Optimal probes for global quantum thermometry

Abstract

Quantum thermodynamics has emerged as a separate sub-discipline, revising the concepts and laws of thermodynamics, at the quantum scale. In particular, there has been a disruptive shift in the way thermometry, and thermometers are perceived and designed. Currently, we face two major challenges in quantum thermometry. First, all of the existing optimally precise temperature probes are local, meaning their operation is optimal only for a narrow range of temperatures. Second, aforesaid optimal local probes mandate complex energy spectrum with immense degeneracy, rendering them impractical. Here, we address these challenges by formalizing the notion of global thermometry leading to the development of optimal temperature sensors over a wide range of temperatures. We observe the emergence of different phases for such optimal probes as the temperature interval is increased. In addition, we show how the best approximation of optimal global probes can be realized in spin chains, implementable in ion traps and quantum dots.

Global Quantum Thermometry

“…Hence, we have derived a local form of thermometry as a limit of the global framework. Note that the quantifier ε ¼ R dθpðθÞFðθÞ −1 has been proposed as an attempt to supersede the local paradigm [41,42]. Notwithstanding its merits-Ref.…”

“…Notwithstanding its merits-Ref. [42] reports results beyond standard local thermometry-such ε is not scale invariant. This might be ignored if the prior probability is narrowly concentrated around some fixed θ 0 , since then εCR…”

Stochastic Collisional Quantum Thermometry

“…Such a situation is clearly not ideal given that the temperature is the very quantity that we wish to estimate [ 33 , 34 ]. Approaches to address this issue include introducing global estimation schemes [ 13 , 46 , 47 , 48 , 49 ] and biased estimators [ 35 ]. Here, we demonstrate that, if the interactions are random and governed by a particular WTD, this randomicity has an important effect on the value of the parameter that determines the possible advantage over the thermal Fisher information.…”

Quantum Scale Estimation

“…The sine error D[ θ(x), θ] = 4 sin 2 {[ θ(x) − θ]/2}, in particular, is often employed for this purpose [1,[42][43][44][45], and while there are other functions D that are appropriate for phase estimation [22,42], it is instructive to appreciate that the square error D[ θ(x), θ] = [ θ(x) − θ] 2 is generally not one of them. 1 In the context of thermometry [33,[47][48][49][50][51][52][53][54][55][56], the unknown parameter, temperature, establishes an energy scale [47,57]. In turn, this motivates the search for an estimation technique that preserves scale invariance [24,58,59], an idea that has recently be shown to lead to a logarithmic deviation function D[ θ(x), θ] = log 2 [ θ(x)/θ] [33].…”