Local invariants of braiding quantum gates -- associated link polynomials and entangling power

TL;DR

This paper investigates two-qubit Yang-Baxter operators of X-type, revealing how their eigenvalues determine non-local entanglement properties, and connects these to link polynomials and entangling power.

Contribution

It introduces a method to characterize non-local properties of X-type Yang-Baxter operators using eigenvalues and link polynomials, linking knot theory with quantum entanglement.

Findings

Eigenvalues fully determine non-local properties of X-type operators

Associated link polynomials are derived for these operators

Entangling power is computed and compared with generic operators

Abstract

For a generic $n$-qubit system, local invariants under the action of $SL(2,\mathbb{C})^{\otimes n}$ characterize non-local properties of entanglement. In general, such properties are not immediately apparent and hard to construct. Here we consider certain two-qubit Yang-Baxter operators, which we dub of the `X-type', and show that their eigenvalues completely determine the non-local properties of the system. Moreover, we apply the Turaev procedure to these operators and obtain their associated link/knot polynomials. We also compute their entangling power and compare it with that of a generic two-qubit operator.