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

TL;DR

This paper introduces a new measure called local distinguishability to evaluate the topological protection of Majorana bound states in quantum-dot chains, showing that longer chains exhibit exponential decay of distinguishability, indicating a transition to a topological phase.

Contribution

The paper proposes a novel quality measure for Majorana states applicable with strong interactions and demonstrates its effectiveness in analyzing chain length effects on topological protection.

Findings

Local distinguishability bounds local measurement discrimination.

Three-dot chains may not outperform two-dot chains in topological quality.

Longer chains show exponential decay in local distinguishability, indicating topological phase transition.

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.