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 𝑆max(𝑔) = log2(⌊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.

Description:
This preprint investigates the fundamental connection between anyonic exchange statistics and quantum information capacity. We demonstrate that the von Neumann entropy of anyonic excitations in fractional quantum Hall states is quantized, with the maximum value given by Smax=log⁡2(m+1)Smax=log2(m+1), where m=1/gm=1/g is the maximum number of anyons in a localized state.

For the ν=1/3ν=1/3 state (g=1/3g=1/3), this yields a maximum entropy of 2 bits, indicating the system behaves as a native four-level quantum system (ququart). We propose a novel hardware-efficient readout scheme for this anyonic qudit, which requires approximately half the physical components of an equivalent two-qubit system.

The work includes a finite-temperature analysis of the entropy and a discussion on experimental realization through quantized conductance measurements. Our results establish a new paradigm for leveraging the intrinsic information capacity of topological phases for quantum information processing.

Keywords: Anyons, Topological Material, Quantum Hall Effect, Quantum Information, Anyons, Entropy, Qumodes, Qudits, Entropy, Quantum Dot Spectroscopy, Quantum Foundations.