Other methods for efficient tomography

Focus on quantum tomography (special issue):
K. Banaszek, M. Cramer, and D. Gross, New J. Phys. 15, 125020 (2013).

Compressed sensing: states with low rank

Quantum state tomography via compressed sensing:
D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, Phys. Rev. Lett. 105, 150401 (2010).
(main paper on tomography based on compressed sensing)

Continuous-variable quantum compressed sensing:
M. Ohliger, V. Nesme, D. Gross, Y.-K. Liu, and J. Eisert, arXiv:1111.0853.

Rank-based model selection for multiple ions quantum tomography
M. Guta, T. Kypraios, and I. Dryden, New J. Phys. 14, 105002 (2012).

Efficient and feasible state tomography of quantum many-body systems
M. Ohliger, V. Nesme, and J. Eisert, New J. Phys. 15, 015024 (2013).

Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators:
S. T. Flammia, D. Gross, Y.-K. Liu, and J. Eisert, New J. Phys. 14, 095022 (2012).

Quantum state tomography by continuous measurement and compressed sensing
A. Smith, C.A. Riofrío, B. E. Anderson, H. Sosa-Martinez, I. H. Deutsch, and P. S. Jessen, Phys. Rev. A 87, 030102(R) (2013).

Uncertainty Quantification for Matrix Compressed Sensing and Quantum Tomography Problems:
A. Carpentier, J. Eisert, D. Gross, R. Nickl, arxiv:1504.03234.

Statistically efficient tomography of low rank states with incomplete measurements
A. Acharya, T. Kypraios, and M. Guta, arxiv:1510.03229.

Improving compressed sensing with the diamond norm
M. Kliesch, R. Kueng, J. Eisert, and D. Gross, arxiv:1511.01513


Matrix product state (MPS) tomography: spin chain states

Efficient quantum state tomography:
M. Cramer, M. B. Plenio, S. T. Flammia, R. Somma, D. Gross, S. D. Bartlett, O. Landon-Cardinal, D. Poulin, and Y.-K. Liu, Nat. Commun. 1, 149 (2010).
(main MPS tomography paper)

Scalable reconstruction of density matrices:
T. Baumgratz, D. Gross, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 111, 020401 (2013); arXiv:1207.0358.
(mixed states, applied to the experimental data of the eight-ion experiment of the Blatt group)

Practical learning method for multi-scale entangled states:
O. Landon-Cardinal and D. Poulin, New J. Phys. 14, 085004 (2012).
(extension to 2D)

A scalable maximum likelihood method for quantum state tomography:
T. Baumgratz, A. Nüßeler, M. Cramer, and M. B. Plenio, New J. Phys. 15, 125004 (2013);
(realization for mixed states)

Quantum field tomography:
A. Steffens, C. A. Riofrío, R. Hübener, J. Eisert, arXiv:1406.3631.

Towards experimental quantum field tomography with ultracold atoms:
A. Steffens, M. Friesdorf, .T Langen, B. Rauer, T. Schweigler, R. Hübener, J. Schmiedmayer, C.A. Riofrío, and J. Eisert, arXiv:1406.3632.

Continuous matrix product state tomography of quantum transport experiments:
J. Eisert, D. Gross, arxiv:1504.04194


Further methods

Information criteria for efficient quantum state estimation:
J. O. S. Yin and S. J. van Enk, Phys. Rev. A 83, 062110 (2011); arXiv:1103.3251.

Statistical Estimation of Quantum Tomography Protocols Quality:
Yu.I.Bogdanov, G. Brida, M. Genovese, S.P.Kulik, E.V.Moreva, and A.P.Shurupov, Phys. Rev. Lett. 105, 010404 (2010); arXiv:1002.3477