On the distribution of the mean energy in the unitary orbit of quantum states

Raffaele Salvia; Vittorio Giovannetti

doi:10.22331/q-2021-08-03-514

On the distribution of the mean energy in the unitary orbit of quantum states

Raffaele Salvia¹ and Vittorio Giovannetti²

¹Scuola Normale Superiore and University of Pisa, I-56127 Pisa, Italy
²NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy

Published:	2021-08-03, volume 5, page 514
Eprint:	arXiv:2012.14342v3
Doi:	https://doi.org/10.22331/q-2021-08-03-514
Citation:	Quantum 5, 514 (2021).

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Abstract

Given a closed quantum system, the states that can be reached with a cyclic process are those with the same spectrum as the initial state. Here we prove that, under a very general assumption on the Hamiltonian, the distribution of the mean extractable work is very close to a gaussian with respect to the Haar measure. We derive bounds for both the moments of the distribution of the mean energy of the state and for its characteristic function, showing that the discrepancy with the normal distribution is increasingly suppressed for large dimensions of the system Hilbert space.

► BibTeX data

@article{Salvia2021distributionofmean,
  doi = {10.22331/q-2021-08-03-514},
  url = {https://doi.org/10.22331/q-2021-08-03-514},
  title = {On the distribution of the mean energy in the unitary orbit of quantum states},
  author = {Salvia, Raffaele and Giovannetti, Vittorio},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {514},
  month = aug,
  year = {2021}
}

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