Geometry of matrix product states: Metric, parallel transport, and curvature
نویسندگان
چکیده
منابع مشابه
Algebraic Geometry of Matrix Product States
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state’s amplitudes which hold if and only if the state is a translation invariant matrix product state or a limit of such states. For systems with few qubits, we give these equations explicitly, considering both periodic and open boundary condition...
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As separable states are a convex combination of product states, the geometry of the manifold of product states, Σ is studied. Prior results by Sanpera, Vidal and Tarrach are extended. Furthermore, it is proven that states in the set tangent to Σ at the maximally mixed state are separable; the set normal constains, among others, all maximally entangled states. A canonical decomposition is given....
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Given connection ∇ on a smooth vector bundle E → M , with connected base space M , the set of the parallel transport maps (associated to ∇) along closed loops based at x ∈M form a subgroup, Hol(∇), of the general linear group on the fibre Ex, GL(Ex). The group Hol(∇) is known as the holonomy group of the connection and it is independent of the base point x under conjugation of elements of the g...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2014
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.4862851