# Nengkun Yu (Theory Seminar)

"Quantum Property Testing: Tomography and Identity Testing"
Nengkun Yu (University of Technology Sydney)
Monday, February 3, 2020, 2:00pm
EBU3B, Room 4258

Abstract: Property testing algorithms are used to decide if some object has a "global" property, or is "far" from having this property, using only a small number of "local" queries to the object. We study the quantum property testing of quantum states using different sampling methods, namely the joint measurements, the independent measurements, and the local measurements. For the joint measurement setting, we resolve the open question of quantum state tomography whose goal is to output a mathematical description of the given quantum state. For the independent measurements and the local measurement setting, we establish an $\ell_2$ norm connection between quantum property testing problems and the corresponding distribution testing problems. This connection enables us to derive efficient algorithms using techniques developed for classical property testing for quantum state tomography and quantum identity testing which can be used to study the independence testing for quantum states; identity and independence testing for quantum state collections; and conditional independence testing for classical-quantum-quantum states.