Tighter generalized monogamy and polygamy relations for multiqubit systems

TL;DR

This paper derives tighter monogamy and polygamy relations for multiqubit systems using concurrence and negativity, providing improved bounds on entanglement distribution among subsystems.

Contribution

It introduces new, tighter bounds on entanglement measures for multiqubit states, enhancing understanding of entanglement sharing constraints.

Findings

Smaller upper bounds for concurrence in multiqubit states.

Tighter monogamy relations for pure states under various partitions.

Derived similar bounds for negativity.

Abstract

We present a different kind of monogamy and polygamy relations based on concurrence and concurrence of assistance for multiqubit systems. By relabeling the subsystems associated with different weights, a smaller upper bound of the $\alpha$th ($0\leq\alpha\leq2$) power of concurrence for multiqubit states is obtained. We also present tighter monogamy relations satisfied by the $\alpha$th ($0\leq\alpha\leq2$) power of concurrence for $N$-qubit pure states under the partition $AB$ and $C_1 . . . C_{N-2}$, as well as under the partition $ABC_1$ and $C_2\cdots C_{N-2}$. These inequalities give rise to the restrictions on entanglement distribution and the trade off of entanglement among the subsystems. Similar results are also derived for negativity.