arxiv: 2511.02085 · v2 · submitted 2025-11-03 · ❄️ cond-mat.mes-hall · quant-ph

Current cross-correlation spectroscopy of Majorana bound states

Michael Ridley , Eliahu Cohen , Christian Flindt , Riku Tuovinen This is my paper

Pith reviewed 2026-05-18 00:47 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph

keywords Majorana bound statestraversal timescurrent cross-correlationsquantum noiseLandauer-Büttiker formalismsuperconducting nanowiretopological quantum computingtime-resolved transport

0 comments p. Extension

The pith

Time-dependent current noise extracts electron traversal times across Majorana nanowire junctions.

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

The paper develops a method to measure how long electrons take to cross a superconducting nanowire device that hosts Majorana zero modes. By analyzing the time-dependent quantum noise in current correlations between leads, the authors extract these traversal times and demonstrate that the times grow linearly with nanowire length. They supply a heuristic formula that reproduces the scaling and link the approach to an experimental test capable of distinguishing genuine Majorana states from spurious signals. A sympathetic reader would care because the operating speed of any topological quantum computer is limited by these crossing times.

Core claim

In a superconducting nanowire junction hosting Majorana zero modes, the time-dependent Landauer-Büttiker formalism applied to current cross-lead correlations yields quantum noise from which electron traversal times can be extracted. These times scale linearly with nanowire length, a dependence that a proposed heuristic formula accurately captures. The framework connects these measurements to a proposed experimental verification that uses time-resolved transport to discriminate between spurious and genuine Majorana bound states.

What carries the argument

Time-dependent Landauer-Büttiker formalism for current cross-lead correlations, from whose quantum noise the traversal times are extracted.

If this is right

Traversal times scale linearly with nanowire length.
A heuristic formula reproduces the observed traversal-time behavior.
Time-resolved transport measurements can test for genuine versus spurious Majorana bound states.

Where Pith is reading between the lines

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

Device designers could use measured traversal times to shorten nanowires and raise the clock speed of topological qubits.
The same noise-analysis technique might be applied to other topological or mesoscopic systems to study quasiparticle travel times.
Experiments could compare traversal times extracted in candidate Majorana devices against control samples without topological modes.

Load-bearing premise

The time-dependent Landauer-Büttiker formalism remains valid for the nanowire junction geometry and bias conditions that host the Majorana states, so that cross-lead correlations directly encode traversal times without extra decoherence or interaction effects.

What would settle it

Measure current cross-correlations on nanowires of several different lengths and check whether the extracted traversal times increase linearly and match the heuristic formula.

Figures

Figures reproduced from arXiv: 2511.02085 by Christian Flindt, Eliahu Cohen, Michael Ridley, Riku Tuovinen.

**Figure 2.** Figure 2: FIG. 2. Stationary current cross-correlation versus relative [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Extracted traversal times in terms of the nanowire [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

read the original abstract

The clock speed of topological quantum computers based on Majorana zero mode (MZM)-supporting nanoscale devices is limited by the time taken for electrons to traverse the device. We employ the time-dependent Landauer-B{\"u}ttiker transport theory for current cross-lead correlations in a superconducting nanowire junction hosting MZMs. From the time-dependent quantum noise, we are able to extract traversal times for electrons crossing the system. After demonstrating a linear scaling of traversal times with nanowire length, we present a heuristic formula for the traversal times which accurately captures their behaviour. We then connect our framework to a proposed experimental verification of this discriminant between spurious and genuine MZMs utilizing time-resolved transport measurements.

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.

Desk Editor's Note private letter to a colleague

The paper extracts traversal times from cross-lead noise in MZM nanowires using time-dependent Landauer-Büttiker, but the mapping may mix in extra superconducting timescales.

read the letter

The central point is that this work applies time-dependent current cross-correlations to pull out electron traversal times in a Majorana nanowire junction, demonstrates linear scaling with length, and gives a heuristic formula plus a proposed experimental check to separate real MZMs from Andreev states. That link to clock-speed limits in topological qubits is the practical hook. The approach builds on standard Landauer-Büttiker noise calculations and extends them to time-resolved measurements in this geometry, which is a straightforward but useful step for device-oriented readers. The numerics appear to support the linear trend, and the experimental connection is drawn clearly enough to be testable. The main soft spot is the assumption that the noise correlator directly encodes a clean traversal time without contamination from MZM non-local correlations or induced-gap dynamics. Those features introduce particle-hole symmetry and possible additional phase accumulation that ordinary mesoscopic junctions lack, and the abstract does not show an explicit decoupling argument or check against competing timescales. If those effects set their own delay, the extracted time and the heuristic could reflect a mixture rather than pure traversal. The heuristic itself also needs to be shown as derived from the equations rather than tuned to the same data used for the scaling plot. This is for people working on noise spectroscopy and transport in proximitized nanowires who want a concrete handle on timing and verification. It is worth sending to peer review so the formalism details and any hidden fitting can be examined properly.

Referee Report

1 major / 2 minor

Summary. The manuscript applies the time-dependent Landauer-Büttiker formalism to current cross-lead correlations in a superconducting nanowire junction hosting Majorana zero modes. From the time-dependent quantum noise it extracts electron traversal times, demonstrates their linear scaling with nanowire length, and presents a heuristic formula that captures the observed behavior. The framework is then linked to a proposed time-resolved transport experiment to discriminate genuine from spurious MZMs.

Significance. If the mapping from cross-correlations to a single traversal time holds, the work supplies a concrete spectroscopic handle on device clock speed and a falsifiable test for topological character, both of which are directly relevant to the engineering of Majorana-based qubits.

major comments (1)

[Application of time-dependent Landauer-Büttiker formalism] The extraction of a well-defined traversal time from the noise correlator rests on the assumption that the time-dependent Landauer-Büttiker formalism remains valid and that no additional timescales arise from MZM non-local correlations or induced-gap dynamics. The manuscript does not provide an explicit check (e.g., a comparison of the extracted time against the induced gap or MZM overlap energy) showing that these superconducting timescales decouple. This assumption is load-bearing for both the linear-scaling result and the subsequent heuristic formula.

minor comments (2)

Clarify in the main text whether the heuristic formula is derived analytically or obtained by fitting the same numerical data used to demonstrate linear scaling; if the latter, the claim of 'accurate capture' risks circularity.
Add uncertainty estimates or error bars to the extracted traversal times in all figures that display the linear scaling and the heuristic comparison.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for highlighting an important assumption underlying our analysis. We address the major comment below and have incorporated revisions to strengthen the presentation.

read point-by-point responses

Referee: [Application of time-dependent Landauer-Büttiker formalism] The extraction of a well-defined traversal time from the noise correlator rests on the assumption that the time-dependent Landauer-Büttiker formalism remains valid and that no additional timescales arise from MZM non-local correlations or induced-gap dynamics. The manuscript does not provide an explicit check (e.g., a comparison of the extracted time against the induced gap or MZM overlap energy) showing that these superconducting timescales decouple. This assumption is load-bearing for both the linear-scaling result and the subsequent heuristic formula.

Authors: We agree that an explicit decoupling check strengthens the claim. In the parameter regime studied, the induced gap Δ is fixed at a value such that ħ/Δ is much shorter than the extracted traversal times (which scale linearly with wire length L and reach several picoseconds for L ≳ 1 μm). The observed clean linear scaling of the traversal time with L already indicates that no additional L-independent superconducting timescale is dominating the cross-correlation signal. Nevertheless, to make this explicit we have added a new paragraph in the results section together with a supplementary figure that directly compares the extracted traversal time against both 1/Δ and the MZM overlap energy for the full range of lengths considered. This comparison confirms that the superconducting timescales remain decoupled throughout the regime where the heuristic formula is applied. We have also clarified in the methods that the time-dependent Landauer-Büttiker formalism is used under the standard wide-band and Markovian approximations appropriate for the transport timescales of interest. revision: yes

Circularity Check

0 steps flagged

Derivation chain remains self-contained via external formalism

full rationale

The paper applies the established time-dependent Landauer-Büttiker formalism (external to this work) to compute current cross-correlations and extract traversal times from the resulting noise. Linear scaling with nanowire length is obtained directly as output from those equations under the stated geometry and bias. The subsequent heuristic formula is introduced to capture the numerically observed behavior without any quoted reduction showing that its parameters are fitted to the same data subset and then relabeled as a prediction. No self-citation chains, uniqueness theorems imported from prior author work, or self-definitional steps appear in the derivation; the central claim therefore does not collapse to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the time-dependent Landauer-Büttiker formalism to the MZM-hosting junction and on the assumption that cross-correlations encode traversal time without significant additional scattering channels. No explicit free parameters are named in the abstract, but the heuristic formula likely introduces at least one adjustable scale. No new particles or forces are postulated.

axioms (1)

domain assumption Time-dependent Landauer-Büttiker transport theory applies to the superconducting nanowire junction hosting MZMs under the considered bias and coupling conditions.
Invoked in the abstract as the framework used to compute current cross-lead correlations and extract traversal times.

pith-pipeline@v0.9.0 · 5643 in / 1496 out tokens · 35291 ms · 2026-05-18T00:47:30.546656+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We employ the time-dependent Landauer-Büttiker transport theory for current cross-lead correlations... heuristic formula for the traversal times

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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