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
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
We study quantum entanglement in a system comprising two quantum dots interconnected through the short topological superconducting nanowire, which hosts overlapping boundary Majorana modes. Inspecting the fermionic negativity, we analyze the variation of entanglement against the position of the energy levels of quantum dots and their hybridization with the topological superconducting nanowire. In the absence of electron correlations, the optimal entanglement occurs when the energy levels coincide with the zero-energy Majorana modes, whereas upon increasing the hybridizations, the entanglement is gradually suppressed. Such monotonous behavior is no longer valid when the quantum dot levels are detuned from the zero-energy. Under these circumstances, the quantum dots become maximally entangled for a certain optimal hybridization. Moreover, we study the thermal concurrence to explore the entanglement properties at finite temperatures. We also compute the quantum mutual information and propose recipes for robust finite-temperature entanglement transmission via Majorana modes.
We study quantum entanglement in a system comprising two quantum dots interconnected through the short topological superconducting nanowire, which hosts overlapping boundary Majorana modes. Inspecting the fermionic negativity, we analyze the variation of entanglement against the position of the energy levels of quantum dots and their hybridization with the topological superconducting nanowire. In the absence of electron correlations, the optimal entanglement occurs when the energy levels coincide with the zero-energy Majorana modes, whereas upon increasing the hybridizations, the entanglement is gradually suppressed. Such monotonous behavior is no longer valid when the quantum dot levels are detuned from the zero-energy. Under these circumstances, the quantum dots become maximally entangled for a certain optimal hybridization. Moreover, we study the thermal concurrence to explore the entanglement properties at finite temperatures. We also compute the quantum mutual information and propose recipes for robust finite-temperature entanglement transmission via Majorana modes.
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.
Minimal Kitaev chains host Majorana quasiparticles, which, although not topologically protected, exhibit spatial nonlocality and hence are expected to be useful for quantum information tasks. In this work, we consider two- and three-site Kitaev chains and investigate the dynamics of bipartite and multipartite entanglement by means of concurrence and geometric measure of entanglement. In two-site Kitaev chains, we find that maximally entangled states can robustly emerge, with their stability and periodicity highly controllable by the interplay between the superconducting pair potential and the on-site energies. At the finely tuned sweet spot, where Majorana quasiparticles appear, the system exhibits oscillations between separable and entangled states, whereas detuning introduces tunable valleys in the entanglement dynamics. Extending to the three-site Kitaev chain, we uncover rich bipartite and multipartite entanglement by generalizing the concepts of concurrence and geometric measure of entanglement. At the sweet spot, the Majorana quasiparticles emerging at the edges suppress concurrence between the edges, while a finite detuning is able to restore it. Depending on the initial state, the three-site Kitaev chain can dynamically generate either a maximally entangled Greenberger-Horne-Zeilinger state or an imperfect W-type state exhibiting multipartite entanglement, although a (maximally entangled) pure W state cannot be realized due to parity constraints. Our results provide a resource for generating and characterizing highly entangled states in minimal Kitaev chains, with potential relevance for quantum applications.
Nonlocal entanglement between two quantum dots (QDs) can be generated through Majorana fermions. The two Majorana fermions at the ends of a one-dimensional topological superconductor form a nonlocal electronic level, which couples the occupation states of the two QDs located close to the two ends and brings the whole system into an entangled state, even at low temperatures and zero bias voltage. Upon introducing a charging energy by a capacitor, entanglement of the whole system can manifest itself through the nonlocal entanglement between the two QDs. Explicitly, the conditional probabilities of electron occupation on one QD with and without electron occupation on the other QD deviate from each other, with the difference proportional to the concurrence of quantum entanglement between the two QDs. Therefore detecting the difference in conditional probabilities, which is achievable experimentally by established techniques, provides evidence of the nonlocal nature of the fermion level constructed by the two end Majorana fermions.
The possibility of engineering artificial Kitaev chains in arrays of quantum dots coupled via narrow superconducting regions has emerged as an attractive way to overcome the disorder issues that complicate the realization and detection of topological superconducting phases in other platforms. Although a true topological phase would require long chains, a two-site chain realized in a double quantum dot can already be tuned to points in parameter space where it hosts zero-energy states that seem identical to the Majorana bound states that characterize a topological phase. These states have been named “poor man’s Majorana bound states” (PMMs) because they lack formal topological protection. In this work, we propose a pathway for next-generation experiments on PMMs. The pathway starts with experiments to characterize a single pair of PMMs by measuring the Majorana quality and then moves on to initialization and readout of the parity of a PMM pair, which allows the measurement of quasiparticle poisoning times. The next step is to couple two PMM systems to form a qubit. We discuss measurements of the coherence time of such a qubit, as well as a test of Majorana fusion rules in the same setup. Finally, we propose and analyze three different types of braidinglike experiments that require more complex device geometries. Our conclusions are supported by calculations based on a realistic model with interacting and spinful quantum dots, as well as by simpler models to gain physical insight. Our calculations show that it is indeed possible to demonstrate non-Abelian physics in minimal two-site Kitaev chains despite the lack of a true topological phase. However, our findings also reveal that doing so requires some extra care, appropriately modified protocols, and awareness of the details of this particular platform. Published by the American Physical Society 2024