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

Authors:
Andris Ambainis;Joseph Emerson
Affiliations:
University of Waterloo, Canada;University of Waterloo, Canada
Venue:
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Year:
2007

Citing 0
Cited 6

An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups

Mathematical Methods in Computer Science
Unitary designs and codes

Designs, Codes and Cryptography
Efficient Quantum Tensor Product Expanders and k-Designs

APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Depolarizing behavior of quantum channels in higher dimensions

Quantum Information & Computation
Limitations on quantum dimensionality reduction

ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Hypercontractivity, sum-of-squares proofs, and their applications

STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.