Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose the incoming radiation into orthogonal transverse modes. Such a demultiplexing procedure, however, must be perfectly calibrated to the transverse profile of the incoming light as any misalignment of the modes effectively restores the diffraction limit for small source separations. We study by how much can one mitigate such an effect at the level of measurement which, after being imperfectly demultiplexed due to inevitable misalignment, may still be partially corrected by linearly transforming the relevant dominating transverse modes. We consider two complementary tasks: the estimation of the separation between the two sources and the discrimination between one and two incoherent point sources. We show that, although one cannot fully restore super-resolving powers even when the value of the misalignment is perfectly known its negative impact on the ultimate sensitivity can be significantly reduced. In the case of estimation we analytically determine the exact relation between the minimal resolvable separation as a function of misalignment whereas for discrimination we analytically determine the relation between misalignment and the probability of error, as well as numerically determine how the latter scales in the limit of long interrogation times.

1 ade Almeida, J., O.1 aKołodyński, J.1 aHirche, C.1 aLewenstein, M1 aSkotiniotis, M. uhttps://link.aps.org/doi/10.1103/PhysRevA.103.022406http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevA.103.022406/fulltexthttps://link.aps.org/article/10.1103/PhysRevA.103.02240600680nas a2200169 4500008003900000022001400039245007000053210006900123260001600192490000800208100001600216700001500232700002000247700002200267700001900289856020200308 2020 d a0031-900700aBeyond the Swap Test: Optimal Estimation of Quantum State Overlap0 aBeyond the Swap Test Optimal Estimation of Quantum State Overlap cJan-02-20200 v1241 aFanizza, M.1 aRosati, M.1 aSkotiniotis, M.1 aCalsamiglia, John1 aGiovannetti, V uhttps://link.aps.org/doi/10.1103/PhysRevLett.124.060503http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevLett.124.060503/fulltexthttps://link.aps.org/article/10.1103/PhysRevLett.124.06050301271nas a2200145 4500008003900000022001400039245004100053210004100094490000800135520088400143100001701027700002001044700001301064856004801077 2017 d a0031-900700aImproved Sensing with a Single Qubit0 aImproved Sensing with a Single Qubit0 v1183 aWe consider quantum metrology with arbitrary prior knowledge of the parameter. We demonstrate that a single sensing two-level system can act as a virtual multilevel system that offers increased sensitivity in a Bayesian single-shot metrology scenario, and that allows one to estimate (arbitrary) large parameter values by avoiding phase wraps. This is achieved by making use of additional degrees of freedom or auxiliary systems not participating in the sensing process. The joint system is manipulated by intermediate control operations in such a way that an effective Hamiltonian, with an arbitrary spectrum, is generated that mimics the spectrum of a multisystem interacting with the field. We show how to use additional internal degrees of freedom of a single trapped ion to achieve a high-sensitivity magnetic field sensor for fields with arbitrary prior knowledge.

1 aSekatski, P.1 aSkotiniotis, M.1 aDuer, W. uhttps://grupsderecerca.uab.cat/giq/node/85100609nas a2200157 4500008003900000022001400039245005900053210005900112260001600171490000700187100002100194700002000215700001300235700001400248856018900262 2016 d a2469-992600aCompressed quantum metrology for the Ising Hamiltonian0 aCompressed quantum metrology for the Ising Hamiltonian cJan-12-20160 v941 aBoyajian, W., L.1 aSkotiniotis, M.1 aDür, W.1 aKraus, B. uhttps://link.aps.org/doi/10.1103/PhysRevA.94.062326http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevA.94.062326/fulltexthttp://link.aps.org/article/10.1103/PhysRevA.94.062326