The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Sample-optimal tomography of quantum states
Open accessAbstract
It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error ε in trace distance required O(dr2/ε2) copies for a d-dimensional density matrix of rank r. Here, we give a theoretical measurement scheme (POVM) that requires O(dr/δ)ln (d/δ) copies to estimate ρ to error δ in infidelity, and a matching lower bound up to logarithmic factors. This implies O((dr/ε2)ln (d/ε)) copies suffice to achieve error ε in trace distance. We also prove that for independent (product) measurements, Ω(dr2/δ2)/ ln(1/δ) copies are necessary in order to achieve error δ in infidelity. For fixed d, our measurement can be implemented on a quantum computer in time polynomial in n.
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Cites
Probabilistic and Statistical Aspects of Quantum Theory
Holevo, A. (2011) · doi:10.1007/978-88-7642-378-9 · Cited by 2,582
Quantum principal component analysis
Lloyd, S., Mohseni, M., & Rebentrost, P. (2014) · Nature Physics · doi:10.1038/nphys3029 · Cited by 1,385
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
Randomizing Quantum States: Constructions and Applications
Hayden, P., Leung, D., Shor, P. W., & Winter, A. (2004) · Communications in Mathematical Physics · doi:10.1007/s00220-004-1087-6 · Cited by 345
Estimating the spectrum of a density operator
Keyl, M., & Werner, R. F. (2001) · Physical Review A · doi:10.1103/physreva.64.052311 · Cited by 168
QUANTUM STATE ESTIMATION AND LARGE DEVIATIONS
KEYL, M. (2006) · Reviews in Mathematical Physics · doi:10.1142/s0129055x06002565 · Cited by 28
Cited by
The Variational Quantum Eigensolver: A review of methods and best practices
Tilly, J., Chen, H., Cao, S., Picozzi, D., Setia, K., Li, Y., Grant, E., Wossnig, L., Rungger, I., Booth, G. H., et al. (2022) · Physics Reports · doi:10.1016/j.physrep.2022.08.003 · Cited by 1,031
Quantum advantage in learning from experiments
Huang, H.-Y., Broughton, M., Cotler, J., Chen, S., Li, J., Mohseni, M., Neven, H., Babbush, R., Kueng, R., Preskill, J., et al. (2022) · Science · doi:10.1126/science.abn7293 · Cited by 519
Mixed-State Entanglement from Local Randomized Measurements
Elben, A., Kueng, R., Huang, H.-Y. (., van Bijnen, R., Kokail, C., Dalmonte, M., Calabrese, P., Kraus, B., Preskill, J., Zoller, P., et al. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.200501 · Cited by 292
Tomography and generative training with quantum Boltzmann machines
Kieferová, M., & Wiebe, N. (2017) · Physical Review A · doi:10.1103/physreva.96.062327 · Cited by 170
Hamiltonian simulation with optimal sample complexity
Kimmel, S., Lin, C. Y.-Y., Low, G. H., Ozols, M., & Yoder, T. J. (2017) · npj Quantum Information · doi:10.1038/s41534-017-0013-7 · Cited by 85
Metadata
- Authors
- Haah, J., Harrow, A. W., Ji, Z., Wu, X., & Yu, N.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2017
- Pages
- 1-1
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2649051464
- Cited by
- 171
- References
- 6
- FWCI
- 5.74
- Type
- journal article
- Language
- en
- Open access
- green
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