Question

I need help with this homework question:

Suppose you are able to perform any quantum operations on a qubit, but you are only able to measure its state in the {|0>,|1>} basis. Explain how you would
go about performing a quantum measurement that would be equivalent to measuring {|+>,|->} basis. Show your result mathematically.

Answer 1

As we basit in l ê & 12 e isits can then can then measure the a A= loft All measure the quantity A Bot 107 117 412 A A AL, AR, A21, A2 known hero, we want to know A in It) & 1-7 basts ty A = (-4 <+117) ALL 7 - Ail now, LAZI AD now 17 / 2 (10) + H) w != tallo)-11) Hanso, As = L4Alt> = 1 / 2 (501 + 2 A 167 +17 (W)x Amo All = 2 2 2 & 41+ A217 A 12 +422) A 12 = + (Alt A21 - AR- A22). A 21 = √ (Ani + A12-A21 - A22) go, we get A n lte H basis. Nou 422) - 22 = / 2 (An - A12-A217