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In collisional thermometry, a system in contact with the thermal bath is probed by a stream of ancillas. Coherences and collective measurements were shown to improve the Fisher information in some parameter regimes, for a stream of independent and identically prepared (i.i.d.) ancillas in some specific states [Seah et al., Phys. Rev. Lett., 180602 (2019)]. Here we refine the analysis of this metrological advantage by optimising over the possible input ancilla states, also for block-i.i.d.~states of block size b=2. For both an indirect measurement interaction and a coherent energy exchange channel, we show when the thermal Cramer-Rao bound can be beaten, and when a collective measurement of $N>1$ ancilla may return advantages over single-copy measurements.
The quantum Fisher information constrains the achievable precision in parameter estimation via the quantum Cramer-Rao bound, which has attracted much attention in Hermitian systems since the 60s of the last century. However, less attention has been p
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We introduce a general framework for thermometry based on collisional models, where ancillas probe the temperature of the environment through an intermediary system. This allows for the generation of correlated ancillas even if they are initially ind
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