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VARIATIONAL QUANTUM TOMOGRAPHY WITH INCOMPLETE INFORMATION BY MEANS OF SEMIDEFINITE PROGRAMS

Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-901, Brazil

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ANDRÉ T. CESÁRIO

Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-901, Brazil

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, and

REINALDO O. VIANNA

Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-901, Brazil

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https://doi.org/10.1142/S0129183111016981Cited by:17 (Source: Crossref)

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 to compressed sensing approaches, 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:

PACS: 03.65.Wj, 03.67.-a

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