Weak approximate unitary designs and applications to quantum encryption

Quantum 4, 313 (2020).

https://doi.org/10.22331/q-2020-08-28-313

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 $d^tmathrm{poly}(t,log d, 1/epsilon)$ 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. 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.

Source Quantum | The open journal for quantum science Weak approximate unitary designs and applications to quantum encryption

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