Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation

TL;DR

This paper explores the connection between topological braiding operators and quantum entanglement, demonstrating how supersymmetry algebras can generate solutions to the generalized Yang-Baxter equation that produce all multi-qubit entangled states.

Contribution

It introduces a method using supersymmetry algebras to construct solutions to the generalized Yang-Baxter equation for multi-qubit systems, linking topological operators to quantum entanglement.

Findings

Constructed families of solutions to the generalized Yang-Baxter equation.

Generated all entangled states classified by SLOCC in multi-qubit systems.

Outlined an algorithm for arbitrary numbers of qubits.

Abstract

Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding operators as quantum entanglers, and is part of a larger speculated connection between topological and quantum entanglement. We push the analysis of this connection forward, by showing that supersymmetry algebras can be used to construct large families of solutions of the spectral parameter-dependent generalized Yang-Baxter equation. We present a number of explicit examples and outline a general algorithm for arbitrary numbers of qubits. The operators we obtain produce, in turn, all the entangled states in a multi-qubit system classified by the Stochastic Local Operations and Classical Communication protocol introduced in quantum information theory.