Full expectation-value statistics for randomly sampled pure states in high-dimensional quantum systems

Reimann, Peter; Gemmer, Jochen

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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DOI

https://doi.org/10.1103/PhysRevE.99.012126

Autor*in

Reimann, Peter^UniBi; Gemmer, Jochen

Einrichtung

Fakultät für Physik

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

Ausgabe

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.

Daten bereitgestellt von European Bioinformatics Institute (EBI)