# Experimental comparison of efficient tomography schemes for a six-qubit state.

@article{Schwemmer2014ExperimentalCO, title={Experimental comparison of efficient tomography schemes for a six-qubit state.}, author={Christian Schwemmer and G{\'e}za T{\'o}th and Alexander Niggebaum and Tobias Moroder and David Gross and Otfried G{\"u}hne and Harald Weinfurter}, journal={Physical review letters}, year={2014}, volume={113 4}, pages={ 040503 } }

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 demonstrate the benefits of combining permutationally invariant tomography with compressed…

## 56 Citations

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## References

SHOWING 1-10 OF 14 REFERENCES

### An Introduction to the Bootstrap

- Economics
- 1993

Statistics is the science of learning from experience, especially experience that arrives a little bit at a time. The earliest information
science was statistics, originating in about 1650. This…

### Convex Optimization

- Computer ScienceIEEE Transactions on Automatic Control
- 2006

A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency.

### An Introduction to the Bootstrap

- Mathematics
- 2007

15 Empirical Bayes Method, 2nd edition J.S. Maritz and T. Lwin (1989) Symmetric Multivariate and Related Distributions K.-T. Fang, S. Kotz and K. Ng (1989) Ieneralized Linear Models, 2nd edition P.…

### Phys

- Rev. Lett. 103, 020504 (2009); R. Prevedel, G. Cronenberg, M. S. Tame, M. Paternostro, P. Walther, M. S. Kim, and A. Zeilinger, Phys. Rev. Lett. 103, 020503
- 2009

### For efficient entanglement detection methods for PI density matrices , see L . Novo , T . Moroder , and O . Gühne

- 2013

### Phys

- Rev. A 87, 012109
- 2013

### Phys

- Rev. Lett. 111, 020401 (2013); T. Baumgratz, A. Nüßeler, M. Cramer, and M. B. Plenio, New J. Phys. 15, 125004
- 2013

### New J

- Phys. 11, 083002
- 2009

### Phys

- Rev. Lett. 105, 150401 (2010); S. T. Flammia, D.Gross, Y.-K. Liu, and J. Eisert, New J. Phys. 14, 095022 (2012); M. Ohliger, V. Nesme, D. Gross, Y.-K. Liu, and J. Eisert, arXiv:1111.0853; M. Guţă, T. Kypraios, and I. Dryden, New J. Phys. 14, 105002 (2012); M. Ohliger, V. Nesme, and J. Eisert, New J.
- 2013

### Phys

- Rev. Lett. 82, 4344
- 1999