All Quantum Adversary Methods Are Equivalent

  • Robert Špalek
  • Mario Szegedy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3580)


The quantum adversary method is one of the most versatile lower-bound methods for quantum algorithms. We show that all known variants of this method are equal: spectral adversary [1], weighted adversary [2], strong weighted adversary [3], and the Kolmogorov complexity adversary [4]. We also present a few new equivalent formulations of the method. This shows that there is essentially one quantum adversary method. From our approach, all known limitations of all versions of the quantum adversary method easily follow.


Weight Scheme Query Complexity Kolmogorov Complexity Polynomial Method Boolean Matrice 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Robert Špalek
    • 1
  • Mario Szegedy
    • 2
  1. 1.CWIAmsterdam
  2. 2.Rutgers University 

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