We address the discrimination of structured baths at different temperatures by dephasing quantum probes. We derive the exact reduced dynamics and evaluate the minimum error probability achievable by three different kinds of quantum probes, namely, a qubit, a qutrit, and a quantum register made of two qubits. Our results indicate that dephasing quantum probes are useful in discriminating low values of temperature and that lower probabilities of error are achieved for intermediate values of the interaction time, where the minimum probability of error scales as $1/2N$, with $N$ the number of energy levels of the probe. A qutrit probe outperforms a qubit one in the discrimination task, whereas entangled probes show smaller optimal times.

• Received 20 August 2020
• Accepted 24 December 2020

DOI:https://doi.org/10.1103/PhysRevA.103.012217