Quantum t-designs: t-wise Independence in the Quantum World

A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate quantum t-designs for arbitrary t. We then show that an approximate 4-design provides a derandomization of the statedistinction problem considered by Sen (quant-ph/0512085), which is relevant to solving certain instances of the hidden subgroup problem.

• Type: Conference
• Year: 2007
• Where: COCO
• Authors: Andris Ambainis, Joseph Emerson
• Keywords: Approximate Quantum T-designs, COCO 2007, Hidden Subgroup Problem, Quantum States