The power of a single Haar random state: constructing and separating quantum pseudorandomness
arxiv(2024)
摘要
In this work, we focus on the following question: what are the cryptographic
implications of having access to an oracle that provides a single Haar random
quantum state? We show, perhaps surprisingly, that such an oracle is sufficient
to construct quantum pseudorandomness.
Pseudorandom states (PRS) are a family of states for which it is hard to
distinguish between polynomially many copies of either a state sampled
uniformly from the family or a Haar random state. A weaker notion, called
single-copy pseudorandom states (1PRS), satisfies this property with respect to
a single copy. Our main result is that 1PRS (as well as bit-commitments) exist
relative to an oracle that provides a single Haar random state. We build on
this result to show the existence of an oracle relative to which 1PRS exist,
but PRS do not. This provides one of the first black-box separations between
different forms of quantum pseudorandomness.
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