Quantum Pseudorandomness and Classical Complexity
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.
pseudorandom quantum states
quantum Merlin-Arthur
Theory of computation~Quantum complexity theory
2:1-2:20
Regular Paper
https://arxiv.org/abs/2103.09320
Thanks to Scott Aaronson for suggestions on the writing, Adam Bouland for insightful discussions, and Qipeng Liu for clarifying some questions about [Kai-Min Chung et al., 2020].
William
Kretschmer
William Kretschmer
University of Texas at Austin, TX, USA
https://www.cs.utexas.edu/~kretsch/
https://orcid.org/0000-0002-7784-9817
Supported by a National Defense Science and Engineering Graduate (NDSEG) Fellowship from the US Department of Defense.
10.4230/LIPIcs.TQC.2021.2
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William Kretschmer
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