Single-qubit probes for temperature estimation in the presence of collective baths

We study the performance of single-qubit probes for temperature estimation in the presence of collective baths. We consider a system of two qubits, each locally dissipating into its own bath while being coupled to a common bath. In this setup, we investigate different scenarios for temperature estimation of both the common and local baths. First, we explore how the precision of a single-qubit probe for estimating the common bath temperature can be enhanced by collective effects arising from the shared bath itself, particularly when the second qubit is in resonance with the probe. Interestingly, we find that the presence of local baths on each qubit can either jeopardize or, if these baths are sufficiently cold, enhance this precision. Next, we demonstrate a remote temperature sensing scheme in which one qubit acts as a probe to estimate the temperature of a local bath affecting the other qubit, by leveraging their indirect interaction through the common bath. This approach enables remote temperature sensing without directly coupling the probe to the target qubit or its local environment, thereby minimizing potential disturbances and practical challenges. Notably, we show that the collective Lamb shift, induced by the common bath, plays a crucial role in enabling remote temperature sensing by generating qubit-qubit correlations, even in the case of noninteracting qubits.