We introduce a new class of quantum channels, the Generalized Multilevel Amplitude Damping (GMAD) channels, to model noise and decoherence effects in a qudit coupled to a thermal environment. The degradation of energetic resources under GMADs is investigated by evaluating work functionals and ergotropic capacitances, with particular attention to the coherent and incoherent contributions to ergotropy, for which we introduce new quantifiers. Our analysis sheds light on how to optimally prepare a qudit in a thermal environment in order to preserve its value from the perspective of work extraction, and reveals several counterintuitive phenomena: the ergotropic capacitance of a GMAD channel is not monotonic in the temperature of the environment; moreover, iterating the map can lead to crossings between ergotropic functionals at different temperatures, indicating the presence of a Markovian Mpemba effect.
We introduce a new class of quantum channels, the Generalized Multilevel Amplitude Damping (GMAD) channels, to model noise and decoherence effects in a qudit coupled to a thermal environment. The degradation of energetic resources under GMADs is investigated by evaluating work functionals and ergotropic capacitances, with particular attention to the coherent and incoherent contributions to ergotropy, for which we introduce new quantifiers. Our analysis sheds light on how to optimally prepare a qudit in a thermal environment in order to preserve its value from the perspective of work extraction, and reveals several counterintuitive phenomena: the ergotropic capacitance of a GMAD channel is not monotonic in the temperature of the environment; moreover, iterating the map can lead to crossings between ergotropic functionals at different temperatures, indicating the presence of a Markovian Mpemba effect.
This paper explores quantum heat engines based on qubit and qutrit working media interacting with thermal environments through generalized amplitude damping (GAD) channels. We investigate how quantum channels can be employed to model heat absorption, dissipation, and work extraction in open quantum thermal machines, and derive the conditions required for positive work extraction. The effects of quantum correlations, emission probability, population redistribution, and system--environment interactions on the thermodynamic performance of the engine are systematically analyzed across different operational regimes. In addition, we examine the ergotropy of qubit and qutrit systems under dissipative dynamics to understand how environmental effects influence the maximum extractable work. Our results demonstrate that multilevel quantum systems exhibit enhanced work extraction capability and improved robustness against decoherence compared to two-level systems, providing further insight into the role of dissipative dynamics and quantum resources in realistic quantum thermodynamic devices.
The quantum Mpemba effect is a counterintuitive phenomenon in which a state initially farther from equilibrium relaxes more rapidly than one that starts nearer to equilibrium. In the context of finite-dimensional quantum batteries interacting with an environment, we introduce the notion of an ergotropic Mpemba crossing (EMC), defined by the intersection of ergotropy trajectories during the dynamics. For qubit batteries subjected to amplitude damping noise, we derive a condition for the occurrence of EMC in terms of the relative coherence of the initial states and fully characterize the region of state space that exhibits EMC with respect to a fixed reference state. Interestingly, our analysis reveals that under anisotropic Pauli noise, the emergence of EMC is jointly governed by the coherence and the energy of the initial states. To elucidate the physical origin of EMC, we decompose ergotropy into coherent and incoherent contributions and show that, in qubit systems, the coherent component plays a crucial role for EMC, an observation that strikingly does not extend to three-level batteries, providing the dimensional role in observing EMC. Further, by extending our analysis to non-Markovian environments, we demonstrate that, unlike the Markovian case, non-Markovian dynamics can give rise to multiple Mpemba crossings, with the total number of crossings always being odd. Also, we propose a set-up showing that EMC can be utilized to suppress the ergotropic loss, occurred due to dissipation. Moreover, analyzing the connection between the EMC and the conventional state Mpemba effect reveals that, for qubits, an EMC necessarily entails a state Mpemba crossing, while this correspondence breaks down for qutrits, where EMCs may arise without any state Mpemba crossing.
We introduce a new set of quantum channels: resonant multilevel amplitude damping (ReMAD) channels. Among other instances, they can describe energy dissipation effects in multilevel atomic systems induced by the interaction with a zero-temperature bosonic environment. At variance with the already known class of multilevel amplitude damping (MAD) channels, this new class of maps allows the presence of an environment unable to discriminate transitions with identical energy gaps. After characterizing the algebra of their composition rules, by analyzing the qutrit case, we show that this new set of channels can exhibit degradability and antidegradability in vast regions of the allowed parameter space. There we compute their quantum capacity and private classical capacity. We show that these capacities can be computed exactly also in regions of the parameter space where the channels aren't degradable nor antidegradable.
Quantum work capacitances and maximal asymptotic work/energy ratios are figures of merit characterizing the robustness against noise of work extraction processes in quantum batteries formed by collections of quantum systems. In this paper we establish a direct connection between these functionals and, exploiting this result, we analyze different types of noise models mimicking self-discharging (amplitude damping channels), thermalization (generalized amplitude damping channels), and dephasing effects (simultaneous phase-amplitude damping channels). In this context we show that input quantum coherence can significantly improve the storage performance of noisy quantum batteries and that the maximum output ergotropy is not always achieved by the maximum available input energy.
We investigate work extraction in open quantum batteries composed of interacting spin chains weakly coupled to engineered environments. Focusing on two- and four-qubit XX models initially prepared in thermal Gibbs states, we analyze how dissipation and dephasing, acting either locally or collectively, can generate and shape ergotropy during both transient and steady-state dynamics. By introducing a continuous interpolation between parallel and collective noise channels, we systematically characterize the impact of environmental structure on work extractability. We show that purely dissipative dynamics can activate finite ergotropy from completely passive thermal states, giving rise to temperature-dependent transient regimes where hotter initial states temporarily outperform colder ones in an ergotropic Mpemba-like fashion. In contrast, collective dissipation leads to steady states whose passivity crucially depends on the initial temperature and system size, a behavior we trace back to the emergence of non-trivial dark subspaces. Finally, we demonstrate that dephasing channels suppress both transient advantages and steady-state work extraction, highlighting the qualitative difference between dissipative and dephasing environments.
The primary objective of quantum Shannon theory is to evaluate the capacity of quantum channels. In spite of the existence of rigorous coding theorems that quantify the transmission of information through quantum channels, superadditivity effects limit our understanding of the channel capacities. In this paper, we mainly focus on a family of channels known as multilevel amplitude damping channels. We investigate some of the information capacities of the simplest member of the multilevel amplitude damping channel, a qutrit channel, in the presence of correlations between successive applications of the channel. We find the upper bounds of the single-shot classical capacities and calculate the quantum capacities associated with a specific class of maps after investigating the degradability property of the channels. Additionally, the quantum and classical capacities of the channels have been computed in entanglement-assisted scenarios.