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arXiv:2507.17586 · Physical review. B./Physical review. B

Entanglement dynamics in minimal Kitaev chains

Vimalesh Kumar Vimal, Jorge Cayao

Published Jun 24, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/mql6-m1rw

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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.
Majorana zero modes provide a route to fault-tolerant qubits by encoding information non-locally in fermion parity. Their sensitivity to noise is expected to decrease exponentially with increasing separation between the Majoranas, a suppression known as topological protection. Kitaev chains engineered in quantum dot-superconductor arrays provide a tunable platform in which separated Majorana zero modes can emerge at the ends of the chain, even in two-site chains. These minimal-chain modes are known as poor man's Majoranas and retain characteristic Majorana properties, including near-zero energy and equal electron-hole character, but have only limited protection. A key outstanding challenge is to move beyond identifying such modes in electrical transport measurements and achieve coherent qubit control in the time domain. Here, we demonstrate a Majorana parity qubit by realizing coherent coupling between two-site Kitaev chains. Since total fermion parity is conserved, the system separates into global even and odd parity manifolds. We observe coherent parity oscillations in both manifolds with equal oscillation frequencies at the Majorana sweet spot, as predicted for isolated Majorana zero modes. We further show that the oscillation frequency and coherence depend systematically on inter-chain coupling and quantum-dot detunings, in close agreement with our model for short, partially protected chains. Our results establish the first coherent control of a Majorana qubit, encoded in the fermion parity of Majorana zero modes in minimal Kitaev chains.
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
Motivated by the recent experimental realization of a minimal Kitaev chain in quantum dot systems, we present our theoretical findings on the dynamics and fusion of MZMs at or near the “sweet spot” th = Δ (where the fermionic hopping th and superconducting coupling Δ are equal). We investigated the dynamics and fusion of MZMs using time-dependent real-space local density-of-states methods. The movement of Majoranas and the detection of fusion channels are crucial for topological quantum computations. Additionally, we discuss our recent discovery of exotic “multi-site” MZMs in Y-shaped Kitaev wires, which is important for the potential braiding of Majoranas in Y-junctions formed from arrays of quantum dots. Finally, we present results on ”non-trivial” fusion using canonical Kitaev wires at the sweet spot.
Few-site implementations of the Kitaev chain offer a minimal platform to study the emergence and stability of Majorana bound states. Here, we realize two- and three-site chains in semiconducting quantum dots coupled via superconductors, and tune them to the sweet spot where zero-energy Majorana modes appear at the chain ends. We demonstrate control of the superconducting phase through both magnetic field and sweet-spot selection, and fully characterize the excitation spectrum under local and global perturbations. All spectral features are identified using the ideal Kitaev chain model. To assess Majorana localization, we couple the system to an additional quantum dot. The absence of energy splitting at the sweet spot is compatible with high-quality Majorana modes, despite the modest chain size.
A recent experiment reported coherent parity oscillations between minimal Kitaev chains, demonstrating a Majorana parity qubit (arXiv:2607.09511). Operations on this qubit are controlled by coupling two Kitaev chains and are intrinsically unprotected against noise in the coupling strength. Here we show how the exponential protection in the underlying chains can nevertheless be revealed through unprotected qubit operations. To this end, we develop an analytical theory of quasistatic dephasing for two coupled NNN-site Kitaev chains at the sweet spot. In Rabi experiments, protection can be resolved by adapting the operating point with chain length: depending on the coupling architecture, it appears as an exponentially increasing optimized number of coherent oscillations or as a longer coherence time. Ramsey experiments show an exponentially increasing coherence time, provided the chains can be sufficiently decoupled. Our analytical theory takes into account the non-Gaussian splitting statistics of the Kitaev chains, allowing us to quantitatively predict the scaling with chain length. Moreover, we determine how residual noise and imperfections limit the range of chain lengths over which this scaling can be observed. Our results show how qubit dynamics can be used to probe Majorana protection in experimentally realistic devices.
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