1. G. Tóth, W. Wieczorek, D. Gross, R. Krischek, C. Schwemmer, and H. Weinfurter, Permutationally invariant quantum tomography [pdf,pdf2], Phys. Rev. Lett. 105, 250403 (2010); arxiv:1005.3313.We present a scalable method for the tomography of large multiqubit quantum registers. It acquires information about the permutationally invariant part of the density operator, which is a good approximation to the true state in many relevant cases. Our method gives the best measurement strategy to minimize the experimental effort as well as the uncertainties of the reconstructed density matrix. We apply our method to the experimental tomography of a photonic four-qubit symmetric Dicke state. 2. T. Moroder, P. Hyllus, G. Tóth, C. Schwemmer, A. Niggebaum, S. Gaile, O. Gühne, and H. Weinfurter, Permutationally invariant state reconstruction, New J. Phys. 14, 105001 (2012) [pdf], Focus issue on Quantum Tomography; arxiv:1205.4941.3. C. Schwemmer, G. Tóth, A. Niggebaum, T. Moroder, D. Gross, O. Gühne, and H. Weinfurter, Efficient Tomographic Analysis of a Six Photon State, [pdf,pdf2], Phys. Rev. Lett. 113, 040503 (2014); arxiv:1401.7526.Quantum state tomography suffers from the measurement effort increasing exponentially with the number of qubits. Here, we demonstrate permutationally invariant tomography for which, contrary to conventional tomography, all resources scale polynomially with the number of qubits both in terms of the measurement effort as well as the computational power needed to process and store the recorded data. We evaluate permutationally invariant tomography by comparing it to full tomography for six-photon states obtained from spontaneous parametric down-conversion. We show that their results are compatible within the statistical errors. For low rank states, we further optimize both schemes using compressed sensing. We demonstrate the benefits of combining permutationally invariant tomography with compressed sensing by studying the influence of the pump power on the noise present in a six-qubit symmetric Dicke state, a case where full tomography is possible only for very high pump powers. LaTeX to make handling accents easierG. T\'oth, W. Wieczorek, D. Gross, R. Krischek, C. Schwemmer, and H. Weinfurter, Phys. Rev. Lett. {\bf 105}, 250403 (2010); T. Moroder, P. Hyllus, G. T\'oth, C. Schwemmer, A. Niggebaum, S. Gaile, O. G\"uhne, and H. Weinfurter, New J. Phys. {\bf 14}, 105001 (2012); C. Schwemmer, G. T\'oth, A. Niggebaum, T. Moroder, D. Gross, O. G\"uhne, and H. Weinfurter, Phys. Rev. Lett., {\bf 113}, 040503 (2014); arxiv:1401.7526. Related publicationsG. M. D'Ariano, L. Maccone, M. Paini, Spin tomography, J. Opt. B: Quantum Semiclass. Opt. 5, 77 (2003); arxiv:quant-ph/0210105.B. A. Chase and J. M. Geremia, Collective processes of an ensemble of spin-1∕2 particles, Phys. Rev. A 78, 052101 (2008).R. B. A. Adamson, P. S. Turner, M. W. Mitchell, and A. M. Steinberg, Detecting Hidden Differences via Permutation Symmetries, Phys. Rev. A 78, 033832 (2008); arXiv:quant-ph/0612081.R. B. A. Adamson , L. K. Shalm, M. W. Mitchell, and A. M. Steinberg, Multiparticle State Tomography: Hidden Differences, Phys. Rev. Lett. 98, 043601 (2007); arXiv:quant-ph/0601134.L. K. Shalm, R. B. A. Adamson, and A. M. Steinberg, Squeezing and over-squeezing of triphoton, Nature 457, 67-70 (2009). A. B. Klimov, G. Björk, and L. L. Sánchez-Soto, Optimal quantum tomography of permutationally invariant qubits, Phys. Rev. A 87, 012109 (2013); arXiv:1301.2123.L. Novo, T. Moroder, and O. Gühne, Genuine multiparticle entanglement of permutationally invariant states, Phys. Rev. A 88, 012305 (2013); arXiv:1302.4100.For other efficient tomographic methods see this link. |