Stochastic local operations and classical communication equations and classification of even $n$ qubits

Abstract

For any even $n$ qubits we establish four SLOCC equations and construct four SLOCC polynomials (not complete) of degree $2^{n/2}$, which can be exploited for SLOCC classification (not complete) of any even $n$ qubits. In light of the SLOCC equations, we propose several different genuine entangled states of even $n$ qubits and show that they are inequivalent to the $|GHZ>$, $|W>$, or $|l,n>$ (the symmetric Dicke states with $l$ excitations) under SLOCC via the vanishing or not of the polynomials. The absolute values of the polynomials can be considered as entanglement measures.

References in corpus (9)

• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• Constructing N-qubit entanglement monotones from anti-linear operators
• Operational Families of Entanglement Classes for Symmetric $N$-Qubit States
• Inductive Entanglement Classification of Four Qubits under SLOCC
• Four-qubit entanglement from string theory
• Entanglement monotones and maximally entangled states in multipartite qubit systems
• On polynomial invariants of several qubits
• On the geometry of four qubit invariants
• Four-tangle for pure states

Cited by in corpus (5)

• Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix
• The n-tangle of odd n qubits
• Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states
• Operational Entanglement Families of Symmetric Mixed N-Qubit States
• Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classification