A Recursive Definition of the Holographic Standard Signature

Abstract

We provide a recursive description of the signatures realizable on the standard basis by a holographic algorithm. The description allows us to prove tight bounds on the size of planar matchgates and efficiently test for standard signatures. Over finite fields, it allows us to count the number of n-bit standard signatures and calculate their expected sparsity.

arXiv commentFixed small typo in Section 3.6