Experimental Reconstruction of Entanglement Quasiprobabilities

We report on the first experimental reconstruction of an entanglement quasiprobability. In contrast to related techniques, the negativities in our distributions are a necessary and sufficient identifier of separability and entanglement and enable a full characterization of the quantum state. A reconstruction algorithm is developed, a polarization Bell state is prepared, and its entanglement is certified based on the reconstructed entanglement quasiprobabilities, with a high significance and without correcting for imperfections.

Figure 1

Ideal EQP of the target state $|\psi ⟩=(|H,V⟩-|V,H⟩)/\sqrt{2}$, which is given by ${\rho }_x={\rho }_y={\rho }_z=-1=-{\rho }_0$, cf. Eqs. (4) and (5). The EQP $P$ over Alice’s and Bob’s subsystems, which is determined through the eigenstates of Pauli operators, takes negative values to account for the presence of quantum entanglement, $P\ngeqq 0$.

Figure 2

Reconstructed EQP including error bars. Significant negativities, up to 13 standard deviations, directly certify the quantum correlation between Alice’s and Bob’s subsystem. A direct comparison with the ideal case is additionally provided in the SM [29].

Figure 3

Reconstruction for a separable target state $(|H⟩+|V⟩)/\sqrt{2}\otimes |H⟩$. Without requiring additional testing, it is directly evident that the produced state is separable, $P\ge 0$. The comparably large error bars are a result of the involved matrix inversion [Eq. (6)].