Searching for Maximally Entangled Seven-Qubit State via Reduced Density Matrices

Maximally quantum entanglement is vital for the application of quantum communications and quantum information, and plays a fundamental role in quantum information. In this paper, we present a new approach, via reduced density matrices, to search the maximally seven-qubit pure states. Through the numerical calculations and analysis, we construct a simple form of maximally seven-qubit pure states. Further, we find maximally entangled seven-qubit states whose marginal density matrices for subsystems of 1, 2 are completely mixed. Moreover, We show that average bipartite entanglement of maximally seven-qubit pure states is also 19/140. Our result provides the research foundation for the development of quantum communication and quantum information.

Automated summary

In this paper, a new approach, using reduced density matrices, is proposed to investigate maximally entangled 7-qubit pure states. Through numerical calculations and analysis, a simple form of maximally entangled 7-qubit pure states is constructed. The paper also demonstrates the existence of maximally entangled 7-qubit states whose marginal density matrices for subsystems of 1, 2 are completely mixed. Furthermore, the average bipartite entanglement of maximally entangled 7-qubit pure states is found to be 19/140. These findings lay the research foundation for the development of quantum communication and quantum information.