Ultimate Precision of Direct Tomography of Wave Functions
- Speaker: Dr. Nguyen, Thi Xuan Hoai
- Date: Wednesday November 27, 2019 10:00am
- Place: Jungho Seminar Room
Reconstruction of the quantum state of a system is of vital importance not only in fundamental studies of quantum mechanics but also in many practical applications of quantum information technology. The standard way to do it requires an indirect computational reconstruction based on the measurement outcomes of a complete set of non-commuting observables on identically prepared systems. Recently, an alternative known as the direct tomography enables the complex-valued wave functions to be extracted directly and in an experimentally less challenging manner. Although originally proposed as a special case of weak measurement, the direct tomography can be extended to arbitrary measurement setup working regardless of the system-pointer coupling strength. In this talk, I will present our recent results. Firstly, we generalize the idea of quantum metrology to the estimation of complex-valued phase, and apply it for the direct tomography. We show that the reformulation can help us easily find the optimal measurements for efficient estimation. Then we propose two different measurement schemes that eventually approach the Heisenberg limit: one is to exploit quantum entanglements in the pointers, the other is to apply the time-reversal transformation. In both methods, the real part of the wave function is estimated with a Ramsey-type interferometry while the imaginary part is estimated by amplitude measurements.