In recent years, the reassessment of quantum physical phenomena under the framework of resource theories has triggered the design of novel quantum technologies that take advantage from quantum resources, such as entanglement and quantum coherence. Bearing this in mind, in this work we study the dynamics of quantum resources for two solid-state fermionic quantum devices: (i) a system composed by a pair of Majorana fermions and (ii) another comprising a pair of regular fermions. In both systems, the fermionic species are coupled to a single-level quantum dot. From the interaction of these tripartite systems with a dissipative reservoir, we were able to characterize the dynamics of the devices for some initial states. By employing a time-nonlocal master-equation approach, we obtain the evolution for fermionic occupations, quantum correlations, and quantum coherences in both the Markovian and non-Markovian dissipating regimes. We investigate the interconversion of local coherence and bipartite correlations for the marginal states in each device. While the dynamics of the entanglement and quantum coherence depend quite strongly on the temperature of the reservoir for regular fermions, we found these evolutions are qualitatively similar for the case of Majorana bound states regardless of temperature. Our results illustrate the use of quantum information-theoretic measures to characterize the role of quantum resources in fermion systems.
In recent years, the reassessment of quantum physical phenomena under the framework of resource theories has triggered the design of novel quantum technologies that take advantage from quantum resources, such as entanglement and quantum coherence. Bearing this in mind, in this work we study the dynamics of quantum resources for two solid-state fermionic quantum devices: (i) a system composed by a pair of Majorana fermions and (ii) another comprising a pair of regular fermions. In both systems, the fermionic species are coupled to a single-level quantum dot. From the interaction of these tripartite systems with a dissipative reservoir, we were able to characterize the dynamics of the devices for some initial states. By employing a time-nonlocal master-equation approach, we obtain the evolution for fermionic occupations, quantum correlations, and quantum coherences in both the Markovian and non-Markovian dissipating regimes. We investigate the interconversion of local coherence and bipartite correlations for the marginal states in each device. While the dynamics of the entanglement and quantum coherence depend quite strongly on the temperature of the reservoir for regular fermions, we found these evolutions are qualitatively similar for the case of Majorana bound states regardless of temperature. Our results illustrate the use of quantum information-theoretic measures to characterize the role of quantum resources in fermion systems.
Quantum dots are nanometer-scale semiconductor particles that exhibit size-dependent quantum mechanical properties. In this work, we investigate the dynamics of quantum correlations, quantified by the concurrence and the quantum coherence, in a bipartite system of coupled double quantum dots. The analysis is carried out within both Markovian and non-Markovian regimes, and further extended to different noisy quantum channels, including amplitude damping, phase flip, and phase damping. Our results show that environmental memory plays a crucial role in the preservation of quantum correlations, leading to oscillatory behavior and partial revivals in the non-Markovian regime, in contrast to the monotonic decay observed under Markovian dynamics. Moreover, distinct decoherence mechanisms induce qualitatively different effects: dissipative channels rapidly suppress correlations, while phase-based channels lead to either redistribution or gradual degradation. A key finding is that quantum coherence exhibits a higher robustness compared to entanglement under all considered conditions, highlighting its relevance as a reliable quantum resource in noisy environments. These results provide valuable insights into the control and protection of quantum correlations in realistic solid-state systems.
Majorana bound states emerge in topological superconductors as zero-energy edge states exhibiting spatial nonlocality. Despite the enormous advances, the detection of Majorana bound states is still challenging, mainly because topologically trivial Andreev bound states produce similar signatures. In this work, we consider a topological superconductor with Majorana bound states coupled to quantum dots and investigate the dynamics of their quantum correlations with the aim to explore their entanglement properties. In particular, we characterize entanglement by using concurrence and discord, which are also complemented by entanglement dynamics and return probability. We find that Majorana bound states at truly zero energy can transform an initially entangled system into its classical state, while they can create maximally entangled states at a finite energy overlap. Interestingly, we show that the system can generate a maximally entangled state between MBSs and a quantum dot by simply controlling the Majorana nonlocality. We demonstrate that these results hold in scenarios when the initial state is either maximally entangled or separable, albeit in the latter, maximally entangled states are achieved in the long time dynamics. Furthermore, we contrast our findings with those produced by a regular fermion and obtain very distinct entanglement signatures. Our work offers an alternative approach to characterizing Majorana bound states, which can also be useful towards their utilization for quantum information tasks. Published by the American Physical Society 2024
ABSTRACT We study the steady‐state quantum Fisher information (QFI) and several quantum resources entanglement, quantum coherence, and quantum discord for a pair of coupled qubits interacting with either bosonic or fermionic reservoirs. Using the Bloch–Redfield master equation beyond the secular approximation, we derive analytical expressions for the steady‐state density matrix and analyze how equilibrium and nonequilibrium conditions shape the resulting quantum correlations. In thermal equilibrium, the quantum resources display distinct behaviors depending on the bath statistics, with fermionic reservoirs enabling stronger stationary correlations due to particle‐exchange processes. Under nonequilibrium driving, generated either by a temperature imbalance or by a chemical potential difference, the system develops steady‐state coherence and enhanced discord, while entanglement and QFI exhibit non‐monotonic dependence governed by the interplay between coherence generation and population mixing. Our results identify the regimes in which steady‐state metrological performance can be optimized, and they provide general guidelines for enhancing quantum correlations in dissipative two‐qubit platforms.
We study the decoherence of a collection of Majorana zero modes weakly coupled to a gapless reservoir of non-interacting fermions. Using the Born-Markov approximation, we derive a Lindblad master equation for the dissipative dynamics of the Majorana zero modes. Due to the long-range coupling between Majorana zero modes mediated by the gapless reservoir, the Lindblad jump operators are non-local linear combinations of the Majorana operators. We show that, as a consequence, the dissipative dynamics can exhibit long relaxation times, i.e. a slow decay of fermion parities. A spectral analysis of the Liouvillian shows that the slow-down is suppressed as a power law of the distance between Majorana zero modes. Finally, we validate the Lindblad equation by comparison with unbiased numerical simulations of the time evolution of the full density matrix. In particular, these illustrate that non-Markovian dynamics establishes non-local correlations at small times.
Majorana fermions (MFs) are exotic particles that are their own anti-particles. Recently, the search for the MFs occurring as quasi-particle excitations in solid-state systems has attracted widespread interest, because of their fundamental importance in fundamental physics and potential applications in topological quantum computation based on solid-state devices. Here we study the quantum correlations between two spatially separate quantum dots induced by a pair of MFs emerging at the two ends of a semiconductor nanowire, in order to develop a new method for probing the MFs. We find that without the tunnel coupling between these paired MFs, quantum entanglement cannot be induced from an unentangled (i.e., product) state, but quantum discord is observed due to the intrinsic nonlocal correlations of the paired MFs. This finding reveals that quantum discord can indeed demonstrate the intrinsic non-locality of the MFs formed in the nanowire. Also, quantum discord can be employed to discriminate the MFs from the regular fermions. Furthermore, we propose an experimental setup to measure the onset of quantum discord due to the nonlocal correlations. Our approach provides a new, and experimentally accessible, method to study the Majorana bound states by probing their intrinsic non-locality signature.
We aim to bridge the gap between quantum coherence, quantum correlations, and nonequilibrium quantum transport in a quantum double-dot (QDD) system interacting with fermionic reservoirs. The system-reservoir coupling is modeled using a Fano-Anderson-type Hamiltonian. The density operator elements of the QDD system are expressed in terms of expectation values involving various combinations of the fermionic creation and annihilation operators associated with the system. By utilizing the quantum Langevin equation and the Heisenberg equation of motion, we derive the precise temporal behavior of these operator averages in terms of nonequilibrium Green's functions and subsequently obtain the time evolution of the density operator elements. Our approach is valid in both the strong coupling and non-Markovian regimes. Additionally, we examine the time evolution of quantum coherence in the QDD system, quantifying it using standard measures such as the l1-norm and the relative entropy of coherence. As observed, coherence reaches a non-zero steady-state value, highlighting its significant potential for applications in quantum information processing and quantum technologies. Furthermore, we establish a connection between quantum coherence and transport current in a QDD system serially coupled to fermionic reservoirs. We then investigate the effects of coupling strength and reservoir memory by tuning the finite spectral width of the reservoir, examining their impact on both transient and steady-state properties, such as quantum coherence and particle current, which could play a crucial role in ultrafast nanodevice applications.