Seminar: Entanglement can be more than transitive

Time Mar. 18, 2022, 10:00 am (Taipei Time)
Speaker Gelo Noel Tabia
Title Entanglement can be more than transitive
Abstract Often in science we want to learn about the relation between a whole and its parts. A typical example in quantum physics is the problem of detecting entanglement in a many-body system from partial information about a few particles. Here we consider a different but related question: can knowledge of certain parts of a system reveal information about some other parts? We show that there exists a collection of (non)entangled marginal states that a different target marginal system must be entangled. We call this phenomenon the (meta)transitivity of entanglement. In this talk, I will describe the general metatransitivity problem and provide a method for identifying marginal states that exhibit metatransitivity. For a certain family of N-qubit states uniquely determined by its two-qubit marginals in tree form, I will show that metatransitivity exists for systems with arbitrarily large number of qubits. For tripartite systems where the two known marginals correspond to Werner or isotropic states, I will prove that metatransitivity happens in all finite dimensions. Using numerical observations, I will discuss the typicality of entanglement transitivity in tripartite pure states. I will also establish a connection between metatransitivity and a k-local Hamiltonian problem. Finally, I will mention some possible future directions.
Personal information Gelo Noel Tabia obtained his PhD at the University of Waterloo in Canada in 2013. He did a postdoc at the Institute of Computer Science at the University of Tartu in Estonia. After that he was a postdoc at the Center for Quantum Technology in NTHU. He is currently a postdoc for the NCTS (Physics Division) and is based in NCKU.