Quantum state and process tomography via adaptive measurements

Publication Type:
Journal Article
Science China: Physics, Mechanics and Astronomy, 2016, 59 (10)
Issue Date:
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© 2016, Science China Press and Springer-Verlag Berlin Heidelberg. We investigate quantum state tomography (QST) for pure states and quantum process tomography (QPT) for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propose an adaptive protocol where only 2d − 1 measurement outcomes are used to accomplish the QST for all pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography (AUPT) protocol of d2+d−1 measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, T gate (π/8 phase gate), and controlled-NOT gate, respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.
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