Suppose that three kinds of quantum systems are given in some unknown states $\ket f^{\otimes N}$, $\ket{g_1}^{\otimes K}$, and $\ket{g_2}^{\otimes K}$, and we want to decide which \textit{template} state $\ket{g_1}$ or $\ket{g_2}$, each representing the feature of the pattern class ${\cal C}_1$ or ${\cal C}_2$, respectively, is closest to the input \textit{feature} state $\ket f$. This is an extension of the pattern matching problem into the quantum domain. Assuming that these states are known a priori to belong to a certain parametric family of pure qubit systems, we derive two kinds of matching strategies. The first is a semiclassical strategy which is obtained by the natural extension of conventional matching strategies and consists of a two-stage procedure: identification (estimation) of the unknown template states to design the classifier (\textit{learning} process to train the classifier) and classification of the input system into the appropriate pattern class based on the estimated results. The other is a fully quantum strategy without any intermediate measurement which we might call as the {\it universal quantum matching machine}. We present the Bayes optimal solutions for both strategies in the case of K=1, showing that there certainly exists a fully quantum matching procedure which is strictly superior to the straightforward semiclassical extension of the conventional matching strategy based on the learning process.
Universal quantum frequency comb measurements by spectral mode-matching
University of Lille（里尔大学）；CNRS（法国国家科学研究中心）；Université Côte d’Azur（蔚蓝海岸大学）；Institut de Physique de Nice (INPHYNI)（尼斯物理研究所）；Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所，意大利国家研究委员会）；QTI S.r.l.（QTI有限公司）；Department of Physics, University of Virginia（弗吉尼亚大学物理系）
Teleportation scheme implementing contextually the Universal Optimal Quantum Cloning Machine and the Universal Not Gate. Complete experimental realization
