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Quantum criticality as a resource for quantum estimation
Open accessAbstract
We address quantum critical systems as a resource in quantum estimation and derive the ultimate quantum limits to the precision of any estimator of the coupling parameters. In particular, if $L$ denotes the size of a system and $\ensuremath{\lambda}$ is the relevant coupling parameters driving a quantum phase transition, we show that a precision improvement of order $1∕L$ may be achieved in the estimation of $\ensuremath{\lambda}$ at the critical point compared to the noncritical case. We show that analog results hold for temperature estimation in classical phase transitions. Results are illustrated by means of a specific example involving a fermion tight-binding model with pair creation (BCS model).
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Cites
Statistical distance and the geometry of quantum states
Braunstein, S. L., & Caves, C. M. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.3439 · Cited by 3,176
Giovannetti, V., Lloyd, S., & Maccone, L. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.010401 · Cited by 2,440
Quantum critical scaling of the geometric tensors
Campos Venuti, L., & Zanardi, P. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.095701 · Cited by 499
Self-citationMinimum mean-squared error of estimates in quantum statistics
Helstrom, C. W. (1967) · Physics Letters A · doi:10.1016/0375-9601(67)90366-0 · Cited by 441
Bures volume of the set of mixed quantum states
Sommers, H.-J. R., & Zyczkowski, K. (2003) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/36/39/308 · Cited by 163
Cited by
Ma, J., Wang, X., Sun, C. P., & Nori, F. (2011) · Physics Reports · doi:10.1016/j.physrep.2011.08.003 · Cited by 846
Quantum Fisher information matrix and multiparameter estimation
Liu, J., Yuan, H., Lu, X.-M., & Wang, X. (2020) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8121/ab5d4d · Cited by 802
Quantum-enhanced measurements without entanglement
Braun, D., Adesso, G., Benatti, F., Floreanini, R., Marzolino, U., Mitchell, M. W., & Pirandola, S. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.035006 · Cited by 434
Geometry and non-adiabatic response in quantum and classical systems
Kolodrubetz, M., Sels, D., Mehta, P., & Polkovnikov, A. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.07.001 · Cited by 326
Generalized Geometric Quantum Speed Limits
Pires, D. P., Cianciaruso, M., Céleri, L. C., Adesso, G., & Soares-Pinto, D. O. (2016) · Physical Review X · doi:10.1103/physrevx.6.021031 · Cited by 265
Metadata
- Authors
- Zanardi, P., Paris, M. G. A., & Campos Venuti, L.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2008-10-09
- Volume
- 78
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2082725659
- Cited by
- 314
- References
- 5
- FWCI
- 2.90
- Type
- journal article
- Language
- en
- Open access
- green
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