From Qubits to Qumodes: Information Capacity of Anyonic Excitations

The interplay between quantum statistics and information encoding is a cornerstone of quantum physics. Here, the maximum information capacity of a quantum state governed by Haldane’s exclusion statistics is derived. The capacity, defined by the maximum von Neumann entropy of its occupancy distribution, follows 𝑆 _max (𝑔) = log ₂ (⌊1/𝑔⌋ + 1). This result continuously interpolates between the fermionic limit of a single qubit (𝑔 = 1) and the bosonic limit of a continuous-variable qumode (𝑔 → 0) For the 𝜈 = 1/3 fractional quantum Hall state (𝑔 = 1/3), we predict a 2-bit capacity, observable as four distinct quantized conductance plateaus in quantum dot spectroscopy, providing a direct signature of anyonic statistics.