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arXiv:1907.04704 · Physical Review A

Quantum bath statistics tagging

Donato Farina, Vasco Cavina, Vittorio Giovannetti

Published Oct 28, 2019• 5 citations
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Abstract

The possibility of discriminating the statistics of a thermal bath using indirect measurements performed on quantum probes is presented. The scheme relies on the fact that, when weakly coupled with the environment of interest, the transient evolution of the probe toward its final thermal configuration is strongly affected by the fermionic or bosonic nature of the bath excitations. Using figures of merit taken from quantum metrology such as the Holevo-Helstrom probability of error and the quantum Chernoff bound, we discuss how to achieve the greatest precision in this statistics tagging procedure, analyzing different models of probes and different initial preparations and by optimizing over the time of exposure of the probe.

DOI
10.1103/physreva.100.042327

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The possibility of discriminating the statistics of a thermal bath using indirect measurements performed on quantum probes is presented. The scheme relies on the fact that, when weakly coupled with the environment of interest, the transient evolution of the probe toward its final thermal configuration is strongly affected by the fermionic or bosonic nature of the bath excitations. Using figures of merit taken from quantum metrology such as the Holevo-Helstrom probability of error and the quantum Chernoff bound, we discuss how to achieve the greatest precision in this statistics tagging procedure, analyzing different models of probes and different initial preparations and by optimizing over the time of exposure of the probe.
We analyze the capability of discriminating the statistical nature of a thermal bath in the presence of three different types of side resources: prior entanglement between the probing system and an external (dynamically neutral) memory element, the interaction between the probe and an auxiliary bath, and the continuous monitoring of the system mediated by real-time measurements of the auxiliary bath. We discuss in detail how to obtain improved performances in the discrimination by considering different kinds of interactions, i.e., different jump operators, and different monitoring strategies corresponding to continuous homodyne detection and photodetection. We find that the presence of the auxiliary environment can be beneficial, allowing bath discrimination in regimes where in the standard scenario discrimination is not possible. We then show how additionally monitoring this environment, via either continuous homodyne detection or photodetection, is naturally advantageous for quantum bath tagging, in particular in the long-time limit where a large improvement in the discrimination performance is indeed observed. Our approach can in principle be implemented in a circuit QED setup and paves the way to further developments of quantum probing via continuous monitoring.
Nonequilibrium states of quantum systems in contact with thermal baths help distinguishing between environments with different temperatures or different statistics.We extend these studies to a more generic problem that consists in discriminating between two baths with disparate constituents at unequal temperatures.Notably there exist temperature regimes in which the presence of coherence in the initial state preparation is beneficial for the discrimination capability.We also find that nonequilibrium states are not universally optimal and detail the conditions in which it becomes advantageous to wait for complete thermalization of the probe.These concepts are illustrated in a linear-optical simulation.
We unveil a fundamental temperature bias in transient quantum thermometry under Markovian dynamics. For qubit probes evolving in a thermal Markovian environment, we prove that transient precision beyond the steady-state benchmark can be achieved if and only if the probe is initially colder than the bath temperature to be estimated. Cold probes are therefore both necessary and sufficient for enhanced transient precision in the Markovian regime. We then investigate the fate of this bias in the presence of environmental memory. In particular, in a non-Markovian scenario generated by an auxiliary-mediated system-bath coupling, we find that the cold-probe requirement for enhanced transient precision persists, indicating that the temperature bias survives certain forms of memory effects. In contrast, for a non-Markovian collisional model with perfect swap interactions between bath ancillas, transient enhancement is entirely absent regardless of the probe's initial temperature. This indicates that strong non-Markovianity can lead to the complete disappearance of the enhancement effect, placing hot and cold probes on equal footing, with neither capable of achieving enhanced precision in this regime.
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 1/2N1/2N1/2N, with NNN 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.
We study the role of bath-induced correlations in temperature estimation of cold bosonic baths. Our protocol includes multiple probes, that are not interacting, nor are they initially correlated to each other. They interact with a bosonic sample and reach a nonthermal steady state, which is measured to estimate the temperature of the sample. It is well known that in the steady state such noninteracting probes may get correlated to each other and even entangled. Nonetheless, the impact of these correlations in metrology has not been deeply investigated yet. Here, we examine their role for thermometry of cold bosonic gases and show that, although being classical, bath-induced correlations can lead to significant enhancement of precision for thermometry. The improvement is especially important at low temperatures, where attaining high precision thermometry is particularly demanding. The proposed thermometry scheme does not require any precise dynamical control of the probes and tuning the parameters and is robust to noise in initial preparation, as it is built upon the steady state generated by the natural dissipative dynamics of the system. Therefore, our results put forward new possibilities in thermometry at low temperatures, of relevance, for instance, in cold gases and Bose-Einstein condensates.
It is often the case that the environment of a quantum system may be described as a bath of oscillators with an ohmic density of states. In turn, the precise characterization of these classes of environments is a crucial tool to engineer decoherence or to tailor quantum information protocols. Recently, the use of quantum probes in characterizing ohmic environments at zero-temperature has been discussed, showing that a single qubit provides precise estimation of the cutoff frequency. On the other hand, thermal noise often spoil quantum probing schemes, and for this reason we here extend the analysis to a complex system at thermal equilibrium. In particular, we discuss the interplay between thermal fluctuations and time evolution in determining the precision attainable by quantum probes. Our results show that the presence of thermal fluctuations degrades the precision for low values of the cutoff frequency, i.e., values of the order ω c ≲ T (in natural units). For larger values of ω c , decoherence is mostly due to the structure of environment, rather than thermal fluctuations, such that quantum probing by a single qubit is still an effective estimation procedure.