Solving the Fully Entangled Fraction on Near-Term Quantum Devices

The fully entangled fraction (FEF) is related to many quantum information processes. In this paper, we propose a variational quantum algorithm to solve the FEF of a given quantum state without density matrix on near-term quantum devices without using quantum state tomography. By constructing parameterized circuit, we convert the problem that solving the FEF into the all-zero measurement probability of the final state. The FEF of Isotropic states and Werner states are simulated numerically and verified to be in agreement with the analytical solution. And the numerical experiments prove the feasibility of our algorithm. Our results can be used to detect entanglement or distillability without knowing the density matrix of quantum states.