SLOCC determinant invariants of order 2^{n/2} for even n qubits

TL;DR

This paper introduces a simple method to construct SLOCC determinant invariants for even n qubits, enabling complete entanglement classification based on the invariants' vanishing properties.

Contribution

It provides a new, straightforward construction of determinant invariants for even qubits and demonstrates their completeness for entanglement classification.

Findings

Constructed determinant invariants for even n qubits

Proved the set of invariants is complete under qubit permutations

Applied method to classify entanglement in six-qubit systems

Abstract

In this paper, we study SLOCC determinant invariants of order 2^{n/2} for any even n qubits which satisfy the SLOCC determinant equations. The determinant invariants can be constructed by a simple method and the set of all these determinant invariants is complete with respect to permutations of qubits. SLOCC entanglement classification can be achieved via the vanishing or not of the determinant invariants. We exemplify the method for several even number of qubits, with an emphasis on six qubits.