Bounds on Bipartitiely Shared Entanglement Reduced from Superposed Tripartite Quantum States

TL;DR

This paper derives bounds on bipartite entanglement in superposed tripartite quantum states, showing how local measurements influence entanglement sharing, with explicit bounds for qubit systems.

Contribution

It provides the first analytical bounds on bipartite entanglement in superposed tripartite states, especially for qubit systems, based on the entanglement of individual states.

Findings

Bounds on bipartite entanglement depend on superposition components.

Explicit bounds for concurrence in 2x2xN systems.

Local measurements can optimize bipartite entanglement sharing.

Abstract

For a tripartite pure state superposed by two individual states, the bipartitely shared entanglement can always be achieved by local measurements of the third party. Consider the different aims of the third party, i.e. maximizing or minimizing the bipartitely shared entanglement, we find bounds on both the possible bipartitely shared entanglement of the superposition state in terms of the corresponding entanglement of the two states being superposed. In particular, by choosing the concurrence as bipartite entanglement measure, we obtain calculable bounds for tripartite $(2\otimes 2\otimes n)$ -dimensional cases.