TY - JOUR
T1 - Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
Y1 - 2006
A1 - Andrew M. Childs
A1 - Aram W. Harrow
A1 - Pawel Wocjan
AB - Schur duality decomposes many copies of a quantum state into subspaces labeled by partitions, a decomposition with applications throughout quantum information theory. Here we consider applying Schur duality to the problem of distinguishing coset states in the standard approach to the hidden subgroup problem. We observe that simply measuring the partition (a procedure we call weak Schur sampling) provides very little information about the hidden subgroup. Furthermore, we show that under quite general assumptions, even a combination of weak Fourier sampling and weak Schur sampling fails to identify the hidden subgroup. We also prove tight bounds on how many coset states are required to solve the hidden subgroup problem by weak Schur sampling, and we relate this question to a quantum version of the collision problem.
UR - http://arxiv.org/abs/quant-ph/0609110v1
J1 - Proc. 24th Symposium on Theoretical Aspects of Computer Science (STACS 2007)
U5 - 10.1007/978-3-540-70918-3_51
ER -