Fig. 2 | Nature Communications

Fig. 2

From: Heisenberg-limited single-mode quantum metrology in a superconducting circuit

Fig. 2

Wigner functions of the maximum variance states. Theoretical (top panel) and experimental (bottom panel) results for \(\left( {\left| 0 \right\rangle + i\left| N \right\rangle } \right)/\sqrt 2\) with state fidelities of 0.94, 0.92, 0.83, 0.70 for N = 3, 6, 9, 12, respectively. The measured state preparation fidelity decays with N, mainly attributed to the larger probability of photon loss and the worse reconstruction measurement to obtain the Wigner functions for larger N. The measured range of the real and imaginary parts of α is [−3.0, 2.9] for N = 3 and 6, [−3.6, 3.5] for N = 9, and [−3.9, 3.8] for N = 12. The angles of the dashed sectors indicate that the sensitivity of phase estimation scales as 1/N

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