https://doi.org/10.1140/epjd/e2006-00204-2
Decomposition of pure states of quantum register
1
EU Marie Curie Reintegration Postdoctoral Research Fellow, Algebra and Geometry Section, Department of Mathematics, University of Athens, Panepistimioupolis, Athens, 157 84, Greece
2
Theoretical Physics Group, Blackett Laboratory, Imperial College of Science, Technology and Medicine, Prince Consort Road, South Kensington, London, SW7 2BZ, UK
3
Theoretical Physics Group, Physics Department, Imperial College, UK
4
Department of Information Science, The State Russian Museum, Inzenernaya 4, 191186 St. Petersburg, Russia
Corresponding author: a zapatrin@rusmuseum.ru
Received:
28
March
2006
Revised:
19
July
2006
Published online:
8
September
2006
The generalization of Schmidt decomposition due to Cartelet-Higuchi-Sudbery applied to quantum register (a system of N qubits) is shown to acquire direct geometrical meaning: any pure state is canonically associated with a chain of a simplicial complex. A leading vector method is presented to calculate the values of the coefficients of appropriate chain.
PACS: 03.67.-a – Quantum information / 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.) / 03.65.Fd – Algebraic methods
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006
