Measurements of an object's temperature are important in many disciplines, from astronomy to engineering, as are estimates of an object's spatial configuration. We present the quantum optimal estimator for the temperature of a distant body based on the black body radiation received in the far-field. We also show how to perform separable quantum optimal estimates of the spatial configuration of a distant object, i.e. imaging. In doing so we necessarily deal with multi-parameter quantum estimation of incompatible observables, a problem that is poorly understood. We compare our optimal observables to the two mode analogue of lensed imaging and find that the latter is far from optimal, even when compared to measurements which are separable. To prove the optimality of the estimators we show that they minimise the cost function weighted by the quantum Fisher information---this is equivalent to maximising the average fidelity between the actual state and the estimated one.
 O. E. Barndorff-Nielsen and R. D. Gill. Journal of Physics A: Mathematical and General, 33 (24): 4481, 2000.
 B. M. Escher, L. Davidovich, N. Zagury, and R. L. de Matos Filho. Phys. Rev. Lett., 109: 190404, 2012.
 D. J. Fixsen. The Astrophysical Journal, 707 (2): 916–920, 2009.
 Marcin Jarzyna and Rafał Demkowicz-Dobrzański. New Journal of Physics, 17 (1): 013010, 2015.
 Steven M. Kay. Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall, 1993.
 Cosmo Lupo and Stefano Pirandola Phys. Rev. Lett., 117: 190802, 2016.
 Katarzyna Macieszczak, Martin Fraas, and Rafal Demkowicz-Dobrzański. New Journal of Physics, 16, 2014.
 Ranjith Nair and Mankei Tsang. The Astrophysical Journal, 808 (2): 125, 2015.
 Dominik Šafránek, Antony R Lee, and Ivette Fuentes. New Journal of Physics, 17 (7): 073016, 2015.
 Rosanna Nichols, Pietro Liuzzo-Scorpo, Paul A. Knott, and Gerardo Adesso, "Multiparameter Gaussian quantum metrology", Physical Review A 98 1, 012114 (2018).
 Mankei Tsang, "Resolving starlight: a quantum perspective", Contemporary Physics 60 4, 279 (2019).
 L. A. Howard, G. G. Gillett, M. E. Pearce, R. A. Abrahao, T. J. Weinhold, P. Kok, and A. G. White, "Optimal Imaging of Remote Bodies Using Quantum Detectors", Physical Review Letters 123 14, 143604 (2019).
 Yunkai Wang, Yujie Zhang, and Virginia O. Lorenz, "Superresolution in interferometric imaging of strong thermal sources", Physical Review A 104 2, 022613 (2021).
 Jesús Rubio, "Quantum scale estimation", Quantum Science and Technology 8 1, 015009 (2023).
 Manuel Bojer, Zixin Huang, Sebastian Karl, Stefan Richter, Pieter Kok, and Joachim von Zanthier, "A quantitative comparison of amplitude versus intensity interferometry for astronomy", New Journal of Physics 24 4, 043026 (2022).
 Andrzej Chrostowski, Rafał Demkowicz-Dobrzański, Marcin Jarzyna, and Konrad Banaszek, "On super-resolution imaging as a multiparameter estimation problem", International Journal of Quantum Information 15 08, 1740005 (2017).
 Jesús Rubio, Janet Anders, and Luis A. Correa, "Global Quantum Thermometry", Physical Review Letters 127 19, 190402 (2021).
 L. A. Howard, G. G. Gillett, M. E. Pearce, R. A. Abrahao, T. J. Weinhold, P. Kok, and A. G. White, Frontiers in Optics / Laser Science FM4A.6 (2020) ISBN:978-1-943580-80-4.
 Cosmo Lupo, Zixin Huang, and Pieter Kok, "Quantum Limits to Incoherent Imaging are Achieved by Linear Interferometry", Physical Review Letters 124 8, 080503 (2020).
 Jasminder S. Sidhu and Pieter Kok, "Geometric perspective on quantum parameter estimation", AVS Quantum Science 2 1, 014701 (2020).
 J. Řehaček, Z. Hradil, B. Stoklasa, M. Paúr, J. Grover, A. Krzic, and L. L. Sánchez-Soto, "Multiparameter quantum metrology of incoherent point sources: Towards realistic superresolution", Physical Review A 96 6, 062107 (2017).
 Erik F. Matlin and Lucas J. Zipp, "Imaging arbitrary incoherent source distributions with near quantum-limited resolution", Scientific Reports 12 1, 2810 (2022).
 Emre Köse, Gerardo Adesso, and Daniel Braun, "Quantum-enhanced passive remote sensing", Physical Review A 106 1, 012601 (2022).
 Zixin Huang, Gavin K. Brennen, and Yingkai Ouyang, "Imaging Stars with Quantum Error Correction", Physical Review Letters 129 21, 210502 (2022).
 Jonas Glatthard, Jesús Rubio, Rahul Sawant, Thomas Hewitt, Giovanni Barontini, and Luis A. Correa, "Optimal Cold Atom Thermometry Using Adaptive Bayesian Strategies", PRX Quantum 3 4, 040330 (2022).
 Mankei Tsang, "Quantum limit to subdiffraction incoherent optical imaging", Physical Review A 99 1, 012305 (2019).
 Jasminder S. Sidhu and Pieter Kok, "Quantum metrology of spatial deformation using arrays of classical and quantum light emitters", Physical Review A 95 6, 063829 (2017).
The above citations are from Crossref's cited-by service (last updated successfully 2023-02-04 07:07:04) and SAO/NASA ADS (last updated successfully 2023-02-04 07:07:05). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.