Approximate quantum state reconstruction without a quantum channel

We investigate the optimal quantum state reconstruction from the cloud to many spatially separated users by a measure-broadcast-prepare scheme without the availability of the quantum channel. The quantum state equally distributed from the cloud to an arbitrary number of users is generated at each port by an ensemble of known quantum states with assistance from classical information of measurement outcomes by broadcasting. The obtained quantum state for each user is optimal in the sense that the fidelity universally achieves the upper bound. We present the universal quantum state distribution by providing physical realizable measurement bases in the cloud as well as the reconstruction method for each user. The quantum state reconstruction scheme works for arbitrary many identical pure input states in the general dimensional system.

Figure 1

Demonstration of quantum state reconstruction in the absence of the quantum channel. The input state $|{\psi }_{in}^{\otimes M}\rangle$ is stored and measured in the cloud. After the measurement, the corresponding measurement result is broadcast to the users. Having obtained the measurement results, each user can re-construct the initial state with the optimal fidelity.