Entropy of non-Abelian anyons: a new measurement method via interferometry ✛ ✦
Context
Detecting non-Abelian anyons is one of the key challenges in modern condensed matter physics, as these exotic particles could become the foundation for fault-tolerant quantum computers. The concept of anyons was first introduced by Frank Wilczek, and their potential for quantum computing was unveiled by Alexei Kitaev. Their unusual exchange statistics leads to ground state degeneracy and the emergence of entropy that is independent of system size and determined solely by the anyon type. However, directly measuring this entropy long remained elusive, requiring simultaneous control of charge at the fractional level and thermodynamic equilibrium. A new approach based on interferometry and quantum measurements opens a path to solving this problem.
Methods
The authors theoretically model an antidot in the fractional quantum Hall regime, where elementary excitations carry charge e/4. The antidot is connected to a long edge, and anyon tunneling is described within conformal field theory. The key idea is to use nonlocal sensing of charge via the Aharonov–Bohm effect: when an anyon enters the antidot, the interference pattern undergoes a phase shift, manifesting as telegraph noise in the current. Then, the second law of thermodynamics and the Boltzmann distribution are applied to relate the temperature shift of the charge curve to the entropy change. Calculations are validated via numerical simulation of stochastic switching.
Results
The analysis showed that in the intermediate temperature regime, where thermal energy exceeds the edge-level spacing but is smaller than the antidot energy gap, the charge curve ⟨N⟩($n_g$, T) contains information about the quantum dimension d. For the non-Abelian 5/2 state with d=√2, an even-odd effect is predicted: states with an unpaired anyon possess excess entropy (1/2)$k_B$ log 2. Integrating the charge derivative with respect to temperature, according to the Maxwell relation, yields the total entropy change ΔS = $k_B$ log d. In the Abelian case (ν=1/3) no such effect exists, and the entropy reduces to peaks of $k_B$ log 2 at charge degeneracy points, highlighting the role of quantum information encoded in topological degrees of freedom. Simulation of the telegraph signal demonstrates how the occupation times $t_{in}$ and $t_{out}$ can be used to recover charge and entropy even in the presence of quantum decoherence caused by slow tunneling.
Implications
The proposed method provides a clear experimental recipe for identifying non-Abelian anyons, a crucial step toward verifying topological order. Unlike thermal conductivity measurements, which sense only the edge entropy density, this approach extracts the entropy of an individual anyon, granting access to its quantum characteristics. It also lays the groundwork for thermodynamic spectroscopy of topological states using Maxwell relations.
Future development
In the coming years, such measurements are expected to be implemented in graphene interferometers, where slow phase switching has already been observed. Improving quantum measurement precision and temperature control will not only confirm d=√2 but also test other candidates for non-Abelian states, such as the anti-Pfaffian. Advances in numerical methods will help optimize device parameters for robust entropy readout.
Impact
The results will impact the development of topological quantum processors and fundamental physics of low-dimensional systems.
Next steps
The key experiment is measuring the temperature dependence of the duty cycle of telegraph noise in an interferometer with a controlled antidot at ν=5/2, for example, based on GaAs/AlGaAs heterostructures.
Key open problems
This work is directly connected to the problem of detecting non-Abelian topological order, which is among the major unsolved challenges in condensed matter physics. It also touches on the fundamental question of the relationship between quantum information and thermodynamics at the microscopic level.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The paper proposes a method to measure the entropy of non-Abelian anyons via antidot interferometry in the fractional quantum Hall regime. The authors theoretically model the tunneling of anyons with charge e/4, linking telegraph noise in the current to phase shifts, and show how to extract the quantum dimension d from the temperature dependence of the charge curve. For the 5/2 state, they predict an even-odd effect with excess entropy of (1/2)k_B log 2, and numerical simulations confirm that charge and entropy can be recovered from dwell times.
Where its strength is
The strength of the work lies in a concrete experimental recipe: using nonlocal charge sensing via the Aharonov–Bohm effect allows direct extraction of topological entropy, which sets the method apart from thermal conductivity measurements that are only sensitive to edge entropy density. This paves the way for unambiguous verification of topological order.
Where it could go next
- It might be interesting to see how ideas from the paper about quantum particles that remember their past could enrich the analysis of temporal correlations in the telegraph signal. Perhaps incorporating memory in the stochastic switching process could refine entropy estimates for slow tunneling.based on: Quantum Particles Remember Their Past arXiv:2603.12675
- A related work on rare quantum jumps investigates the statistics of rare events. It might be useful to apply its large deviation analysis methods to the distribution of anyon dwell times in the antidot, thereby improving the accuracy of entropy extraction from experimental data.based on: Rare Quantum Jumps: A Fresh Look at Randomness arXiv:2608.06319v1
- In our archive, there is a review on entanglement under the microscope that discusses ways to detect quantum correlations. Adapting the measurement schemes proposed there might allow direct confirmation of the non-Abelian nature of anyons through observation of topological entanglement.based on: Entanglement in the Crosshairs arXiv:2604.24854
Worth trying
- Test whether accounting for non-Gaussian noise in the telegraph signal model improves entropy estimation at finite temperatures.
- Apply the method to other fractional states, such as ν=7/3, to compare predictions for different quantum dimensions.
- Explore the use of machine learning to extract dwell times from noisy current and subsequently compute entropy.
Why this may matter
Direct measurement of non-Abelian anyon entropy would be a major step toward experimental confirmation of topological order, which is critical for building fault-tolerant quantum computers based on topological qubits. The proposed method could become a standard tool in studies of the fractional quantum Hall effect and other topological phases.
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Original abstract
as written by the authors arXiv:2607.02188
Non-Abelian anyons emerging in fractional quantum Hall states carry a characteristic entropy, $$\Delta S = k_B \log d$$, where $$d$$ is the anyon's quantum dimension. This $$\mathcal{O}(1)$$ entropy can, in principle, be extracted from charge measurements of an antidot via Maxwell relations. However, equilibrium charge measurements in fractional antidots have proven to be challenging with conventional charge detectors. Here, we propose a scheme based on an antidot embedded in an interferometer, in which the charge can be inferred from the recently observed time-dependent switching of the interference phase. Performing such non-local charge measurements at equilibrium, the characteristic $$\mathcal{O}(1)$$ entropy of non-Abelian anyons (e.g., $$d = \sqrt{2}$$ for the $$ u = 5/2$$ state) can be extracted for intermediate temperatures, which exceed the level spacing of the interferometer edge, but are much smaller than the level spacing of the antidot.
The entropy of a single non-Abelian anyon is roughly 0.35 $k_B$ — almost three times smaller than the entropy of an electron spin ($k_B$ log 2 ≈ 0.69 $k_B$), as if nature is economizing on information.
Key numbers
- quantum dimension d for ν=5/2: √2 ≈ 1.414
- quasiparticle charge: e/4
- entropy per anyon: k_B log √2 ≈ 0.35 k_B
- transition peak entropy: k_B log(1+√2) ≈ 0.88 k_B
- temperature regime: E_edge ≪ k_B T ≪ E_antidot