Information flow-enhanced precision in collisional quantum thermometry

TL;DR

This work presents a multilayer collisional quantum thermometer that probes an environment at temperature $T$ without full thermalization of the system. By introducing inter-layer interactions among ancillae, information flow accumulates across the layered structure, yielding a dramatic enhancement of the quantum Fisher information $QFI$ beyond the thermal bound $QFI^{th}$. The authors connect the metrological gain to information-flow dynamics quantified by the Breuer–Laine–Piilo non-Markovianity measure and mutual information, showing that even partial system–ancilla exchanges can drive large sensitivity improvements. The results offer a path toward highly precise, non-thermalized quantum thermometers for non-equilibrium environments, while noting scalability challenges and opportunities to leverage additional quantum resources.

Abstract

We describe and analyze a quantum thermometer based on a multilayered collisional model. We propose a qubit system whose architecture provides significant sensitivity even for short interaction times between the ancillae that compose the thermometer probe and the system to be probed. The assessment of the flow of information taking place within the layered thermometer and between system and thermometer reveals that the tuning of the mutual backflow of information has a positive influence on the precision of thermometry, and helps unveiling the information-theoretic mechanisms behind the working principles of the proposed architecture.

Figures (7)

• Figure 1: (a) Illustration of the scheme of interctions for multi-layered collisional thermometry. System $S$ thermalizes with an environment in equilibrium at temperature $T$. The inference of such parameter is made through the sequence of collisional interactions illustrated in the main text. The numbered steps of the scheme [from (1) to (6) in panel (a)] illustrate the first few steps of the sequence leading to the measurements entailed by our metrological approach to the estimate of $T$. (b) Circuit-model representation of interactions of the steps (1)-to-(6) of our protocol. Each inter-ancilla collision is depicted by a full phased-SWAP gate [colored in blue], while the green-colored gates stand for is used for partial SWAPs.
• Figure 2: (a) QFI versus temperature and (b) ratio between maximum QFI and maximum QFI of the thermalized probe versus number of ancilla on each chain in the optimized temperature and (c) maximum QFI versus number of ancilla chains. Here we used $g\tau_{SA}\ll{\pi/2}$ and $J\tau_{A}=\pi/2$, $\text{QFI}_{max}^{th}=3.80$.
• Figure 3: Measure of non-Markovianity. (a) and (b) are respectively the results for the trace distance of the system and ancillae. (c) and (d) are the results for the derivative of the trace distance (measure of information flow) of the system and ancillae, respectively. Here we used $g\tau_{SA}\ll{\pi/2}$ and $J\tau_{A}=\pi/2$.
• Figure 4: (a) Trace distance and (b) Information flow between the qubits involved in interactions $2$, $3$ and $4$ in Fig. \ref{['fig:Sistema']}, the measurements are performed for an complete exchange of information between system and ancillae. Solid lines show information leaving one qubit as it arrives at another qubit, shown in dot-dashed, dashed and dotted lines. Here we used $g\tau_{SA}={\pi/2}$ and $J\tau_{A}=\pi/2$.
• Figure 5: QFI performed on qubits involved in interactions $2$, $3$ and $4$ in Fig. \ref{['fig:Sistema']}. We consider a full exchange of information between system and ancillae. Measurements are performed on qubits when information is (a) leaving and (b) entering. Here we used $g\tau_{SA}={\pi/2}$ and $J\tau_{A}=\pi/2$.