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Quantum State Tomography via Compressed Sensing
Open accessAbstract
We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rdlog²d) measurement settings, compared to standard methods that require d² settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed.
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Cites
Demonstration of an all-optical quantum controlled-NOT gate
O'Brien, J. L., Pryde, G. J., White, A. G., Ralph, T. C., & Branning, D. (2003) · Nature · doi:10.1038/nature02054 · Cited by 992
Cited by
Degen, C. L., Reinhard, F., & Cappellaro, P. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.035002 · Cited by 4,045
Quantum principal component analysis
Lloyd, S., Mohseni, M., & Rebentrost, P. (2014) · Nature Physics · doi:10.1038/nphys3029 · Cited by 1,385
Multidimensional quantum entanglement with large-scale integrated optics
Wang, J., Paesani, S., Ding, Y., Santagati, R., Skrzypczyk, P., Salavrakos, A., Tura, J., Augusiak, R., Mančinska, L., Bacco, D., et al. (2018) · Science · doi:10.1126/science.aar7053 · Cited by 816
Quantum Algorithm for Data Fitting
Wiebe, N., Braun, D., & Lloyd, S. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.050505 · Cited by 528
Direct Fidelity Estimation from Few Pauli Measurements
Flammia, S. T., & Liu, Y.-K. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.230501 · Cited by 449
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Metadata
- Authors
- Gross, D., Liu, Y.-K., Flammia, S. T., Becker, S., & Eisert, J.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2010-10-04
- Volume
- 105
- Issue
- 15
- Pages
- 150401-150401
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1529624360
- Cited by
- 1,093
- References
- 1
- FWCI
- 46.25
- Type
- journal article
- Language
- en
- Open access
- green
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- Gross, D., Liu, Y.-K., Flammia, S. T., Becker, S., & Eisert, J. (2010). Quantum State Tomography via Compressed Sensing. Physical Review Letters. https://doi.org/10.1103/physrevlett.105.150401
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