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Full Quantum state tomography with Maximum Likelihood Estimation: Difference between revisions
Full Quantum state tomography with Maximum Likelihood Estimation (edit)
Revision as of 11:50, 25 October 2019
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Quantum state tomography attempts to characterize an unknown state ρ by measuring its components, usually in the Pauli basis or a different selected basis of measurement operators. Multiple identical copies of the quantum state are required as different measurements need to be performed on each copy. To fully reconstruct the density matrix for a mixed state, this method is used. This procedure can be used to completely characterize an unknown apparatus. | Quantum state tomography attempts to characterize an unknown state ρ by measuring its components, usually in the Pauli basis or a different selected basis of measurement operators. Multiple identical copies of the quantum state are required as different measurements need to be performed on each copy. To fully reconstruct the density matrix for a mixed state, this method is used. This procedure can be used to completely characterize an unknown apparatus. | ||
When [[matrix inversion]] technique is used, some of the results produced can violate important basic properties such as positivity leading to a density matrix which is not valid. To avoid this problem, the maximum likelihood estimation of density matrices is employed. In practice, analytically calculating this maximally likely state is prohibitively difficult, and a numerical search is necessary. Three elements are required: a manifestly legal parametrization of a density matrix, a likelihood function which can be maximized, and a technique for numerically finding this maximum over a search of the density matrix’s parameters. | |||
This method consists of the following steps: | This method consists of the following steps: | ||