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We develop a simple method for constructing polynomial invariants of degree 4for even-$n$ qubits and give explicit expressions for these polynomialinvariants. We demonstrate the invariance of the polynomials under stochasticlocal operations and classical communication and exemplify the use of theinvariance in classifying entangled states. The absolute values of thesepolynomial invariants are entanglement monotones, thereby allowing entanglementmeasures to be built. Finally, we discuss the properties of these entanglementmeasures.

Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classification