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 propos...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.1measurement 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(/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.展开更多
基金supported by the Natural Sciences and Engineering Research Council of Canada(NSERC)the Canadian Institute for Advanced Research(CIFAR)+3 种基金the National Natural Science Foundation of China(Grant Nos11175094,91221205,11375167,11227901 and 91021005)the National Basic Research Program of China(Grant No.2015CB921002)the National Key Basic Research Program(NKBRP)(Grant Nos.2013CB921800and 2014CB848700)the National Science Fund for Distinguished Young Scholars(Grant No.11425523)
文摘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.1measurement 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(/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.
