Even the seasoned oak, however, is not always true, and to be certain on the point Tibbald had a millstaff prover.
"Round About a Great Estate" by Richard Jefferies
Your chairman, T. L. Hazard, in his usual characteristic manner, went vigorously to work and secured all the provers possible.
"New, Old, and Forgotten Remedies: Papers by Many Writers" by Various
Your marshal wishes to know if my powder is good; he instructs you to be the gunpowder prover.
"The Knight of Malta" by Eugene Sue
The stone can then be passed to the prover or transferrer.
"Practical Lithography" by Alfred Seymour
Lov af 9de June 1903 om forandret Prover ved Universitetet.
"The School System of Norway" by David Allen Anderson
The mirror in this case is mounted somewhat after the fashion of a linen-prover; and precisely resembles a small hinge.
"Sharps and Flats" by John Nevil Maskelyne
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As discussed above, this represents the acceptance probability of a QMA(2) protocol when the measurement is ﬁxed and the provers use an optimal strategy.
Testing product states, quantum Merlin-Arthur games and tensor optimisation
As a result of Eq. (26), a k-prover soundness-s protocol can be simulated by a 2-prover protocol If k ≤ poly(n), then the messages will still have a polynomial number of with soundness s(cid:48) .
Testing product states, quantum Merlin-Arthur games and tensor optimisation
For the modiﬁed protocol, each of the k provers submits (cid:96)m qubits, and Arthur’s measurement is M ⊗(cid:96) .
Testing product states, quantum Merlin-Arthur games and tensor optimisation
If the input is a YES instance, then the provers can submit (cid:96) copies of the optimal input to the original protocol.
Testing product states, quantum Merlin-Arthur games and tensor optimisation
This state is still product (across the k provers) and has probability ≥ c(cid:96) of being accepted.
Testing product states, quantum Merlin-Arthur games and tensor optimisation
In general, the provers can submit states that are entangled across the (cid:96) different parts of their message.
Testing product states, quantum Merlin-Arthur games and tensor optimisation
However, there cannot be any entanglement between the k different provers.
Testing product states, quantum Merlin-Arthur games and tensor optimisation
The ﬁnal step of the proof is to show that applying the measurement {M , I − M } to the ﬁrst system of a multipartite product state and obtaining outcome M will not create any entanglement across the k provers.
Testing product states, quantum Merlin-Arthur games and tensor optimisation
For YES instances, the provers can send (cid:96) copies of the same proofs, each of which will be accepted with probability ≥ c.
Testing product states, quantum Merlin-Arthur games and tensor optimisation
Non-deterministic exponential time has two-prover interactive protocols.
A Unified Framework for Testing Linear-Invariant Properties
In the context of interactive proof systems, the individual we have called Alice is called the veriﬁer and Bob is called the prover.
Hedging bets with correlated quantum strategies
The veriﬁer ’s computational ability is limited (usually to probabilistic or quantum polynomial time) while the prover ’s computational ability is unrestricted.
Hedging bets with correlated quantum strategies
For each yes-instance x to L, it is possible for a prover to convince the veriﬁer to accept with probability at least α.
Hedging bets with correlated quantum strategies
For each no-instance x to L, the veriﬁer always rejects with probability at most β, regardless of the prover ’s actions.
Hedging bets with correlated quantum strategies
In the situation under consideration, one is to understand that it is important for the new veriﬁer to run these independent tests in parallel (as opposed to requiring the prover to respond sequentially to the individual tests).
Hedging bets with correlated quantum strategies
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