Entanglement Measures for Many-Body Quantum Systems: Limitations and New Approaches

TL;DR

This paper examines limitations of traditional entanglement measures in many-body quantum systems and introduces new measures and a strong monogamy concept that remain effective as system size increases.

Contribution

The authors identify limitations of existing entanglement measures for large systems and propose alternative measures and a stronger monogamy relation that better capture entanglement in many-body states.

Findings

Traditional measures approach zero for large systems in certain states.

New measures remain significant as the number of particles increases.

Proposed strong monogamy relation does not converge to equality with system size.

Abstract

In this research, the entanglement within two entangled n-qubit systems is analyzed using the one-tangle, two-tangle, and {\pi}-tangle. The findings indicate that for certain quantum states, such as the generalized W state, where the probability coefficients depend on the number of qubits, increasing the number of particles causes these measures to approach zero, with the monogamy of entanglement converging to equality. This implies that for quantum states whose probability coefficients are dependent on the number of qubits, the one-tangle and {\pi}-tangle become ineffective in capturing entanglement as the system size increases. To address this, we introduced three alternative measures: the sum of two-tangles, the sum of squared one-tangles, and the generalized residual entanglement. Unlike the one-tangle and {\pi}-tangle, these measures do not diminish to zero as the number of particles increases. Furthermore, we proposed a strong monogamy of entanglement that does not converge to equality as the number of particles grows.