Główne pojęcia
Quantum one-way state generators (OWSGs) with O(n/log(n)) copies are equivalent to quantum commitments and to polytime-copy OWSGs. The weakest OWSGs from which quantum commitments can be obtained are those with O(n/log(n)) copies.
Streszczenie
The content discusses the relationship between quantum one-way state generators (OWSGs) and quantum commitments.
Key highlights:
OWSGs are quantum analogues of classical one-way functions, where the output is a quantum state rather than a classical string.
It is shown that O(n/log(n))-copy OWSGs are equivalent to polytime-copy OWSGs and to quantum commitments.
This establishes that O(n/log(n))-copy OWSGs are the weakest OWSGs from which quantum commitments can be obtained.
The proof follows a construction similar to the classical case of obtaining pseudorandom generators from one-way functions, but with crucial modifications to handle the quantum setting.
The construction involves flattening the quantum state, using properties of Rényi entropies, and applying quantum extractors to amplify the statistical difference between the commitment states.
The reverse direction, showing that quantum commitments imply polytime-copy OWSGs, is also established.
These results connect quantum commitments to the fundamental primitive of OWSGs, and have implications for secure multi-party computation in the quantum setting.