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

Abstract

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

References in corpus (8)

• 14-qubit entanglement: creation and coherence
• Constructing N-qubit entanglement monotones from anti-linear operators
• Inductive Entanglement Classification of Four Qubits under SLOCC
• Four-qubit entanglement from string theory
• On polynomial invariants of several qubits
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• On the geometry of a class of N-qubit entanglement monotones
• Classification of Multipartite Entanglement via Negativity Fonts

Cited by in corpus (7)

• SLOCC classification of n qubits invoking the proportional relationships for spectrums and for standard Jordan normal forms
• Stochastic local operations and classical communication (SLOCC) and local unitary operations (LU) classifications of n qubits via ranks and singular values of the spin-flipping matrices
• Relations among $k$-ME concurrence, negativity, polynomial invariants, and tangle
• Sequential generation of Polynomial Invariants and N-body non-local correlations
• Entanglement classification via integer partitions
• Absolutely maximally entangled pure states of multipartite quantum systems
• Monogamy constraints on entanglement of four-qubit pure states