{"id":"724949fa-3aeb-4f03-a7e2-7b5f2dde3fba","arxiv_id":"2608.12897","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Shot-noise measurements of dilute e/4 quasiparticles at ν=5/2 show an excess Fano factor consistent with time-domain braiding of non-Abelian Ising anyons in the particle-hole Pfaffian edge.","lead":"An experiment measures shot noise from partitioning dilute quasiparticles at the ν=5/2 fractional quantum Hall state, comparing the noise with theoretical predictions for non-Abelian anyon braiding. The data favor the particle-hole Pfaffian topological order, providing evidence for non-Abelian anyons, though the neutral-mode measurement alone cannot distinguish the candidate orders.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central claim presumes the 1.4 μm inter-QPC edge is at the ideal PH-Pf fixed point; this coherence assumption is untested and partial equilibration could mimic the neutral Fano factor.","rationale":"The reader's weakest_assumption is exactly the coherence/fixed-point assumption for the 1.4 μm segment, and the reader's CONDITIONAL verdict already reflects this. My stress-test confirms that this assumption is the most load-bearing: the non-Abelian claim rests on the neutral Fano factor matching the M_n=0 prediction, which only holds for the ideal PH-Pf edge with no inter-mode equilibration. The paper's own Supplementary Note 3 addresses only the extreme l_ch-eq << L limit and finds it under-predicts; however, it does not constrain intermediate equilibration, which could produce a Fano factor near the observed value without braiding. The proposed L-dependence experiment would discriminate between the coherent braiding and partial-equilibration scenarios. The absence of error bars in the published figures and the closeness of the A-Pf prediction in the neutral configuration further support the CONDITIONAL verdict, but they are secondary to the coherence assumption. Therefore, my analysis does not change the reader's verdict.","tokens_in":42977,"tokens_out":3967,"duration_ms":43280,"concrete_test":"Fabricate two additional devices with inter-QPC separations L=0.7 μm and L=2.8 μm on the same heterostructure, and measure the neutral Fano factor at e*V_S/(2k_BT)=5.0 for all three L values. If time-domain braiding is the origin, F_neutral should remain near 2.3 for both new separations, as long as L is shorter than the phase-coherence length. If partial equilibration or incoherent heating contributes, F_neutral should vary systematically with L according to the relevant equilibration length, which would falsify the unique braiding interpretation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing premise is that the edge segment between QPC2 and QPC1 (L=1.4 μm) realizes the ideal PH-Pf fixed point, so the neutral anyon monodromy is exactly M_n=0 and the theoretical Fano factors in Eqs. (S38)-(S42) apply. The paper states this assumption explicitly in the Methods: \"The calculation assumes that the inter-QPC separation of 1.4 μm is shorter than the inter-mode equilibration lengths,\" and in the main text: \"Time-domain braiding requires that the QPCs' separation should be shorter than the phase-coherence length and other inter-mode equilibration lengths.\" The only alternative considered is the \"incoherent-heating\" model of Supplementary Note 3, which assumes the opposite hierarchy l_ch-eq << L and underestimates the measured noise by roughly a factor of two. But that model does not rule out an intermediate regime with l_ch-eq ~ L, where partial inter-mode charge tunneling would modify the effective scaling dimensions and generate excess neutral noise that is neither the braiding prediction nor the heating prediction. Since the neutral Fano factor is normalized by the measured differential reflection probability R_QPC2_diff, a partial-equilibration model could plausibly yield F_neutral close to the measured 2.37 at e*V_S/(2k_BT)=5.0 without invoking braiding. The data therefore do not uniquely imply time-domain braiding unless the fixed-point assumption is independently established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports shot-noise measurements on the ν=5/2 fractional quantum Hall edge in two complementary two-QPC geometries. In the charged-anyon configuration, a dilute beam of e/4 quasiparticles generated at QPC2 impinges on QPC1, and the measured excess noise gives a charge Fano factor of 1.54 at e*V_S/(2k_BT)=4.6, compared with the PH-Pf prediction 1.49 and the A-Pf prediction 0.94. In the neutral-anyon configuration, upstream neutral anyons generated at QPC1 propagate to QPC2, and the measured neutral Fano factor is 2.37 at e*V_S/(2k_BT)=5.0, compared with the PH-Pf prediction 2.33 and the A-Pf prediction 2.0. The theoretical curves are obtained from CFT edge models and measured QPC reflection probabilities, with no experimental fitting parameters. The authors conclude that the two independent measurements together provide evidence for time-domain braiding of non-Abelian neutral anyons and that the edge realizes the particle-hole Pfaffian (PH-Pf) topological order.","tokens_in":43284,"tokens_out":4659,"duration_ms":49225,"significance":"If correct, this would be a milestone: the first time-domain braiding evidence for non-Abelian anyons and a clean PH-Pf versus A-Pf discriminator in the charge configuration. The paper's strengths include four data sets from three devices, independent probes of the downstream charged and upstream neutral anyon beams, and a detailed theoretical treatment in Supplementary Note 2 that includes time-domain braiding, trivial partitioning, intermediate processes, and subleading braiding channels. The comparison is parameter-free in the sense that the CFT parameters are fixed by the topological order, and the measured reflection probabilities enter as inputs. The neutral-anyon configuration, even if not by itself fully discriminating PH-Pf from A-Pf, is a novel direct probe of the upstream non-Abelian sector. These features make the work potentially very significant for the quantum Hall and topological quantum computation communities.","major_comments":[{"comment":"No error bars or quantitative uncertainty estimates are shown in any of the noise or Fano-factor plots, yet the text repeatedly claims agreement 'within experimental uncertainty' (main text discussion of Figs. 2b and 3b; Supplementary Note 1). This is load-bearing because the PH-Pf and A-Pf predictions in the neutral configuration differ by only about 0.3 in the Fano factor (F=2.33 versus 2.0 at the representative point, with measured F=2.37), and the statement that the data are 'slightly closer' to PH-Pf cannot be evaluated without a quantitative uncertainty budget. The authors should provide error bars, confidence intervals, or at minimum a stated uncertainty budget for the extracted Fano factors.","section":"Figures 2b, 3b, and S1–S4"},{"comment":"The calculation assumes that the 1.4 μm inter-QPC separation is shorter than the inter-mode equilibration lengths, i.e., that the edge segment realizes the ideal PH-Pf fixed point. This assumption is explicitly stated but not independently established. The incoherent-heating model in Supplementary Note 3 treats only the opposite hierarchy l_ch-eq << L, and the intermediate regime l_ch-eq ~ L is not considered; partial inter-mode equilibration could produce excess neutral noise that is neither the braiding prediction nor the heating prediction. Since the neutral Fano factor is normalized by the separately measured differential reflection probability R_QPC2^diff, a partial-equilibration model could in principle mimic the observed values without invoking braiding. The authors should provide a diagnostic that validates the fixed-point and coherence assumption, such as a length-dependence measurement, a bias-dependence check, or an independent equilibration probe.","section":"Methods, 'Theory of the Fano factors'; main text, 'Time-domain braiding of neutral anyons'"},{"comment":"Supplementary Note 1 states that in the neutral-anyon configuration the data 'also agree well with the PH-Pf prediction, although the A-Pf prediction lies closer to the measured values,' whereas the main text states that the data are 'slightly closer to the PH-Pf prediction.' This inconsistency is material because the two configurations are presented as cross-validating the PH-Pf order. If the representative data set of Fig. 3b is the exception rather than the rule, this should be stated explicitly, and the combined-evidence argument should be reformulated accordingly.","section":"Supplementary Note 1 vs. main text, Fig. 3b discussion"}],"minor_comments":[{"comment":"The numerical factors C_rd^c and C_rd^n are introduced in the main text only as 'numerical factors.' Their values (0.47, 0.44, 0.09, and 0.59 in Supplementary Note 2D) and the fact that they are internal calibration constants obtained by comparing saddle-point and exact numerical integration should be stated in the main text, so that the 'without any fitting parameter' claim is unambiguous.","section":"Methods, Eq. (7) and accompanying text; Supplementary Note 2D"},{"comment":"There is a typo in the definition of the thermal equilibration length: 'legnth' should read 'length.'","section":"Supplementary Note 3"},{"comment":"The binomial distribution is said to be 'approximately described' for weaker dilutions, but no criterion is given for when the binomial approximation is valid. Since R_iQPC values are not tabulated for the four data sets, the authors should state the range of R_iQPC used and justify the binomial approximation in that range.","section":"Main text, after Eq. (2)"}],"recommendation":"major_revision","confidential_remarks":"This is a strong and potentially landmark experiment, and the theoretical framework is well developed. However, the conclusiveness of the 'observation' claim is currently limited by the absence of any error-bar or uncertainty analysis and by the untested coherent fixed-point assumption for the 1.4 μm edge segment. I recommend major revision rather than rejection, because the central idea is sound and the reported agreement is suggestive; the needed additions are experimental or theoretical diagnostics that would make the braiding interpretation unique."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, the short version: this is the first shot-noise experiment claiming time-domain braiding of non-Abelian anyons at ν=5/2, and if the interpretation holds it's a genuine milestone. The group extends its own Abelian anyon-braiding method from ν=1/3 to the non-Abelian case by separately measuring partition noise of the downstream charged anyons and the upstream neutral anyons in two QPC configurations. The data are new: four measurement sets from three devices, and the representative charge Fano factor of 1.54 sits between the PH-Pf prediction (1.49) and A-Pf (0.94), a clean separation. The neutral Fano factor (2.37) agrees better with PH-Pf (2.33) than A-Pf (2.0), but there the two predictions are close.\n\nWhat is genuinely good: the two-way cross-validation, the honesty of the text about the neutral channel's limited discriminating power, and the explicit incoherent-heating model that underestimates the observed noise by about a factor of two. The theoretical parameters (monodromies, scaling dimensions) are standard CFT inputs, not fitted to the data. Source data are promised with the paper, which is a plus.\n\nThe soft spots are real but not fatal. The load-bearing premise is that the 1.4 μm edge segment between the QPCs is at the ideal PH-Pf fixed point, with coherent upstream Majorana propagation and no charge or thermal equilibration. The paper states this, but offers no independent check. The heating model only treats the limit where charge equilibration is much shorter than L; an intermediate partial-equilibration regime could generate extra neutral noise that mimics the braiding prediction. So the neutral-channel evidence is not uniquely braiding unless the fixed-point assumption is directly established. Also, no error bars appear in the main figures; in some supplementary sets the A-Pf curve lies closer to the neutral data, and the theory contains internal reduction factors (C_rd) that are not data fits but are ad hoc enough to raise an eyebrow.\n\nThis is a paper for FQH theorists and experimentalists working on anyonic statistics. It deserves a serious referee. I would send it to peer review and push the authors to provide error analysis, a direct or at least stronger indirect test of the coherence assumption, and a discussion of the partial-equilibration window. The central claim is conditional, not conclusive, but it is substantial and worth engaging with.","headline":"A credible but conditional experimental claim of non-Abelian time-domain braiding at ν=5/2; the charge-channel PH-Pf vs A-Pf distinction is clean, but the untested 1.4 μm fixed-point assumption leaves room for alternative equilibration explanations.","tokens_in":43885,"tokens_out":3302,"would_cite":true,"duration_ms":33631,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["73.43.-f","72.70.+m","73.43.Lp"],"model":"deepseek-v4-flash","headline":"Shot-noise measurements at the ν=5/2 fractional quantum Hall state match, without fitting parameters, theoretical predictions for time-domain braiding of charged Abelian anyons and upstream non-Abelian neutral anyons in the particle-hole…","keywords":["non-Abelian anyons","time-domain braiding","fractional quantum Hall effect","ν=5/2 state","particle-hole Pfaffian","shot noise","Fano factor","Ising anyons"],"falsifier":"Measure the neutral Fano factor in a device whose two point contacts are separated by a distance much larger than the expected phase-coherence length (for example, 10 micrometres); if the excess neutral noise at the detection drain stays at the same magnitude, the signal cannot be time-domain braiding and would point instead to incoherent heating or equilibration of the edge modes.","tokens_in":42747,"feed_emoji":"⚛️","tokens_out":8963,"duration_ms":76010,"temperature":0.7,"pith_summary":"The paper claims that current-fluctuation (shot-noise) measurements in the $\\nu=5/2$ fractional quantum Hall state reveal the statistical phase of Abelian anyons and the non-Abelian braiding of Ising anyons through a 'time-domain braiding' mechanism, with no adjustable parameters. Two independent configurations are used: one partitions a dilute beam of downstream charged anyons at a second quantum point contact, and the other partitions the dilute upstream neutral anyon beam. In both cases the measured noise spectral densities agree with conformal-field-theory predictions for the particle-hole Pfaffian (PH-Pf) edge, and disagree with the anti-Pfaffian predictions in the charged-anyon configuration. The authors take this as evidence that non-Abelian anyons exist at $\\nu=5/2$ and that the edge realizes the PH-Pf topological order.","feed_headline":"Noise at ν=5/2 matches non-Abelian braiding predictions","feed_subtitle":"Separate probes of charged and neutral anyons both match particle-hole Pfaffian theory—evidence for non-Abelian statistics.","key_machinery":"The load-bearing object is the time-domain braiding loop. A quasiparticle excitation at the detection QPC, with energy of order $k_B T$, can tunnel out and tunnel back within a time window of order $\\hbar/k_B T$; these two trajectories are indistinguishable and interfere, forming a closed loop in the (1+1)-dimensional spacetime of the edge. Any dilute anyon that passes the QPC within this window is enclosed by the loop and braided with the excited anyon's charged or neutral component. The unit monodromies are $M_c=e^{-i\\pi/4}$ for the charged Abelian anyon and $M_n=0$ for the neutral non-Abelian Ising anyon; the relative weight of braiding versus trivial partition noise is controlled by the total scaling dimension $\\delta=\\delta_c+\\delta_n$, which is $1/4$ for the PH-Pf edge and $1/2$ for the anti-Pfaffian edge. The experimental Fano factors are computed by substituting the measured reflection probabilities into the theoretical expressions, so the comparison involves no fitting parameters.","core_discovery":"On its own terms, the paper's central claim is that the excess shot noise generated when a dilute beam of $e/4$ quasiparticles is partitioned by a second quantum point contact is dominated by 'time-domain braiding': a thermally excited quasiparticle tunnels across the detection QPC and tunnels back within the energy-time uncertainty window $\\hbar/k_B T$, forming a closed loop in time, and any dilute anyons passing the QPC within that window are enclosed by the loop and acquire a braiding monodromy. For the charged-anyon configuration the relevant unit monodromy is $M_c=e^{-i\\pi/4}$; for the neutral-anyon configuration the relevant unit monodromy is $M_n=0$, the hallmark of non-Abelian Ising anyons, for which braiding takes the state into an orthogonal state. The measured noise at the detection drains, normalized to Fano factors $\\mathcal{F}_{\\rm charge}$ and $\\mathcal{F}_{\\rm neutral}$, agrees with the theoretical predictions for the PH-Pf edge, whose charged and neutral scaling dimensions are $\\delta_c=\\delta_n=1/8$, and lies closer to PH-Pf than to anti-Pfaffian in the charged-anyon configuration. The agreement is obtained without fitting parameters.","pith_inferences":["If the braiding interpretation is correct, the neutral Fano factor near 2.3 should be insensitive to the transmission of the injection QPC; a strong dependence would instead point to subdominant processes dominating the signal.","The same time-domain loop picture predicts that the charged Fano factor should approach the Poisson-limit value 1.5 in the high-dilution limit, a regime that could be checked in devices with much weaker injection-QPC reflection.","A direct test would be the temperature dependence: as $T$ rises, the $\\hbar/k_B T$ time window shrinks, so the braiding-induced excess noise should decrease with temperature in a way that an incoherent heating model would not reproduce."],"forward_implications":["If the central claim is right, shot-noise measurements of this kind constitute a direct, parameter-free probe of non-Abelian braiding statistics that does not require spatial interferometry.","The data single out the particle-hole Pfaffian order over the anti-Pfaffian order, in line with earlier thermal Hall measurements.","The same two-QPC scheme can be extended to other candidate non-Abelian states, such as the anti-Read-Rezayi state at $\\nu=12/5$ or the $\\nu=1/2$ state in wide quantum wells.","The order-of-magnitude estimate in the paper rules out incoherent heating of the neutral mode as the origin of the excess neutral noise."],"supporting_citations":[{"why":"The prior ν=1/3 experiment that established the time-domain braiding signal and the binomial-distribution analysis used here.","marker":"[24]"},{"why":"Supplies the conformal-field-theory and Keldysh formalism for time-domain braiding, including the Poisson-limit expressions and the Mn=0 monodromy.","marker":"[26]"},{"why":"Proposes the scheme for detecting braiding statistics of neutral modes that underlies the neutral-anyon configuration.","marker":"[41]"},{"why":"Predicted that anyon braiding in the time domain yields anomalous shot noise distinct from trivial partitioning.","marker":"[25]"},{"why":"Established the e/4 quasiparticle charge at ν=5/2 used to normalize the measured Fano factors.","marker":"[16]"},{"why":"Established the existence of upstream neutral modes in the ν=5/2 state, which the neutral-anyon configuration exploits.","marker":"[19]"},{"why":"Reported half-integer thermal Hall conductance, prior evidence for a single upstream Majorana mode and PH-Pf order.","marker":"[20,21]"},{"why":"Provide the particle-hole Pfaffian edge-model and scaling-dimension values used in the theoretical Fano factors.","marker":"[27-29]"},{"why":"Reported absence of thermal equilibration on fractional quantum Hall edges over macroscopic distances, supporting the coherent-edge assumption.","marker":"[42]"},{"why":"Provide the shot-noise method for measuring fractional quasiparticle charge, used to characterize the injected beam.","marker":"[35-36]"}],"fun_headline_variants":["Time-domain braiding signals non-Abelian anyons at ν=5/2","Non-Abelian anyon braiding seen in noise at ν=5/2","Noise reveals time-domain braiding of non-Abelian anyons"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole interpretation rests on the assumption that the 1.4-micrometre edge segment between the two point contacts is phase-coherent and free of charge or thermal equilibration, so the neutral braiding effect is exactly zero; if that segment equilibrates, the extra neutral noise could come from incoherent heating rather than braiding.","fun_headline_variants_meta":{"raw":{"variants":["Time-domain braiding signals non-Abelian anyons at ν=5/2","Non-Abelian anyon braiding seen in noise at ν=5/2","Noise reveals time-domain braiding of non-Abelian anyons"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000729,"raw_usage":{"total_tokens":3315,"prompt_tokens":1048,"completion_tokens":2267,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":664,"completion_tokens_details":{"reasoning_tokens":2199}},"tokens_in":664,"tokens_out":2267,"duration_ms":14428,"temperature":1.0,"reasoning_tokens":2199,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:03:07.028900+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the neutral Fano factor in a device whose two point contacts are separated by a distance much larger than the expected phase-coherence length (for example, 10 micrometres); if the excess neutral noise at the detection drain stays at the same magnitude, the signal cannot be time-domain braiding and would point instead to incoherent heating or equilibration of the edge modes.","supporting_citations":[{"cited_title":"M Lee et al., Partitioning of diluted anyons reveals their braiding statistics, Nature 617, 277 (2023)","cited_arxiv_id":null,"evidence_quote":"The prior ν=1/3 experiment that established the time-domain braiding signal and the binomial-distribution analysis used here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the conformal-field-theory and Keldysh formalism for time-domain braiding, including the Poisson-limit expressions and the Mn=0 monodromy."},{"cited_title":"Han, J.-Y","cited_arxiv_id":null,"evidence_quote":"Proposes the scheme for detecting braiding statistics of neutral modes that underlies the neutral-anyon configuration."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Predicted that anyon braiding in the time domain yields anomalous shot noise distinct from trivial partitioning."},{"cited_title":"Dolev et al., Observation of a quarter of an electron charge at the ν=5/2 quantum Hall state, Nature 452, 829 (2008)","cited_arxiv_id":null,"evidence_quote":"Established the e/4 quasiparticle charge at ν=5/2 used to normalize the measured Fano factors."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Established the existence of upstream neutral modes in the ν=5/2 state, which the neutral-anyon configuration exploits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reported absence of thermal equilibration on fractional quantum Hall edges over macroscopic distances, supporting the coherent-edge assumption."}],"review_version":1}