The European Physical Journal D

, Volume 41, Issue 1, pp 185–188 | Cite as

Decomposition of pure states of quantum register

  • I. Raptis
  • P. Wallden
  • R. R. ZapatrinEmail author
Quantum Optics and Quantum Information


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.


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 


31.40.+d Multiparty entanglement distribution 


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  2. H.A. Carteret, A. Higuchi, A. Sudbery; J. Math. Phys. 41, 7932 (2000); e-print arXiv:quant-ph/0006125 CrossRefADSMathSciNetGoogle Scholar
  3. I. Raptis, P. Wallden, R.R. Zapatrin, to appear in a special proceedings issue (Glafka, 2004) of Int. J. Theor. Phys.; e-print arXiv:gr-qc/0506088 Google Scholar
  4. I. Raptis, P. Wallden, R.R. Zapatrin; e-print arXiv:gr-qc/0510053 Google Scholar
  5. R.R. Zapatrin, J. Mod. Opt. 50, 891 (2003); e-print arXiv:quant-ph/0207058 CrossRefADSMathSciNetGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  1. 1.EU Marie Curie Reintegration Postdoctoral Research Fellow, Algebra and Geometry Section, Department of MathematicsUniversity of AthensAthensGreece
  2. 2.Theoretical Physics Group, Blackett LaboratoryLondonUK
  3. 3.Theoretical Physics Group, Physics DepartmentImperial CollegeUK
  4. 4.Department of Information ScienceSt. PetersburgRussia

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