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تسجيل مستخدم جديدQuantum error correction and entanglement spectrum in tensor networks
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A sort of planar tensor networks with tensor constraints is investigated as a model for holography. We study the greedy algorithm generated by tensor constraints and propose the notion of critical protection (CP) against the action of greedy algorithm. For given tensor constraints, a CP tensor chain can be defined. We further find that the ability of quantum error correction (QEC), the non-flatness of entanglement spectrum (ES) and the correlation function can be quantitatively evaluated by the geometric structure of CP tensor chain. Four classes of tensor networks with different properties of entanglement is discussed. Thanks to tensor constraints and CP, the correlation function is reduced into a bracket of Matrix Production State and the result agrees with the one in conformal field theory.
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This paper accompanies with our recent work on quantum error correction (QEC) and entanglement spectrum (ES) in tensor networks (arXiv:1806.05007). We propose a general framework for planar tensor network state with tensor constraints as a model for
$AdS_3/CFT_2$ correspondence, which could be viewed as a generalization of hyperinvariant tensor networks recently proposed by Evenbly. We elaborate our proposal on tensor chains in a tensor network by tiling $H^2$ space and provide a diagrammatical description for general multi-tensor constraints in terms of tensor chains, which forms a generalized greedy algorithm. The behavior of tensor chains under the action of greedy algorithm is investigated in detail. In particular, for a given set of tensor constraints, a critically protected (CP) tensor chain can be figured out and evaluated by its average reduced interior angle. We classify tensor networks according to their ability of QEC and the flatness of ES. The corresponding geometric description of critical protection over the hyperbolic space is also given.
Recent progress in studies of holographic dualities, originally motivated by insights from string theory, has led to a confluence with concepts and techniques from quantum information theory. A particularly successful approach has involved capturing
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We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context of quantum
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