Random Unitary Matrices Associated to a Graph

• Authors: P. Kondratiuk , K. Życzkowski
• Languages of publication: EN

Abstracts

EN

We analyze composed quantum systems consisting of k subsystems, each described by states in the n-}dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual subsystems and edges denoting a generic interaction, modeled by random unitary matrices of order n^2. The global evolution operator is represented by a unitary matrix of size N = n^{k}. We investigate statistical properties of such matrices and show that they display spectral properties characteristic to the Haar random unitary matrices provided the corresponding graph is connected. Thus basing on random unitary matrices of a small size n^2 one can construct a fair approximation of large random unitary matrices of size n^{k}. Graph-structured random unitary matrices investigated here allow one to define the corresponding structured ensembles of random pure states.

Keywords

EN

02.10.Yn; 03.65.Aa; 03.67.Mn; 05.45.Mt; 05.45.Pq

Discipline

• 02.10.Yn: Matrix theory
• 03.67.Mn: Entanglement measures, witnesses, and other characterizations(see also 03.65.Ud Entanglement and quantum nonlocality; 42.50.Dv Quantum state engineering and measurements in quantum optics)
• 03.65.Aa: Quantum systems with finite Hilbert space
• 05.45.Pq: Numerical simulations of chaotic systems
• 05.45.Mt: Quantum chaos; semiclassical methods

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2013
• Volume: 124
• Issue: 6
• Pages: 1098-1105

Dates

published

2013-12

Contributors

author

P. Kondratiuk

• Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland

author

K. Życzkowski

• Institute of Physics, Jagiellonian University, W.S. Reymonta 4, 30-059 Kraków, Poland
• Center for Theoretical Physics, PAS, al. Lotników 32/44, 02-668 Warszawa, Poland

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Identifiers

DOI

10.12693/APhysPolA.124.1098