VARIATIONAL QUANTUM TOMOGRAPHY WITH INCOMPLETE INFORMATION BY MEANS OF SEMIDEFINITE PROGRAMS

Thiago O. Maciel (), André T. Cesário () and Reinaldo O. Vianna ()
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Thiago O. Maciel: Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-901, Brazil
André T. Cesário: Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-901, Brazil
Reinaldo O. Vianna: Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-901, Brazil

International Journal of Modern Physics C (IJMPC), 2011, vol. 22, issue 12, 1361-1372

Abstract: We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite Programs. Numerical simulations indicate that the estimated state does not overestimate purity, and neither the expectation value of optimal entanglement witnesses. The convergence properties of the method are similar tocompressed sensingapproaches, in the sense that, in order to reconstruct low rank states, it needs just a fraction of the effort corresponding to an informationally complete measurement.

Keywords: Quantum tomography; semidefinite programs; compressed sensing approaches; 03.65.Wj; 03.67.-a (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183111016981

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