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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 59 , Issue 10 : 100313(2016) https://doi.org/10.1007/s11433-016-0287-y

Quantum state and process tomography via adaptive measurements

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  • ReceivedJul 18, 2016
  • AcceptedJul 28, 2016
  • PublishedAug 18, 2016
PACS numbers

Abstract

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 $d^2+d-1$ 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 ($\pi/8$ 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.


Funded by

National Natural Science Foundation of China(11175094)

National Natural Science Foundation of China(91221205)

National Natural Science Foundation of China(11375167)

National Natural Science Foundation of China(11227901)

National Natural Science Foundation of China(91021005)

(2013CB921800)

(2014CB848700)


Acknowledgment

Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canadian Institute for Advanced Research (CIFAR), the National Natural Science Foundation of China (Grant Nos. 11175094, 91221205, 11375167, 11227901 and 91021005), the National Basic Research Program of China (Grant No. 2015CB921002), the National Key Basic Research Program (NKBRP) (Grant Nos. 2013CB921800 and 2014CB848700) and the National Science Fund for Distinguished Young Scholars (Grant No. 11425523).


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