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arXiv · 1911.06742

Weak approximate unitary designs and applications to quantum encryption

Cécilia Lancien·Christian Majenz
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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 $d^t\mathrm{poly}(t,\log d, 1/\epsilon)$ unitaries from an exact $t$-design provides with positive probability an $\epsilon$-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.

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Cécilia Lancien, Christian Majenz. 2019-11-15. Weak approximate unitary designs and applications to quantum encryption. https://doi.org/10.22331/q-2020-08-28-313

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