An entanglement measure for n-qubits

Abstract

Recently, Coffman, Kundu, and Wootters introduced the residual entanglement for three qubits to quantify the three-qubit entanglement in Phys. Rev. A 61, 052306 (2000). In Phys. Rev. A 65, 032304 (2007), we defined the residual entanglement for $n$ qubits, whose values are between 0 and 1. In this paper, we want to show that the residual entanglement for $n$ qubits is a natural measure of entanglement by demonstrating the following properties. (1). It is SL-invariant, especially LU-invariant. (2). It is an entanglement monotone. (3). It is invariant under permutations of the qubits. (4). It vanishes or is multiplicative for product states.

16 pages, no figures

References in corpus (7)

• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Constructing N-qubit entanglement monotones from anti-linear operators
• Multipartite Entanglement Measure
• SLOCC invariant and semi-invariants for SLOCC classification of four-qubits
• The SLOCC invariant and the residual entanglement for n-qubits
• The Simple Criteria of SLOCC Equivalence Classes
• Reply to the comment on "Stochastic local operations and classical communication invariant and the residual entanglement for n qubits"

Cited by in corpus (12)

• The n-tangle of odd n qubits
• Four-tangle for pure states
• 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
• Bell-type inequality and quantum nonlocality in four-qubit systems
• SLOCC determinant invariants of order 2^{n/2} for even n qubits
• Stochastic local operations and classical communication equations and classification of even $n$ qubits
• Production of entangled x rays through nonlinear double Compton scattering
• Generating GHZ state in 2m-qubit spin network
• Characterizing scalable measures of quantum resources
• Rank-based SLOCC classification for odd n qubits
• Enlarging the notion of additivity of resource quantifiers