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arXiv:2202.12239 · Physical Review A

Entanglement-assisted, noise-assisted, and monitoring-enhanced quantum bath tagging

Donato Farina, Vasco Cavina, Marco G. Genoni, Vittorio Giovannetti

Published Oct 13, 2022• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.106.042609

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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.
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.
Continuous weak measurements of quantum systems are of great relevance in quantum foundations and applications. They can be achieved by probing the quantum system of interest by repeatedly measuring an auxiliary system weakly coupled to it. Here we study two qubits coupled in different points to a common one-dimensional electromagnetic field and simultaneously monitored in the right- and left-propagating output channels by homodyne detection. Using a collision-model description, we derive an analytical Stochastic Master Equation (SME) governing the resulting diffusive quantum trajectories, including the interference between the two measurement channels. For nonlinear functions of the quantum state, such as entropies, averages over quantum trajectories generally differ from the corresponding quantities evaluated on the unconditional state. Through this mechanism, we show that continuous monitoring generates entanglement, absent in the unconditional dynamics, and enhances quantum magic in the qubit pair during the decay. Both resources can be tuned through the optical phase accumulated between the qubits and the phases of homodyne local oscillators. Our results establish continuous homodyne monitoring of multiple emitters as a tunable mechanism for generating quantum resources.
Preserving quantum resources in dissipative environments is a fundamental challenge in quantum information processing. While environmental interactions usually degrade quantum resources, we theoretically show that in a Quantum Brownian Motion (QBM) channel, continuous-variable state discrimination can be improved by increasing, rather than minimizing, the initial thermal noise. Specifically, without suppressing the inherent environmental dissipation, when combined with squeezing, this initial noise induces a coherence preservation mechanism driven by the transient non-thermalization of the probe with the bath. This preservation translates into a pronounced reduction in error probabilities for state discrimination between orthogonal squeezing directions. Furthermore, we also show that quadrature homodyne detection achieves near-optimal performance, approaching the Helstrom limit. These results highlight the advantage of exploiting thermal-squeezed states, offering a robust physical architecture for quantum communication in high-temperature environments.
We discuss recent developments in measurement protocols that generate quantum entanglement between two remote qubits, focusing on the theory of joint continuous detection of their spontaneous emission. We consider a device geometry similar to that used in well-known Bell state measurements, which we analyze using a conceptually transparent model of stochastic quantum trajectories; we use this to review photodetection, the most straightforward case, and then generalize to the diffusive trajectories from homodyne and heterodyne detection as well. Such quadrature measurement schemes are a realistic two-qubit extension of existing circuit QED experiments, which obtain quantum trajectories by homodyning or heterodyning a superconducting qubit’s spontaneous emission, or an adaptation of existing optical measurement schemes to obtain jump trajectories from emitters. We mention key results, presented from within a single theoretical framework, and draw connections to concepts in the wider literature on entanglement generation by measurement (such as path information erasure and entanglement swapping). The photon which-path information acquisition, and therefore the two-qubit entanglement yield, is tunable under the homodyne detection scheme we discuss, at best generating equivalent average entanglement dynamics as in the comparable photodetection case. In addition to deriving this known equivalence, we extend past analyses in our characterization of the measurement dynamics: we include derivations of bounds on the fastest possible evolution toward a Bell state under joint homodyne measurement dynamics and characterize the maximal entanglement yield possible using inefficient (lossy) measurements.
It is intuitively expected, and supported by earlier studies, that many-body quantum chaos is suppressed, or even destroyed, by dissipative effects induced by continuous monitoring. We show here that this is not always the case. For this purpose, we study the quenched dynamics of a continuously monitored Sachdev-Ye-Kitaev (SYK) model, described by the Lindblad formalism, coupled to a thermal environment modeled by another SYK maintained at constant temperature. We find that the combined effect of monitoring and the thermal bath drives the system toward a non-thermal steady state independently of the initial conditions. The corresponding retarded Green's function exhibits two stages of exponential decay, with rates that depend non-monotonously on the thermal bath coupling and the monitoring strength. In the limit of weak coupling, the late time decay of the Green's function, computed analytically, is closely related to that of the thermal bath. Strikingly, we identify a range of parameters in which continuous monitoring, despite being a source of decoherence, induces or enhances quantum chaotic dynamics suppressed by the thermal bath. For instance, in the limit of weak coupling to the thermal bath, the Lyapunov exponent increases sharply when monitoring is turned on. For intermediate values of the thermal bath coupling, the Lyapunov exponent exhibits re-entrant behavior: it vanishes at zero or sufficiently weak monitoring strength, and becomes positive again as the monitoring strength is increased. Our results offer intriguing insights on the mechanisms leading to quantum scrambling which paves the way to its experimental control and consequently to a performance enhancement of quantum information devices.
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.