From Qubits to Qumodes: Information Capacity of Anyonic Excitations

Abstract

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) = log2(\lfloor 1/g \rfloor + 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 nu = 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.