Quantum Information Processing

, Volume 15, Issue 11, pp 4391–4413 | Cite as

Grover’s algorithm and the secant varieties

  • Frédéric Holweck
  • Hamza Jaffali
  • Ismaël Nounouh


In this paper we investigate the entanglement nature of quantum states generated by Grover’s search algorithm by means of algebraic geometry. More precisely we establish a link between entanglement of states generated by the algorithm and auxiliary algebraic varieties built from the set of separable states. This new perspective enables us to propose qualitative interpretations of earlier numerical results obtained by M. Rossi et al. We also illustrate our purpose with a couple of examples investigated in details.


Quantum algorithm Entangled states Secant varieties 



The authors would like to thank Prof. Jean-Gabriel Luque for kindly providing them his Maple code to compute the invariants/covariants used in the calculation of Sect. 5.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.IRTES/UTBMUniversité de Bourgogne-Franche-ComtéBelfort CedexFrance

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