Trade-off between information and disturbance in qubit thermometry

Abstract

We address the trade-off between information and disturbance in qubit thermometry from the perspective of quantum estimation theory. Given a quantum measurement, we quantify information via the Fisher information of the measurement and disturbance via four different figures of merit, which capture different aspects (statistical, thermodynamical, geometrical) of the trade-off. For each disturbance measure, the efficient measurements, i.e. the measurements that introduce a disturbance not greater than any other measurement extracting the same amount of information, are determined explicitly. The family of efficient measurements varies with the choice of the disturbance measure. On the other hand, commutativity between the elements of the probability operatorvalued measure (POVM) and the equilibrium state of the thermometer is a necessary condition for efficiency with respect to any figure of disturbance. *

A Survey of the Concept of Disturbance in Quantum Mechanics

“…A paper by Seveso and Paris [ 51 ] worthy of mention analyses the trade-off between information and disturbance in the Estimation IDT approach by using four measures of disturbance: the already mentioned average information [ 33 ], the fidelity based disturbance [ 7 ], the -disturbance and the -disturbance. As a consequence, they found interesting outcomes and they also give plots of the trade-off relations.…”

Quantum precision thermometry with weak measurement

“…Using the value of A w together with a priori knowledge of |ψ f , Â, and the energy eigen spectrum of the system Hamiltonian Ĥ, one can, in principle, find out the value of the temperature T -with the help of eqn. (7). Let us note in passing that the operator A must not commute with the relevant energy eigenbasis, else the weak value ceases to depend on the inverse temperature β, and thus, measuring the weak value furnishes no thermometric advantage.…”

“…Nanoscale probes, which follow laws of quantum physics, are thus required to measure the temperature of such baths without disturbing them too much. Quantum thermometry thus aims at improving the technique of temperature sensing using small probes [4][5][6][7][8][9][10]. The analysis of quantum thermometry so far has focused on seeking to find and saturate the quantum Cramer Rao bound for various partially and fully thermalized configurations of systems [11,12].…”

Nonequilibrium readiness and precision of Gaussian quantum thermometers

“…Most of the current investigations in quantum thermometry use two-level systems as thermometers [8][9][10][11], shedding light on the link between the equilibrium heat capacity of such microscopic probes and the amount of information that can be gathered on the temperature of the environment [12][13][14], introducing bounds on the irreversible entropy production of the probe [15][16][17], and clarifying the extent of the advantages resulting from finite-time interactions for both temperature discrimination and estimation [14,18]. Such investigations have ultimately opened the path to the exploration of the role played by genuine quantum features in the enhancement of the thermometric performance of two-level quantum probes [19][20][21][22][23][24][25][26][27][28][29].…”