Super-resolved angular displacement estimation based upon a Sagnac interferometer and parity measurement.

Super-resolved angular displacement estimation is of crucial significance to the field of quantum information processing. Here we report an estimation protocol based on a Sagnac interferometer fed by a coherent state carrying orbital angular momentum. In a lossless scenario, through the use of parity measurement, our protocol can achieve a 4ℓ-fold super-resolved output with quantum number ℓ; meanwhile, a shot-noise-limited sensitivity saturating the quantum Cramér-Rao bound is reachable. We also consider the effects of several realistic factors, including nonideal state preparation, photon loss, and inefficient measurement. Finally, with mean photon number N¯=2.297 and ℓ = 1 taken, we experimentally demonstrate a super-resolved effect of angular displacement with a factor of 7.88.

Tried-and-true binary strategy for angular displacement estimation based upon fidelity appraisal.

We demonstrate a tried-and-true binary strategy for angular displacement estimation, of which the measuring system is a modified Mach-Zehnder interferometer fed by a coherent state carrying orbital angular momentum, and two Dove prisms are embedded in two arms. Unlike previous protocols, in this paper, we use fidelity instead of standard deviation to evaluate the detection strategies. Two binary strategy candidates, parity detection and Z detection, are considered and compared. In addition, we study the effects of several realistic scenarios on the estimation protocol, including transmission loss, detection efficiency, dark counts, and those which are a combination thereof. Finally, we exhibit a proof-of-principle experiment, the results suggest a resolution enhancement effect with a factor of 3.72.

Orbital-angular-momentum-enhanced estimation of sub-Heisenberg-limited angular displacement with two-mode squeezed vacuum and parity detection.

We report on an orbital-angular-momentum-enhanced scheme for angular displacement estimation based on two-mode squeezed vacuum and parity detection. The sub-Heisenberg-limited sensitivity for angular displacement estimation is obtained in an ideal situation. Several realistic factors are also considered, including photon loss, dark counts, response-time delay, and thermal photon noise. Our results indicate that the effects of realistic factors on the sensitivity can be offset by raising orbital angular momentum quantum number ℓ. This implies that the robustness and the practicability of the system can be improved via raising ℓ without changing mean photon number N.

Super-sensitive angular displacement estimation via an SU(1,1)-SU(2) hybrid interferometer.

In this paper, we propose a protocol for the estimation of angular displacement based upon orbital angular momentum and an SU(1,1)-SU(2) hybrid interferometer. This interferometer consists of an optical parametric amplifier, a beam splitter, and reflection mirrors; the balanced homodyne detection is used as the detection strategy. The results indicate that super-resolution and super-sensitivity can be achieved with an ideal scenario. Additionally, we study the effect of photon loss on resolution and sensitivity, and the robustness of our protocol is also discussed. Finally, the advantage of our protocol compared with an SU(1,1) protocol is demonstrated, and the merits of orbital angular momentum-enhanced protocol are summarized.