On Nonzero Kronecker Coefficients and their Consequences for Spectra
| dc.creator | Christandl, Matthias | |
| dc.creator | Harrow, Aram | |
| dc.creator | Mitchison, Graeme | |
| dc.date | 2005-11-03 | |
| dc.date.accessioned | 2026-07-07T07:45:26Z | |
| dc.date.available | 2026-07-07T07:45:26Z | |
| dc.description | A triple of spectra (r^A, r^B, r^{AB}) is said to be admissible if there is a density operator rho^{AB} with (Spec rho^A, Spec rho^B, Spec rho^{AB})=(r^A, r^B, r^{AB}). How can we characterise such triples? It turns out that the admissible spectral triples correspond to Young diagrams (mu, nu, lambda) with nonzero Kronecker coefficient [M. Christandl and G. Mitchison, to appear in Comm. Math. Phys., quant-ph/0409016; A. Klyachko, quant-ph/0409113]. This means that the irreducible representation V_lambda is contained in the tensor product of V_mu and V_nu. Here, we show that such triples form a finitely generated semigroup, thereby resolving a conjecture of Klyachko. As a consequence we are able to obtain stronger results than in [M. Ch. and G. M. op. cit.] and give a complete information-theoretic proof of the correspondence between triples of spectra and representations. Finally, we show that spectral triples form a convex polytope. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0511029 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0511029 | |
| dc.identifier | Commun. Math. Phys., 270, 575-585 (2007) | |
| dc.identifier | doi:10.1007/s00220-006-0157-3 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123526 | |
| dc.subject | Quantum Physics | |
| dc.title | On Nonzero Kronecker Coefficients and their Consequences for Spectra | |
| dc.type | text |