DEPARTMENT OF PHYSICS DISSERTATION: Kfir Dolev

Ph.D. Candidate:  Kfir Dolev

Research Advisor:  Ayfer Ozgur & Patrick Hayden

Date: June 7, 2024  Time: 10:00 AM

Location: Varian 355

Zoom Link: https://stanford.zoom.us/j/93529058839?pwd=RnhYNDNJZXBsTTF6aExXc29EaUplUT09 

Zoom Password: 884601  

Title: On Information Processing in Holographic Spacetimes and the Non-Local Computation Problem

Abstract: If two parties share sufficient entanglement, they are able to implement any channel on a shared bipartite state via non-local quantum computation -- a protocol consisting of local operations and a single simultaneous round of quantum communication. Such a protocol can occur in the AdS/CFT correspondence, with the two parties represented by regions of the CFT, and the holographic state serving as a resource to provide the necessary entanglement. However, an apparent tension arises between the fact that AdS/CFT uses a small amount of entanglement in the protocol, and expectations from position-based cryptography that such a protocol should require a large amount. Therefore, understanding the mechanism by which AdS/CFT implements the protocol will have significant implications, as it would imply either harsh restrictions on information processing in its bulk, or provide a protocol which would break position-based cryptography.In this defense, I present a number of results towards resolving this tension: First, I will review a general theorem restricting information processing in any given spacetime in terms of its causal structure, revealing that such information processing is in principle always compatible with holography.  Second, I give a toy model of symmetry properties in holography responsible for its dynamics. Finally, I give the first rigorous proof that holography performs non-local computation. During this process, I derive a concise subset of properties that, if replicated by a toy model, would successfully implement the protocol.