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Register a new userSurpassing the Thermal Cramer-Rao Bound with Collisional Thermometry
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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.
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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 paid to non-Hermitian systems. In this Letter, working with different logarithmic operators, we derive two previously unknown expressions for quantum Fisher information, and two Cramer-Rao bounds lower than the well-known one are found for non-Hermitian systems. These lower bounds are due to the merit of non-Hermitian observable and it can be understood as a result of extended regimes of optimization. Two experimentally feasible examples are presented to illustrate the theory, saturation of these bounds and estimation precisions beyond the Heisenberg limit are predicted and discussed. A setup to measure non-Hermitian observable is also proposed.
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