The Symmetric Group Defies Strong Fourier Sampling: Part II

Details The Symmetric Group Defies Strong Fourier Sampling: Part II The Symmetric Group Defies Strong Fourier Sampling: Part II

2005-01-13

arxiv.org/abs/quant-ph/0501066v3

Physics

Quantum Physics

18 pages; v2: fix typos, v3: adds technical lemma and revises Lemma 19

Scientific paper

Part I of this paper showed that the hidden subgroup problem over the symmetric group--including the special case relevant to Graph Isomorphism--cannot be efficiently solved by strong Fourier sampling, even if one may perform an arbitrary POVM on the coset state. In this paper, we extend these results to entangled measurements. Specifically, we show that the hidden subgroup problem on the symmetric group cannot be solved by any POVM applied to pairs of coset states. In particular, these hidden subgroups cannot be determined by any polynomial number of one- or two-register experiments on coset states.

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