Urbana Campus Research Calendar (OVCRI)

Speaker: Jack Spilecki (UC Berkeley)
Title: Mixed state tomography reduces to pure state tomography

Abstract:
Quantum state tomography is the task of learning an unknown quantum state from measurements on copies of that state. While tomography of pure states is well understood, tomography of mixed states has long been considered substantially harder, both conceptually and technically.

In this talk, I will describe a new approach showing how mixed-state tomography reduces to pure-state tomography. The key tool is the recently discovered random purification channel, which converts copies of an unknown mixed state into copies of a random purification on a larger Hilbert space. We can then apply a pure-state tomography algorithm to learn this purification and recover the original mixed state.

This simple strategy yields the first tomography algorithm which is sample-optimal in all standard parameters: the Hilbert space dimension d, the rank r, the error ϵ, and the success probability 1−δ. It also gives the first algorithm which is simultaneously sample-optimal and gate-efficient. More broadly, a small adjustment to this framework recovers essentially all existing results on mixed-state tomography, including settings with limited entanglement, classical shadows, and applications to quantum metrology.

Based on joint work with Angelos Pelecanos, Ewin Tang, and John Wright.