Entanglement measures for multipartite quantum systems:limitations and new approaches

Abstract

In this research, we investigate the distribution of entanglement within two entangled $n$-qubit systems using the one-tangle and $\pi$-tangle. Our analysis reveals that for certain quantum states such as the generalized $W$ state, where the probability coefficients depend on the number of qubits, increasing the system size causes these traditional measures to gradually diminish, with the monogamy relation tending toward equality. This behavior highlights a limitation of conventional tangle-based measures in capturing multipartite correlations in large systems. To overcome this, we introduce two alternative measures: the sum of squared one-tangles and the generalized residual entanglement. Unlike the standard one-tangle and $\pi$-tangle, these new quantities remain robust as the number of qubits increases. Moreover, we propose a strong monogamy relation that preserves nontrivial entanglement distribution even in the large-$n$ limit. Our results provide a refined framework for quantifying entanglement in high-dimensional multipartite systems.

References in corpus (16)

• Quantum entanglement
• A computable measure of entanglement
• Distributed Entanglement
• Qubit teleportation between non-neighboring nodes in a quantum network
• Entanglement purification and quantum error correction
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• Probing quantum correlations in many-body systems: a review of scalable methods
• Detecting entanglement in quantum many-body systems via permutation moments
• Strong monogamy inequalities for four qubits
• Multipartite Entanglement: A Journey Through Geometry
• Monogamy of quantum entanglement
• Single-photon pulse induced giant response in N$>$100 qubit system
• Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
• Tighter monogamy inequalities of multiqubit entanglement
• A secure deterministic remote state preparation via a seven-qubit entangled channel of an arbitrary two-qubit state under the impact of quantum noise