Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states
Open accessAbstract
We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models. In particular, we discuss the theoretical details underlying the recent measurement of the second R\'enyi entropy of highly mixed quantum states consisting of up to ten qubits in a trapped-ion quantum simulator [Brydges et al., Science 364, 260 (2019)]. We generalize the protocol to access the overlap of quantum states, prepared sequentially in one experiment. Furthermore, we discuss proposals for quantum state tomography based on randomized measurements within our framework and the respective scaling of statistical errors with system size.
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Randomized measurements can be used to measure the overlap Tr(ρ1 ρ2) of two density matrices.
“Alternatively, one can use randomized measurements to measure the overlap Tr ( ρ 1 ρ 2 ) of two density matrices ρ 1 , ρ 2 (Elben et al. , 2020, 2019; van Enk and Beenakker, 2012).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Elben et al., 2019
Cites
Quantum Computing in the NISQ era and beyond
Preskill, J. (2018) · Quantum · doi:10.22331/q-2018-08-06-79 · Cited by 8,830 · see citing works
Quantum simulations with ultracold quantum gases
Bloch, I., Dalibard, J., & Nascimbène, S. (2012) · Nature Physics · doi:10.1038/nphys2259 · Cited by 2,339 · see citing works
Quantum simulations with trapped ions
Blatt, R., & Roos, C. F. (2012) · Nature Physics · doi:10.1038/nphys2252 · Cited by 1,629 · see citing works
Self-citationObservation of a many-body dynamical phase transition with a 53-qubit quantum simulator
Zhang, J., Pagano, G., Hess, P. W., Kyprianidis, A., Becker, P., Kaplan, H., Gorshkov, A. V., Gong, Z.-X., & Monroe, C. (2017) · Nature · doi:10.1038/nature24654 · Cited by 1,079 · see citing works
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Noisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 1,726 · see citing works
Hawking radiation correlations of evaporating black holes in JT gravity
Hollowood, T. J., Kumar, S. P., & Legramandi, A. (2020) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8121/abbc51 · Cited by 36 · see citing works
- Authors
- Elben, A., Vermersch, B., Roos, C. F., & Zoller, P.
- Affiliations
- Austrian Academy of Sciences (AT)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2019-05-15
- Volume
- 99
- Issue
- 5
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W2949799464
- Cited by
- 168
- References
- 4
- Citations by year
- 2026: 16 · 2025: 27 · 2024: 35 · 2023: 21 · 2022: 27 · 2021: 22 · 2020: 16 · 2019: 4
- FWCI
- 7.58
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Funders
- European Research Council (817482)
- Austrian Science Fund (F4016-N23)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- entanglement detection, quantum many-body states, quantum lattice models, trapped-ion quantum simulator, quantum state tomography
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