Checking the homework
This is Abstractly abstract and in that abstractnezz it is poerty...juzz need be zome help or three to ζet it fλree...ear we go Jh...
Abstract
Suppose that we are given a quantum computer programmed ready to perform a computation if it is switched on. Counterfactual computation is a process by which the result of the computation may be learnt without actually running the computer. Such processes are possible within quantum physics and to achieve this effect a computer embodying the possibility of running the computation must be available, even though the computation is, in fact, not run. We study the possibilities and limitations of protocols for the counterfactual computation of decision problems (where the result r is either 0 or 1). If p⊂r denotes the probability of learning the result r 'for free' in a protocol, then one might hope to design a protocol which simultaneously has large p⊂0 and p⊂1. However, we prove that p⊂0 + p⊂1 ≤ 1 in any protocol of this type and derive further constraints on p⊂0 and p⊂1 in terms of N, the number of times that the computer is not run. In particular, we show that any protocol with p⊂0 + p⊂1 = 1 – ∈ must have N tending to infinity as ∈ tends to 0. We show that ‘interaction–free’ measurements can be regarded as counterfactual computations, and our results then imply that N must be large if the probability of interaction is to be close to zero. Finally, we consider some ways in which our formulation of counterfactual computation can be generalized...ear eye am jH...
Suppose that
[ we ]
are given
a
( quantum computer )
((programmed))
[(ready to perform])
a
{{{((([[[]]])))}}}{?computation?}
if
it
is
switched on.
Counterfactual
computation
is a process by which
the result
of
the computation
may be learnt
without actually running
the computer.
Such processes are possible within quantum physics
and
((((to achieve this effect))))
a
((((computer embodying0)))
[[[[ the possibility ]]]]
(({({of})}))
[(]) running ([(]
?the computation?
must be available, even though the computation is, in fact, not run.
We study
the possibilities and limitations
of protocols
for the counterfactual computation
of
decision problems
(where the result r is either 0 or 1)
.
If p⊂r denotes the probability of learning the result r 'for free' in a protocol, then one might hope to design a protocol which simultaneously has large p⊂0 and p⊂1.
((( However, we)))
[ prove that]
p⊂0 + p⊂1 ≤ 1
in any protocol of this type and
derive further constraints on
p⊂0 and p⊂1
in terms of N,
the number of times
that the computer is not run
.
In particular,
we show
that
any
protocol
with
p⊂0 + p⊂1 = 1 – ∈
must have N tending to infinity as ∈ tends to 0
We show that ‘interaction–free’ measurements
can be
regarded
as counterfactual computations,
and our results
then imply
that N must be large
if the probability
of interaction is
to be close to zero.
Finally, we consider some ways in which our formulation of counterfactual computation can be generalized
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