Quantum entropies of realistic states of a topological insulator

TL;DR

This paper investigates topological states in BiSe nanowires by calculating known and new entropy measures, demonstrating a constant topological entropy and a distinguishable new entropy for topological states.

Contribution

It introduces a new entropy measure based on reduced density matrices to identify topological states, complementing existing topological entropy calculations.

Findings

Topological entropy remains constant regardless of state parameters.

The new entropy measure is consistently larger for topological states.

Explicit construction of reduced density matrices using Kraus operators.

Abstract

Nanowires of BiSe show topological states localized near the surface of the material. The topological nature of these states can be analyzed using well-known quantities. In this paper, we calculate the topological entropy suggested by Kitaev and Preskill for these states together with a new entropy based on a reduced density matrix that we propose as a measure to distinguish topological one-electron states. Our results show that the topological entropy is a constant independent of the parameters that characterize a topological state as its angular momentum, longitudinal wave vector, and radius of the nanowire. The new entropy is always larger for topological states than for normal ones, allowing the identification of the topological ones. We show how the reduced density matrices associated with both entropies are constructed from the pure state using positive maps and explicitly obtaining the Krauss operators.