DeepAI AI Chat
Log In Sign Up

Weak approximate unitary designs and applications to quantum encryption

by   Cécilia Lancien, et al.
Centrum Wiskunde & Informatica
Université de Toulouse

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 d^tpoly(t,log d, 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 distance of the corresponding t-twirling channels. As an application, we give a partially derandomized 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.


page 1

page 2

page 3

page 4


Efficient Quantum Public-Key Encryption From Learning With Errors

Our main result is a quantum public-key encryption scheme based on the E...

Powerful Primitives in the Bounded Quantum Storage Model

The bounded quantum storage model aims to achieve security against compu...

Mosaics of Combinatorial Designs for Semantic Security on Quantum Wiretap Channels

We study semantic security for classical-quantum channels. Our security ...

Non-malleability for quantum public-key encryption

Non-malleability is an important security property for public-key encryp...

Limitations on Uncloneable Encryption and Simultaneous One-Way-to-Hiding

We study uncloneable quantum encryption schemes for classical messages a...

Ascent with Quadratic Assistance for the Construction of Exact Experimental Designs

In the area of experimental design, there is a large body of theoretical...

Efficient simulation of random states and random unitaries

We consider the problem of efficiently simulating random quantum states ...