SLOCC polynomial invariants of degree 6 for even n qubits

Abstract

We give a practical, necessary and sufficient condition for two pure n-qubit states to be stochastic local operations and classical communication (SLOCC) equivalent. We also construct the SLOCC polynomial invariants of degree 6 for even n-qubit (n ⩾ 4) states. The polynomials are in the explicit form of 3 × 3 determinants whose entries are polynomials of degree 2 in the coefficients of the states. Further, the polynomials satisfy an SLOCC equation and therefore are invariant under SLOCC. The SLOCC equations can be used for the SLOCC classification of even n qubits.