′sin 2 μ?τ4 ? = x 2 4 μ1? x 2 4 ?+ μ1? x 2 4 ?x 2 4 = x 2 2 This is half the probability in part (a). (d) After three measurements: p 1(τ) = 3× x 2 9 μ1? x 2 9 ?μ1? x 2 9 ? = x 2 3 Afternmeasurements p 1(τ) = x 2 n p 0(τ) = 1? x 2 n 'e ?x/n The Fourier theorem sets a limit on the min- imum frequency width for a measurement in a ?nite timeτ(c.f. transit-time broadening in eqn 8.10). (13.6)Initial state: α(a|000i+b|111i) +β(a|100i+b|011i) + γ(a|010i+b|101i) +δ(a|001i+b|110i). OT(1,2) α(a|000i+b|101i) +β(a|110i+b|011i) + γ(a|010i+b|111i) +δ(a|001i+b|100i). OT(1,3) α(a|000i+b|100i) +β(a|111i+b|011i) + γ(a|010i+b|110i) +δ(a|001i+b|101i) = (a|0i+b|1i){α|00i+γ|10i+δ|01i}+ (a|1i+b|0i)β|11i. Measure qubits 2 and 3; if|11i(≡|x11iwith xarbitrary) then perform NOT operation on qubit 1. 10
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