Genuine tripartite entanglement in quantum brachistochrone evolution of a three-qubit system

TL;DR

This paper investigates the role of genuine tripartite entanglement, specifically three-tangle, in the quantum brachistochrone evolution of a three-qubit system, revealing that three-tangle is essential for certain state transitions.

Contribution

It demonstrates that three-tangle is necessary for non-trivial brachistochrone evolutions between distinct states in a three-qubit system, highlighting the importance of tripartite entanglement.

Findings

Two-qubit entanglement is not required for some evolutions.

Three-tangle is essential for non-trivial state transitions.

Distribution of three-tangle becomes more uniform with decreasing angles of separation.

Abstract

We explore the connection between quantum brachistochrone (time-optimal) evolution of a three-qubit system and its residual entanglement called three-tangle. The result shows that the entanglement between two qubits is not required for some brachistochrone evolutions of a three-qubit system. However, the evolution between two distinct states cannot be implemented without its three-tangle, except for the trivial cases in which less than three qubits attend evolution. Although both the probability density function of the time-averaged three-tangle and that of the time-averaged squared concurrence between two subsystems become more and more uniform with the decrease in angles of separation between an initial state and a final state, the features of their most probable values exhibit a different trend.