Tytuł artykułu

Symbolic integration with respect to the Haar measure on the unitary groups

Tytuł czasopisma

Bulletin of the Polish Academy of Sciences Technical Sciences

Rocznik

2017

Wolumin

65

Numer

No 1

Autorzy

Puchała, Z. ; Miszczak, J.A.

Wydział PAN

Nauki Techniczne

Zakres

21-27

Data

2017

Identyfikator

DOI: 10.1515/bpasts-2017-0003 ; ISSN 2300-1917

Źródło

Bulletin of the Polish Academy of Sciences: Technical Sciences; 2017; 65; No 1; 21-27

Referencje

Enríquez (2015), Minimal Rényi - - Ingarden - Urbanik entropy of multipartite quantum states, Entropy, 17, 5063, doi.org/10.3390/e17075063 ; Bernstein (2004), The computational complexity of rules for the character table of Sn of, Journal Symbolic Computation, 37, 727, doi.org/10.1016/j.jsc.2003.11.001 ; Fulton (1991), Representation First Course - Graduate Texts in Mathematics vol Springer Verlag, Theory, 129. ; Puchała (2012), Restricted numerical shadow and the geometry of quantum entanglement Journal of Physics A : Mathematical and, Theoretical, 45, 41. ; Dunkl (2011), Numerical shadows : measures and densities on the numerical range Linear, Algebra Appl, 434. ; Hiai (2006), The semicircle law free random variables and entropy Amer Mathematical, Society, 77. ; Collins (2006), Integration with respect to the Haar measure on unitary orthogonal and symplectic group, Commun Math Phys, 264. ; Weingarten (1978), Asymptotic behavior of group integrals in the limit of infinite rank of, Journal Mathematical Physics, 19, 999, doi.org/10.1063/1.523807 ; Dunkl (2011), Numerical shadow and geometry of quantum states, Phys A Math Theor, 44, 33. ; Ullah (1963), Expectation value fluctuations in the unitary ensemble, Physical Review, 132. ; Miszczak (2012), Generating and using truly random quantum states in Mathematica, Comput Phys Commun, 183.