lower bounds; Physics; Physics and Astronomy; Quantum entanglement; Quantum Field Theories; Quantum Field Theory; Quantum phenomena; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Simulation; Spacetime; String Theory; Velocity; Verification; Lattice Models of Gravity; AdS-CFT Correspondence; Holography and Condensed Matter Physics (AdS/CMT)
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2024)152

A bstract We investigate the link between quantum position-verification (QPV) and holography established in [ 1 ] 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.