Construct maximally seven-qubit entangled state via Brown state

Abstract

It is worth studying recurrence relation of multi-qubit states due to its benefits to the criterion and measurement of quantum entanglement. Recently, Huang et al. presented an expand recurrence relation of multi-qubit state. Using this expand recurrence relation and Brown state, we construct a new seven-qubit maximally entangled states of 32 and 3 balanced purities equal to 1/8 and 1/4, whose averaged subsystem purity is equal to 19/140. We found that the marginal density matrices for subsystems of 1 and 2 qubits all completely mixed in these states.