Fig. 1 | Nature Communications

Fig. 1

From: Experimental optical phase measurement approaching the exact Heisenberg limit

Fig. 1

Optical phase measurement concept. a Basic interferometric setup for estimation of an unknown phase ϕ. b Conceptual scheme of an advanced interferometer that includes multiple (p) passes of the phase shift ϕ and a controllable phase θ in the reference arm. c Quantum circuit representation of the interferometer shown in b. The interferometer is represented by a Hadamard gate \({\cal H}\) and a projective measurement in the X-basis, and the application of reference and unknown phases (p passes) is represented by unitary operators \({\cal R}(\theta )\) and Up, respectively. d Quantum circuit for Heisenberg-limited interferometric phase estimation with N = 3 resources. The protocol is extensible to higher N, in principle15. e Quantum circuit for the preparation of the optimal state \(|\psi _{{\mathrm{opt}}}\rangle\), Eq. (2), using a CNOT gate with control and target qubits prepared in \(|\psi _{\mathrm{C}}\rangle\) and \(|\psi _{\mathrm{T}}\rangle\), respectively

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