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Quantum Process Tomography: A New Approach Based on Moments

Ghalaii, Masoud | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45354 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Tayefeh Rezakhani, Ali
  7. Abstract:
  8. In this report, we have formulated a new technique for characterizing quantum optical processes based on probing unknown processes only with coherent states and simply by measuring normally-ordered moments of output states. Our method has two substantial advantages in comparison with previous methods.First, for practical purposes of uantum-optical communications and information, predicting of the classicality or nonclassicality of output states from an unknown quantum process is generally important. Because of truncation of the Hilbert space in the Fock basis and/or exploiting Klauder theorem, antecedent methods failed to carry out foretelling the [non]classicality features of the process’ output. It is of particular practical interest to predict how specific nonclassical effects such as squeezing or anti-bunching, evolve or can be generated through the action of quantum processes. As the nonclassical effects can be checked in terms of normally-ordered oments of a quantum state, discerning the relationship between the moments of the input and output states, one can investigate specific nonclassical effects after the process.Furthermore, there are some quantum states such as Gaussian states which can be uniquely represented by a finite number of their moments whereas their density matrices in the Fock basis are infinite dimensional. Thus, for those processes which preserve Gaussianity of the states (Gausssian processes), it is more efficient to perform quantum process tomography in terms of the normally-ordered moments basis rather than the Fock basis. Interestingly as well, all normally-ordered moments can be experimentally specified using relatively simple apparatus—homodyne correlation measurements that compromises simply of beam splitters and photon detectors. We demonstrate analytically how an unknown quantum process can be identified based on these moments.Moreover, for a set of practically important quantum optical processes—M-mode Gaussian processes—we show that probing only 2M + 1 different coherent states is sufficient for process to be completely characterized
  9. Keywords:
  10. Quantum Computation ; Quantum Information Theory ; Quantum Optics ; Coherent State Quantum Computation ; Quantum Tomography ; Optical Moments

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