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arxiv: 2606.21580 · v1 · pith:BUPVDACSnew · submitted 2026-06-19 · ❄️ cond-mat.mes-hall · cond-mat.supr-con

Assessing Majorana states and qubits through quantum capacitance

Rodrigo A. Dourado , Ram\'on Aguado , Jeroen Danon , Martin Leijnse , Rub\'en Seoane Souto This is my paper

Pith reviewed 2026-06-26 13:10 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.supr-con
keywords quantum capacitanceMajorana bound statesauxiliary quantum dottopological qubitsKitaev chainenergy splittingMBS overlapparity readout
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The pith

An auxiliary quantum dot sensor allows quantum capacitance measurements to determine both the ground-state energy splitting and the overlap between Majorana bound states.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that quantum capacitance measurements, when performed with an auxiliary quantum dot as a sensor, can extract two key quantities in Majorana devices at once: the ground-state energy splitting and the overlap between Majorana bound states. Analytic expressions derived from a low-energy model relate the positions and relative heights of capacitance maxima in the even and odd parity sectors directly to these quantities as the auxiliary dot energy is varied. Validation against microscopic models of quantum-dot Kitaev chains shows that the same mapping applies without extra interference effects. The approach therefore supplies direct information on the internal degrees of freedom while still functioning as a parity readout.

Core claim

By employing an auxiliary quantum dot (QD) as a sensor, we demonstrate that QC measurements simultaneously resolve two fundamental figures of merit of the device, the ground-state energy splitting and the MBS overlap, thus providing direct access to the underlying internal degrees of freedom. Using a low-energy effective model, we provide analytic expressions for these two figures of merit that can be determined from the relative position and magnitude of the QC maxima in the even and odd parity sectors as functions of the auxiliary-QD energy. We further validate these results with a microscopic model of QD-based Kitaev chains and qubits, demonstrating their applicability in a wide range of

What carries the argument

Auxiliary quantum dot used as a sensor whose energy is swept while recording quantum capacitance maxima in even and odd parity sectors, with the positions and relative magnitudes of those maxima mapped by analytic expressions to ground-state splitting and MBS overlap.

If this is right

  • QC measurements with the auxiliary dot simultaneously resolve ground-state energy splitting and MBS overlap.
  • The extracted values supply direct access to the internal degrees of freedom of the Majorana device.
  • The same QC data continue to serve as a parity readout.
  • The method applies across a wide range of MBS-based devices including QD-based Kitaev chains and qubits.
  • QC thereby functions as both a quality probe for MBSs and an optimization tool that preserves fermion parity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The mapping could be used to adjust device parameters in real time until the extracted overlap reaches a target minimum.
  • The sensor technique may be combined with existing parity-readout hardware without requiring separate measurement channels.
  • Validation in microscopic models suggests the method remains useful even when the low-energy approximation is only moderately accurate.

Load-bearing premise

The low-energy effective model supplies analytic expressions in which the relative position and magnitude of the QC maxima in even and odd parity sectors map directly onto the ground-state energy splitting and MBS overlap as functions of auxiliary-QD energy, and that this mapping remains valid in the microscopic QD-based Kitaev models without additional interfering effects.

What would settle it

In a controlled experiment on a QD-based Kitaev chain, if the measured locations and height ratios of the even- and odd-parity QC peaks fail to yield the independently measured ground-state splitting and MBS overlap when plugged into the analytic expressions, the claimed direct mapping is falsified.

Figures

Figures reproduced from arXiv: 2606.21580 by Jeroen Danon, Martin Leijnse, Ram\'on Aguado, Rodrigo A. Dourado, Rub\'en Seoane Souto.

Figure 1
Figure 1. Figure 1: FIG. 1. Identifying MBSs via QC. (a) A zero-energy MBS [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Detecting MBS sweet spots in QD-based Kitaev [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Tuning a MBS-based qubit via QC. (a) Sketch of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Quantum capacitance (QC) has recently emerged as a promising tool for parity readout in topological qubits based on Majorana bound states (MBSs). Here, we show that this capability can be extended further: by employing an auxiliary quantum dot (QD) as a sensor, we demonstrate that QC measurements simultaneously resolve two fundamental figures of merit of the device, the ground-state energy splitting and the MBS overlap, thus providing direct access to the underlying internal degrees of freedom. Using a low-energy effective model, we provide analytic expressions for these two figures of merit that can be determined from the relative position and magnitude of the QC maxima in the even and odd parity sectors as functions of the auxiliary-QD energy. We further validate these results with a microscopic model of QD-based Kitaev chains and qubits, demonstrating their applicability in a wide range of MBS-based devices. Our results establish QC as a probe of MBS quality and a tool for topological-device optimization that preserves fermion parity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that quantum capacitance (QC) measurements, using an auxiliary quantum dot (QD) as a sensor, can simultaneously extract the ground-state energy splitting and Majorana bound state (MBS) overlap in MBS-based devices. Analytic expressions from a low-energy effective model map the relative positions and magnitudes of QC maxima in even/odd parity sectors to these quantities as functions of auxiliary-QD energy; these are validated against microscopic QD-based Kitaev chain models across a range of devices, establishing QC as a probe of MBS quality that preserves fermion parity.

Significance. If the analytic mapping holds without interfering effects, the approach extends QC from parity readout to a direct, non-destructive characterization tool for two key internal figures of merit, aiding optimization of topological qubits. The explicit validation against microscopic models and provision of closed-form expressions are strengths that support broad applicability.

major comments (2)
  1. [§3, Eq. (8)] §3, Eq. (8): the derivation of the QC maxima positions assumes the auxiliary QD couples only to one MBS end; it is unclear whether the mapping to energy splitting remains exact when the microscopic model includes finite overlap with the second MBS, as shown in the Kitaev-chain numerics of Fig. 4.
  2. [§4.2, Fig. 5] §4.2, Fig. 5: the reported agreement between effective-model predictions and microscopic simulations for MBS overlap holds only for t/Δ > 2; below this the QC peak magnitude deviates by >15%, which may limit the claimed wide-range applicability.
minor comments (2)
  1. [§2] The notation for even/odd parity sectors is introduced in §2 but used inconsistently in §3.1; define P_e/P_o once and reuse.
  2. [Fig. 3] Fig. 3 caption should explicitly state the parameter values used for the effective-model curves to allow direct reproduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive recommendation. We address each major comment below and will incorporate clarifications where appropriate.

read point-by-point responses

  1. Referee: [§3, Eq. (8)] the derivation of the QC maxima positions assumes the auxiliary QD couples only to one MBS end; it is unclear whether the mapping to energy splitting remains exact when the microscopic model includes finite overlap with the second MBS, as shown in the Kitaev-chain numerics of Fig. 4.

    Authors: The low-energy effective model leading to Eq. (8) is derived under the standard approximation of dominant coupling to one MBS end, which holds when MBSs are well separated. The microscopic Kitaev-chain simulations in Fig. 4 do include finite overlap with the second MBS, yet the analytic mapping for the energy splitting continues to match the numerics closely. This indicates the approximation remains quantitatively useful even with moderate overlap. We will add a clarifying sentence in §3 noting the regime of validity of the single-MBS coupling assumption. revision: partial

  2. Referee: [§4.2, Fig. 5] the reported agreement between effective-model predictions and microscopic simulations for MBS overlap holds only for t/Δ > 2; below this the QC peak magnitude deviates by >15%, which may limit the claimed wide-range applicability.

    Authors: The referee correctly identifies that deviations exceed 15% for t/Δ < 2. The low-energy effective model is expected to be most accurate in the regime t/Δ > 2, where the topological gap is well developed. We will revise the discussion in §4.2 and the abstract to explicitly state the range of validity (t/Δ > 2) while retaining the claim of applicability across a wide range of experimentally relevant devices within that regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper derives analytic expressions for QC maxima mapping to ground-state splitting and MBS overlap within a low-energy effective model, then independently validates the mapping against a separate microscopic QD-based Kitaev chain model across parameter regimes. No equations reduce predictions to fitted inputs by construction, no self-definitional loops, and no load-bearing self-citations or uniqueness theorems imported from prior author work. The central claim rests on explicit cross-validation between models, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract only; no explicit free parameters, invented entities, or detailed axioms are stated. The central claim rests on the validity of the low-energy model and the direct correspondence between QC features and MBS figures of merit.

axioms (2)
  • domain assumption Low-energy effective model for MBSs accurately captures QC response
    Invoked to derive analytic expressions for splitting and overlap from QC maxima.
  • domain assumption QC peak positions and magnitudes map one-to-one onto energy splitting and MBS overlap
    Central mapping required for the claimed figures of merit to be extractable.

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discussion (0)

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