Algebraic Geometry of Matrix Product States
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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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2014
ISSN: 1815-0659
DOI: 10.3842/sigma.2014.095