The SLOCC invariant and the residual entanglement for n-qubits

Abstract

In this paper, we find the invariant for $n$-qubits and propose the residual entanglement for $n$-qubits by means of the invariant. Thus, we establish a relation between SLOCC entanglement and the residual entanglement. The invariant and the residual entanglement can be used for SLOCC entanglement classification for $n$-qubits.

22 pages, no figure, lemma 4 and corollary 3 and the conjecture for odd n-qubits in the previous version were deleted because they are not always true

References in corpus (4)

• Constructing N-qubit entanglement monotones from anti-linear operators
• Entanglement monotones and maximally entangled states in multipartite qubit systems
• Multipartite Entanglement Measure
• The Simple Criteria of SLOCC Equivalence Classes

Cited by in corpus (24)

• SLOCC classification of n qubits invoking the proportional relationships for spectrums and for standard Jordan normal forms
• Black Holes, Qubits and Octonions
• Entanglement Equivalence of $N$-qubit Symmetric States
• Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix
• SLOCC invariant and semi-invariants for SLOCC classification of four-qubits
• The n-tangle of odd n qubits
• An entanglement measure for n-qubits
• Local Unitary Invariants for N-qubit Pure State
• Classification of Multipartite Entanglement via Negativity Fonts
• Stochastic local operations and classical communication properties of the n-qubit symmetric Dicke states
• Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classification
• 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
• Entanglement Structure Detection via Computer Vision
• SLOCC determinant invariants of order 2^{n/2} for even n qubits
• Negativity Fonts, multiqubit invariants and Four qubit Maximally Entangled States
• Stochastic local operations and classical communication equations and classification of even $n$ qubits
• Reply to the comment on "Stochastic local operations and classical communication invariant and the residual entanglement for n qubits"
• Characterizing scalable measures of quantum resources
• SLOCC classification for nine families of four-qubits
• Comment on: Stochastic local operations and classical communication Invariant and the residual entanglement for n qubits
• Enlarging the notion of additivity of resource quantifiers
• Computable constraints on entanglement-sharing of multipartite quantum states
• Entanglement classification via integer partitions
• Rank-based SLOCC classification for odd n qubits