Weak approximate unitary designs and applications to quantum encryption
| Autor: | Christian Majenz, Cécilia Lancien |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Centrum Wiskunde & Informatica, Amsterdam (CWI), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Cryptography and Security Physics and Astronomy (miscellaneous) Approximations of π FOS: Physical sciences [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Unitary state [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR] [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] 0103 physical sciences FOS: Mathematics 0101 mathematics Quantum information 010306 general physics Quantum Mathematics Key size Computer Science::Cryptography and Security Discrete mathematics Quantum Physics 010102 general mathematics Probability (math.PR) lcsh:QC1-999 Atomic and Molecular Physics and Optics Functional Analysis (math.FA) Mathematics - Functional Analysis [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Quantum cryptography Norm (mathematics) Side information Quantum Physics (quant-ph) Cryptography and Security (cs.CR) lcsh:Physics Mathematics - Probability |
| Zdroj: | Quantum Quantum, 2020, ⟨10.22331/q-2020-08-28-313⟩ Quantum, Verein, 2020, ⟨10.22331/q-2020-08-28-313⟩ Quantum, 4 Quantum, Vol 4, p 313 (2020) |
| ISSN: | 2521-327X |
| 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: | OpenAIRE |
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