
Perfect zero knowledge for quantum multiprover interactive proofs
In this work we consider the interplay between multiprover interactive p...
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Interactive Proofs with PolynomialTime Quantum Prover for Computing the Order of Solvable Groups
In this paper we consider what can be computed by a user interacting wit...
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Quantum proof systems for iterated exponential time, and beyond
We show that any language in nondeterministic time ((...(n))), where the...
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Quantum Pseudorandomness and Classical Complexity
We construct a quantum oracle relative to which π‘π°π― = π°π¬π but cryptograp...
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Analysis of Quantum MultiProver ZeroKnowledge Systems: Elimination of the Honest Condition and Computational ZeroKnowledge Systems for QMIP*
Zeroknowledge and multiprover systems are both central notions in clas...
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Algorithmic Randomness and Kolmogorov Complexity for Qubits
Nies and Scholz defined quantum MartinLΓΆf randomness (qMLR) for states...
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Transforming graph states using singlequbit operations
Stabilizer states form an important class of states in quantum informati...
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Interactive Proofs for Synthesizing Quantum States and Unitaries
Whereas quantum complexity theory has traditionally been concerned with problems arising from classical complexity theory (such as computing boolean functions), it also makes sense to study the complexity of inherently quantum operations such as constructing quantum states or performing unitary transformations. With this motivation, we define models of interactive proofs for synthesizing quantum states and unitaries, where a polynomialtime quantum verifier interacts with an untrusted quantum prover, and a verifier who accepts also outputs an approximation of the target state (for the state synthesis problem) or the result of the target unitary applied to the input state (for the unitary synthesis problem); furthermore there should exist an "honest" prover which the verifier accepts with probability 1. Our main result is a "state synthesis" analogue of the inclusion π―π²π―π π’π€βπ¨π―: any sequence of states computable by a polynomialspace quantum algorithm (which may run for exponential time) admits an interactive protocol of the form described above. Leveraging this state synthesis protocol, we also give a unitary synthesis protocol for polynomial spacecomputable unitaries that act nontrivially on only a polynomialdimensional subspace. We obtain analogous results in the setting with multiple entangled provers as well.
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