Title

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

Journal title

Bulletin of the Polish Academy of Sciences Technical Sciences

Yearbook

2017

Volume

65

Issue

No 1

Authors

Puchała, Z. ; Miszczak, J.A.

Divisions of PAS

Nauki Techniczne

Coverage

21-27

Date

2017

Identifier

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

Source

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

References

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.