Video URL
https://pirsa.org/20100049Weak approximate unitary designs and applications to quantum encryption
APA
Majenz, C. (2020). Weak approximate unitary designs and applications to quantum encryption. Perimeter Institute for Theoretical Physics. https://pirsa.org/20100049
MLA
Majenz, Christian. Weak approximate unitary designs and applications to quantum encryption. Perimeter Institute for Theoretical Physics, Oct. 14, 2020, https://pirsa.org/20100049
BibTex
@misc{ scivideos_PIRSA:20100049, doi = {10.48660/20100049}, url = {https://pirsa.org/20100049}, author = {Majenz, Christian}, keywords = {Quantum Information}, language = {en}, title = {Weak approximate unitary designs and applications to quantum encryption}, publisher = {Perimeter Institute for Theoretical Physics}, year = {2020}, month = {oct}, note = {PIRSA:20100049 see, \url{https://scivideos.org/index.php/pirsa/20100049}} }
Christian Majenz Centrum Wiskunde & Informatica
Abstract
Unitary t-designs are the bread and butter of quantum information theory and beyond. An important issue in practice is that of efficiently constructing good approximations of such unitary t-designs. Building on results by Aubrun (Comm. Math. Phys. 2009), we prove that sampling dtpoly(t,logd,1/ϵ) unitaries from an exact t-design provides with positive probability an ϵ-approximate t-design, if the error is measured in one-to-one norm. As an application, we give a randomized construction of a quantum encryption scheme that has roughly the same key size and security as the quantum one-time pad, but possesses the additional property of being non-malleable against adversaries without quantum side information. Joint work with Cécilia Lancien.