PIRSA:20100049

Weak approximate unitary designs and applications to quantum encryption

Majenz, C. (2020). Weak approximate unitary designs and applications to quantum encryption. Perimeter Institute. https://pirsa.org/20100049

Majenz, Christian. Weak approximate unitary designs and applications to quantum encryption. Perimeter Institute, Oct. 14, 2020, https://pirsa.org/20100049 

          @misc{ pirsa_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},
            year = {2020},
            month = {oct},
            note = {PIRSA:20100049 see, \url{https://pirsa.org}}
          }

Christian Majenz

Centrum Wiskunde & Informatica

Talk number
PIRSA:20100049
Collection
Talk Type
Subject
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.