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).
 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).
 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).
 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).
 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).
 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).
 Erik F. Matlin and Lucas J. Zipp, "Adaptive Imaging of Arbitrary Thermal Source Distributions with Near Quantum-Limited Resolution", arXiv:2106.13332.
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