Weak approximate unitary designs and applications to quantum encryption
| Autor: | Lancien, Cécilia, Majenz, Christian |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Quantum 4, 313 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.22331/q-2020-08-28-313 |
| Popis: | 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. Comment: 20 pages. Published version |
| Databáze: | arXiv |
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