eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-06-22
2:1
2:20
10.4230/LIPIcs.TQC.2021.2
article
Quantum Pseudorandomness and Classical Complexity
Kretschmer, William
1
https://orcid.org/0000-0002-7784-9817
University of Texas at Austin, TX, USA
We construct a quantum oracle relative to which BQP = QMA but cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist, a counterintuitive result in light of the fact that pseudorandom states can be "broken" by quantum Merlin-Arthur adversaries. We explain how this nuance arises as the result of a distinction between algorithms that operate on quantum and classical inputs. On the other hand, we show that some computational complexity assumption is needed to construct pseudorandom states, by proving that pseudorandom states do not exist if BQP = PP. We discuss implications of these results for cryptography, complexity theory, and quantum tomography.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol197-tqc2021/LIPIcs.TQC.2021.2/LIPIcs.TQC.2021.2.pdf
pseudorandom quantum states
quantum Merlin-Arthur