A measurement device for performing projective measurements onto higher-dimensional quantum states which are defined by a computational basis {|m>|m∈{0, 1, . . . , d−1}} of d-dimensional quantum states made up of states of orthogonal light, and mutually unbiased bases of label r (integer of 0 or more) that are non-orthogonal to the computational basis and define a quantum state of label n (0, 1, . . . , d−1),
- wherein d=2N (N is a natural number of 2 or more),
- the quantum state of the label n is expressed by the following equation,
- ❘
- "\[LeftBracketingBar]"
- ψ
- n
- (
- r
- )
- 〉
- =
- ∑
- m
- B
- mn
- (
- r
- )
-
- ❘
- "\[LeftBracketingBar]"
- m
- 〉
- wherein a probability amplitude Bmn(r) is decomposed into a diagonal unitary matrix and a Hadamard transform matrix, the measurement device comprises:
- a phase modulation unit which corresponds to the diagonal unitary matrix, and applies a phase modulation to each of the state of the computational basis of a received d-dimensional quantum state;
- and
- a measurement unit which corresponds to the Hadamard transform matrix and determines the label n of the d-dimensional quantum state.