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It is conjectured that classical (BPP) client blind quantum computing is implausible according to Aaronson et al:

https://www.researchgate.net/publication/316538667_On_the_implausibility_of_classical_client_blind_quantum_computing

What are the minimal quantum capabilities that a classical client must have in order to verify a single BQP quantum prover with the following requirements?

  1. Information-secure communication (no cryptographic assumptions)
  2. Only the size of the input is revealed to the quantum prover
  3. Single prover server

My understanding is that the paper above leaves this as an open problem.

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According to this paper:

https://arxiv.org/pdf/1509.09180.pdf

The client only needs the ability to prepare random single-qubit pure states.

You may also look at this paper for more information:

https://link.springer.com/article/10.1007/s00224-018-9872-3

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    $\begingroup$ Thanks. I saw these papers. Can the client do with less quantum capabilities? $\endgroup$
    – Avi Tal
    Jun 6 '19 at 0:25
  • $\begingroup$ As per the second paper (Gheorghiu, Kapourniotis, Kashefi), there are also protocols where the client only needs single qubit measurements (but no preparation), or with purely classical client, but several server which share entanglement bu are not allowed to communicate classically, which is a rather strong constraint. There are also papers replacing qubit preparation with more realistic weak coherent pulses arXiv:1108.5571. It is difficult to be less quantum, except going fully classical, as done very recently ... $\endgroup$
    – Frédéric Grosshans
    Jun 6 '19 at 17:29
  • $\begingroup$ ... A work by Urmila Mahadev leverages postquantum cryptography to do (not unconditionally secure) blind QC with classical client: arxiv:1708.02130. It was followed by other works: IACR:2018/338 and arXiv:1904.06303. $\endgroup$
    – Frédéric Grosshans
    Jun 6 '19 at 17:38

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