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arXiv · 2407.09211

Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length

Viktor Svensson·Martin Leijnse
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Abstract

Realizing Majorana bound states (MBSs) in short, well-controllable chains of coupled quantum dots sidesteps the problem of disorder, but requires fine-tuning and does not give the true topological protection inherent to long chains. Here, we introduce a new quality measure that is applicable also in the presence of strong electron-electron interactions and that quantifies the closeness to topological protection of finetuned MBSs in short quantum-dot chains. We call this measure local distinguishability because it puts a bound to the degree an arbitrary local measurement can distinguish between two states. We study the local distinguishability for quantum-dot chains of different length. The three-dot chain is studied in detail, and we find that it may not always be an improvement over the two-dot case, a fact that can be understood within an effective model derived from perturbation theory. For longer chains, the local distinguishability vanishes exponentially, signalling a transition to a topological phase with two ground states that cannot be distinguished by any local measurement.

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Viktor Svensson, Martin Leijnse. 2024-12-05. Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length. https://doi.org/10.1103/physrevb.110.155436

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