Speaker
Description
The second-ordered anti-coherent state is known to achieve the ultimate limit for sensing rotation around an unknown axis, thereby saturating the quantum Cramér-Rao bound. It is convenient to map these states into an angular-momentum basis. Limited to measuring a small rotation angle, a corresponding set of bases has also been selected, postulated to provide the ultimate precision in rotation sensing. Let a second-ordered anti-coherent state serve as the initial state. An optimal basis measurement for rotation-angle extraction consists of projecting the resultant state onto the initial state, and onto the states corresponding to the angular momentum operators J_x, J_y, and J_z acting on the initial state. However, making these projection measurements is not easy, since the measurement bases correspond to highly entangled states. Therefore, no currently known strategies can perform the optimal basis measurement efficiently.
To solve this problem, we showed that the probability given by making a measurement in the optimal basis can be written as a sum over pairwise Bell-basis measurements between different quanta. Furthermore, due to the symmetry of the second-order anti-coherent state, a fully optical procedure for Bell-state analysis is possible. Since the second-order anti-coherent states contain only symmetric Bell states, and a unitary operation describing the rotation cannot change the symmetry of the state, only the symmetric Bell triplet state will be presented in the decomposition of the final state after rotation. Thus, with additional single-qubit operations, using only linear-optical components and single-photon detectors is sufficient to achieve near-unity readout as long as we assign a path degree of freedom to each photon. We theoretically showed that our scheme is achievable with four-photon tetrahedron states and six-photon balanced NOON states.
| Keyword-1 | Rotation Sensing |
|---|---|
| Keyword-2 | Bell State Analysis |
| Keyword-3 | Cramér-Rao bound |