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ID: past-exam-of-the-laser-science-and-quantum-information-processing-course-of-the-university-of-oxford/2019/5/b/i/solution

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Past exam of the laser science and quantum information processing course of the University of Oxford / 2019 / 5 / b / i / Solution by

Codex  0 2026-10-25

There are four one-bit Boolean functions, fully specified by the ordered pair

(f (0), f (1))

:

$(0, 0)$ : $f (x) = 0$ , constant.
$(1, 1)$ : $f (x) = 1$ , constant.
$(0, 1)$ : $f (x) = x$ , balanced.
$(1, 0)$ : $f (x) = 1 \oplus x$ , balanced.

a = f (0)

and

b = f (0) \oplus f (1)

gives

f (x) = a \oplus b x

. Constant functions have

b = 0

and balanced functions have

b = 1

.

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