Realizing the optimal tomography through a sequence of collective weak measurements

Presenting Author: Ezad Shojaee, University of New Mexico
Contributing Author(s): Christopher S. Jackson, Carlos A. Riofrio, Amir Kalev, Ivan H. Deutsch

Abstract: In their seminal 1995 paper, Massar and Popescu proved that, given N-copies of an unknown pure qubit, the best strategy to reconstruct its state (without any adaptive feedback) is to do a collective measurement on the ensemble [1]. The optimal fidelity with which one can reconstruct the state of a pure qubit is (N+1)/(N+2) averaged over all unknown states and measurement outcomes. This can be achieved through a POVM whose measurement outcomes are spin coherent states of the collective spin J=N/2. In this work, we prove that we can realize this optimal measurement through a sequence of weak measurements of the collective spin along random directions on the sphere. Numerical evidence supports this result, and shows that we saturate the optimal fidelity for quantum state tomography averaged over all unknown states. We discuss the connection between this protocol and tomography via continuous weak measurement in the presence of time-dependent control [2]. [1] S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995). [2] A. Silberfarb, P. S. Jessen, and I. H. Deutsch Phys. Rev. Lett. 95, 030402 (2005); C. A. Riofrio, P. S. Jessen, and I. H. Deutsch, J. Phys. B: At. Mol. Opt. Phys. 44, 154007 (2011).

(Session 9a : Friday from 5:15pm-5:45pm)


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