Ph.D. Candidate: Grant Salton
Research Advisor: Prof. Patrick Hayden
Date: Thursday, July 12, 2018
Location: Varian 355
Title: Quantum Error Correction and Spacetime
Quantum error correction (QEC) -- originally invented for quantum computing -- has proven itself useful in a variety of non-computational physical systems, as the ideas of QEC are broadly applicable. In this talk, I'll describe two such scenarios in which QEC appears outside of the paradigm of quantum computing: replicating quantum information in spacetime, and AdS/CFT. In the first part of the talk, we'll answer the following basic question: which laws govern the flow of quantum information through spacetime? Relativity tells us that no information can travel faster than light, and the unitarity of quantum mechanics demands that quantum information cannot be cloned. Are there other fundamental constraints on the passage of quantum information through spacetime? The answer is no: the only such restrictions are (1) no cloning of quantum information and (2) no superluminal signalling. We'll see that any transmission that does not violate (1) or (2) is physically realizable as a so-called information replication task. I'll outline the information replication problem, and then I'll show how we can use QEC to succeed at transmitting quantum information in seemingly impossible ways. In the second part of the talk, we'll turn our attention to QEC in quantum gravity, specifically the recent discovery that the AdS/CFT correspondence implements quantum error correction. AdS/CFT is a duality between a gravitational theory and a conformal field theory (CFT). A long-standing problem in the subject concerns "subregion duality": which regions of the bulk gravity theory are dual to a subregion of the CFT? The hypothesis is that any local bulk operator in AdS can be reconstructed using only a causally disconnected subregion of the CFT (the so-called entanglement wedge reconstruction hypothesis). We'll tackle this problem by generalizing recent information theoretic results on approximate quantum error correction, proving that entanglement wedge reconstruction can be done robustly, and finding an explicit formula for reconstructed bulk operators. If time permits, I'll even highlight a bonus, third application of QEC.