Compensating the cross talk in continuous-variable multimode photonic entanglement distribution

We consider the effect of a liner cross talk in the task of entanglement distribution for the two-mode Gaussian states. We consider multimode idler and multimode signal beams emitted by a source and shared between two parties... [ view full abstract ]

We consider the effect of a liner cross talk in the task of entanglement distribution for the two-mode Gaussian states. We consider multimode idler and multimode signal beams emitted by a source and shared between two parties (Alice and Bob). Each local party is performing homodyne measurement on each of the modes of their respective beams after the modes travel through attenuating and noisy quantum channel. We assume that initially the twin-beam states are independent, but the linear cross talk occurs on the side of the source prior to the channel, as shown in the attached scheme. We show that the cross talk degrades the shared entanglement and that the initial amount of entanglement should be optimized in the presence of cross talk. We consider use of the local operations (phase flip and linear coupling, see the attached scheme) prior to detection on the remote side (Bob) in order to compensate the cross talk. Effectiveness of this method depends on the channel transmittance: if it is the same for both of the modes, the method allows to fully compensate the cross talk, but if the transmittance values are different, the cross talk can be only partially compensated. We compare these results to the results of applying conditional measurement on one mode to increase entanglement in another mode and also with the combination of both methods (applying first the reverse coupling and then either heterodyne or homodyne conditional measurement). The figure that illustrates these results is attached to the abstract. The best possible result for a single pair of modes is achieved by combining reverse coupling with homodyne measurement. But the difference in the effectiveness of two methods, the one that adds conditional measurement prior to the reverse coupling and the one that uses only the reverse coupling, is significant only in cases where initial entanglement is strong. Generally the cross talk compensation scheme that uses phase flipping and reverse coupling, which is equal to the cross-talk coupling, gives better results than conditional measurement, but the latter does not rely on the knowledge of the cross-talk coupling.