Entanglement and Closest Product States of Graph States with 9 to 11 Qubits

Cuifeng Wang, Li-zhen Jiang, Lei Wang

The numbers of local complimentary inequivalent graph states for 9, 10 and 11 qubit systems are 440, 3132, 40457, respectively. We calculate the entanglement, the lower and upper bounds of the entanglement and obtain the closest product states for all these graph states. New patterns of closest product states are analyzed.

Adán Cabello, Antonio J. López-Tarrida, Pilar Moreno +1 more

Mahmoud Bordbar, Negar Naderi, Mohammad Alimoradi Chamgordani

Guowei Chen, Xiaoyu Chen

The number of inequivalent classes of 10-qubit graph states is 3132. All 3132 local inequivalent graphs are classified as two categories: graphs with equal bound, graphs with unequal bounds. We will use different methods to calculate the entanglement of graph states of ten qubits for the different categories. For graph states with different entanglement bounds, the closest product states are given, and they have different structural characters.

M Murao

We address the question of quantifying entanglement in pure graph states. The evaluation of multipartite entanglement measures is extremely difficult for most pure quantum states. In this paper, we demonstrate how solving one problem in graph theory, namely the identification of a maximum independent set, allows us to evaluate three multipartite entanglement measures for pure graph states. We construct the minimal linear decomposition into product states for a large group of pure graph states, allowing us to evaluate the Schmidt measure. Furthermore, we show that the computation of distance-like measures such as relative entropy of entanglement and geometric measure becomes tractable for these states by the explicit construction of the closest separable and closest product states, respectively. We show how these separable states can be described using stabilizer formalism as well as projected entangled pairs-like construction. Finally, we discuss how introducing noise into the system can optimally destroy entanglement.

Ahmad Akhound, Mohammad Ali Chaman Motlagh