Weak approximate unitary designs and applications to quantum encryption - Archive ouverte HAL
Article Dans Une Revue Quantum Année : 2020

Weak approximate unitary designs and applications to quantum encryption

Résumé

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.

Dates et versions

hal-03024389 , version 1 (25-11-2020)

Identifiants

Citer

Cécilia Lancien, Christian Majenz. Weak approximate unitary designs and applications to quantum encryption. Quantum, 2020, ⟨10.22331/q-2020-08-28-313⟩. ⟨hal-03024389⟩
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