TY - JOUR

T1 - Discrimination and estimation of incoherent sources under misalignment

AU - De Almeida, J. O.

AU - Kołodyński, J.

AU - Hirche, C.

AU - Lewenstein, M.

AU - Skotiniotis, M.

N1 - Funding Information: We thank Wojciech Wasilewski and Michał Parniak for helpful comments. J.O.d.A. and M.L. acknowledge support from ERC AdG NOQIA, Spanish Ministry of Economy and Competitiveness (“Severo Ochoa” program for Centres of Excellence in R&D (CEX2019-000910-S), Plan National FIDEUA PID2019-106901GB-I00/10.13039/501100011033, FPI), Fundació Privada Cellex, Fundació Mir-Puig, and from Generalitat de Catalunya (AGAUR Grant No. 2017 SGR 1341, CERCA program, QuantumCAT U16-011424, co-funded by ERDF Operational Program of Catalonia 2014-2020), MINECO-EU QUANTERA MAQS (funded by State Research Agency (AEI) PCI2019-111828-2/10.13039/501100011033), EU Horizon 2020 FET-OPEN OPTOLogic (Grant No. 899794), and the National Science Centre, Poland-Symfonia Grant No. 2016/20/W/ST4/00314. J.K. is supported by the Foundation for Polish Science under the “Quantum Optical Technologies” project carried out within the International Research Agendas programme, co-financed by the European Union under the European Regional Development Fund. C.H. acknowledges financial support from the VILLUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059). M.S. acknowledges support from Spanish MINECO reference FIS2016-80681-P (with the support of AEI/FEDER,EU); the Generalitat de Catalunya, project CIRIT 2017-SGR-1127 and the Baidu-UAB collaborative project “Learning of Quantum Hidden Markov Models.”

PY - 2021/2/3

Y1 - 2021/2/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85100649396&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.103.022406

DO - 10.1103/PhysRevA.103.022406

M3 - Article

AN - SCOPUS:85100649396

VL - 103

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

M1 - 022406

ER -