We investigate the optimal quantum state reconstruction from cloud to many spatially separated users by measure-broadcast-prepare scheme without the availability of quantum channel. The quantum state equally distributed from cloud to arbitrary number of users is generated at each port by ensemble of known quantum states with assistance of 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 general dimensional system.
We generalize the concept of a weak value of a quantum observable to cover arbitrary real positive operator measures. We show that the definition is operationally meaningful in the sense that it can be understood within the quantum theory of sequential measurements. We then present a detailed analysis of the recent experiment of Lundeen et al. concerning the reconstruction of the state of a photon using weak measurements. We compare their method with the reconstruction method through informationally complete phase space measurements and show that it lacks the generality of the phase space method. In particular, a completely unknown state can never be reconstructed using the method of weak measurements.
We propose a decoherence protected protocol for sending single photon quantum states through depolarizing channels. This protocol is implemented via an approximate quantum adder engineered through spontaneous parametric down converters, and shows higher success probability than distilled quantum teleportation protocols for distances below a threshold depending on the properties of the channel.
We demonstrate that there exists a universal, near-optimal recovery map---the transpose channel---for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we provide an alternative interpretation of the standard quantum error correction (QEC) conditions, and generalize them to a set of conditions for approximate QEC (AQEC) codes. This forms the basis of a simple algorithm for finding AQEC codes. Our analytical approach is a departure from earlier work relying on exhaustive numerical search for the optimal recovery map, with optimality defined based on entanglement fidelity. For the practically useful case of codes encoding a single qubit of information, our algorithm is particularly easy to implement.
We demonstrate quantum many-body state reconstruction from experimental data generated by a programmable quantum simulator, by means of a neural network model incorporating known experimental errors. Specifically, we extract restricted Boltzmann machine (RBM) wavefunctions from data produced by a Rydberg quantum simulator with eight and nine atoms in a single measurement basis, and apply a novel regularization technique to mitigate the effects of measurement errors in the training data. Reconstructions of modest complexity are able to capture one- and two-body observables not accessible to experimentalists, as well as more sophisticated observables such as the Renyi mutual information. Our results open the door to integration of machine learning architectures with intermediate-scale quantum hardware.
We study efficient quantum certification algorithms for quantum state set and unitary quantum channel. We present an algorithm that uses $O(varepsilon^{-4}ln |mathcal{P}|)$ copies of an unknown state to distinguish whether the unknown state is contained in or $varepsilon$-far from a finite set $mathcal{P}$ of known states with respect to the trace distance. This algorithm is more sample-efficient in some settings. Previous study showed that one can distinguish whether an unknown unitary $U$ is equal to or $varepsilon$-far from a known or unknown unitary $V$ in fixed dimension with $O(varepsilon^{-2})$ uses of the unitary, in which the Choi state is used and thus an ancilla system is needed. We give an algorithm that distinguishes the two cases with $O(varepsilon^{-1})$ uses of the unitary, using much fewer or no ancilla compared with previous results.