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Variational Quantum Tomography With Incomplete Information By Means Of Semidefinite Programs

Author

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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)

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.

Suggested Citation

  • Thiago O. Maciel & André T. Cesário & Reinaldo O. Vianna, 2011. "Variational Quantum Tomography With Incomplete Information By Means Of Semidefinite Programs," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(12), pages 1361-1372.
    • Handle: RePEc:wsi:ijmpcx:v:22:y:2011:i:12:n:s0129183111016981
    DOI: 10.1142/S0129183111016981
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    Cited by:

    1. Corte, Inés & Losada, Marcelo & Tielas, Diego & Holik, Federico & Rebón, Lorena, 2023. "Parameterizing density operators with arbitrary symmetries to gain advantage in quantum state estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).

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