Next Article in Journal
Multiscale Entropy Feature Extraction Method of Running Power Equipment Sound
Previous Article in Journal
Research on Extraction of Compound Fault Characteristics for Rolling Bearings in Wind Turbines
Previous Article in Special Issue
What Does the Operator Algebra of Quantum Statistics Tell Us about the Objective Causes of Observable Effects?
Open AccessFeature PaperArticle

Generic Entanglement Entropy for Quantum States with Symmetry

by Yoshifumi Nakata 1,2,*,† and Mio Murao 3,†
1
Photon Science Center, Graduate School of Engineering, The University of Tokyo, 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan
2
Japan Science and Technology Agency (JST), Precursory Research for Embryonic Science and Technology (PRESTO), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
3
Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
*
Author to whom correspondence should be addressed.
Both authors contributed to the formulation of the problem. The main analysis was done by Y.N. in collaboration with M.M.
Entropy 2020, 22(6), 684; https://doi.org/10.3390/e22060684
Received: 1 June 2020 / Revised: 16 June 2020 / Accepted: 17 June 2020 / Published: 19 June 2020
(This article belongs to the Special Issue Quantum Probability, Statistics and Control)
When a quantum pure state is drawn uniformly at random from a Hilbert space, the state is typically highly entangled. This property of a random state is known as generic entanglement of quantum states and has been long investigated from many perspectives, ranging from the black hole science to quantum information science. In this paper, we address the question of how symmetry of quantum states changes the properties of generic entanglement. More specifically, we study bipartite entanglement entropy of a quantum state that is drawn uniformly at random from an invariant subspace of a given symmetry. We first extend the well-known concentration formula to the one applicable to any subspace and then show that 1. quantum states in the subspaces associated with an axial symmetry are still highly entangled, though it is less than that of the quantum states without symmetry, 2. quantum states associated with the permutation symmetry are significantly less entangled, and 3. quantum states with translation symmetry are as entangled as the generic one. We also numerically investigate the phase-transition behavior of the distribution of generic entanglement, which indicates that the phase transition seems to still exist even when random states have symmetry. View Full-Text
Keywords: entanglement entropy; symmetry; random states entanglement entropy; symmetry; random states
Show Figures

Figure 1

MDPI and ACS Style

Nakata, Y.; Murao, M. Generic Entanglement Entropy for Quantum States with Symmetry. Entropy 2020, 22, 684.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop