We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel-we here consider the so-called Werner channel. To characterize our results, we introduce a two-dimensional space defined by the aforementioned measures, in which the performance of the teleportation is represented as a point with the channel noise parameter. Through further analysis, we specify some regions drawn for different channel conditions, establishing the connection to the dissimilar contributions of the entanglement to the teleportation and the Bell inequality violation.
We compare quantum and classical machines designed for learning an N-bit Boolean function in order to address how a quantum system improves the machine learning behavior. The machines of the two types consist of the same number of operations and control parameters, but only the quantum machines utilize the quantum coherence naturally induced by unitary operators. We show that quantum superposition enables quantum learning that is faster than classical learning by expanding the approximate solution regions, i.e., the acceptable regions. This is also demonstrated by means of numerical simulations with a standard feedback model, namely random search, and a practical model, namely differential evolution.
We consider procedures to realize an approximate universal-NOT gate in terms of average fidelity and fidelity deviation. The average fidelity indicates the optimality of operation on average, while the fidelity deviation does the universality of operation. We show that one-qubit operations have a sharp trade-off relation between average fidelity and fidelity deviation, and two-qubit operations show a looser trade-off relation. The genuine universality holds for operations of more than two qubits, and those of even more qubits are beneficial to compensating imperfection of control. In addition, we take into account operational noises which contaminate quantum operation in realistic circumstances. We show that the operation recovers from the contamination by a feedback procedure of differential evolution. Our feedback scheme is also applicable to finding an optimal and universal NOT operation.
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