Full expectation-value statistics for randomly sampled pure states in high-dimensional quantum systems
Reimann P, Gemmer J (2019)
PHYSICAL REVIEW E 99(1): 12126.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Reimann, PeterUniBi;
Gemmer, Jochen
Einrichtung
Abstract / Bemerkung
We explore how the expectation values of a largely arbitrary observable A are distributed when normalized vectors vertical bar psi > are randomly sampled from a high-dimensional Hilbert space. Our analytical results predict that the distribution exhibits a very narrow peak of approximately Gaussian shape, while the tails significantly deviate from a Gaussian behavior. In the important special case that the eigenvalues of A satisfy Wigner's semicircle law, the expectation-value distribution for asymptotically large dimensions is explicitly obtained in terms of a large deviation function, which exhibits two symmetric nonanalyticities akin to critical points in thermodynamics.
Erscheinungsjahr
2019
Zeitschriftentitel
PHYSICAL REVIEW E
Band
99
Ausgabe
1
Art.-Nr.
12126
ISSN
2470-0045
eISSN
2470-0053
Page URI
https://pub.uni-bielefeld.de/record/2933516
Zitieren
Reimann P, Gemmer J. Full expectation-value statistics for randomly sampled pure states in high-dimensional quantum systems. PHYSICAL REVIEW E. 2019;99(1): 12126.
Reimann, P., & Gemmer, J. (2019). Full expectation-value statistics for randomly sampled pure states in high-dimensional quantum systems. PHYSICAL REVIEW E, 99(1), 12126. doi:10.1103/PhysRevE.99.012126
Reimann, Peter, and Gemmer, Jochen. 2019. “Full expectation-value statistics for randomly sampled pure states in high-dimensional quantum systems”. PHYSICAL REVIEW E 99 (1): 12126.
Reimann, P., and Gemmer, J. (2019). Full expectation-value statistics for randomly sampled pure states in high-dimensional quantum systems. PHYSICAL REVIEW E 99:12126.
Reimann, P., & Gemmer, J., 2019. Full expectation-value statistics for randomly sampled pure states in high-dimensional quantum systems. PHYSICAL REVIEW E, 99(1): 12126.
P. Reimann and J. Gemmer, “Full expectation-value statistics for randomly sampled pure states in high-dimensional quantum systems”, PHYSICAL REVIEW E, vol. 99, 2019, : 12126.
Reimann, P., Gemmer, J.: Full expectation-value statistics for randomly sampled pure states in high-dimensional quantum systems. PHYSICAL REVIEW E. 99, : 12126 (2019).
Reimann, Peter, and Gemmer, Jochen. “Full expectation-value statistics for randomly sampled pure states in high-dimensional quantum systems”. PHYSICAL REVIEW E 99.1 (2019): 12126.
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