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We use projection methods to construct (global) quantum states with prescribed reduced (marginal) states, and possibly with some special properties such as having specific eigenvalues, having specific rank and extreme von Neumann or Renyi entropy. Using convex analysis, optimization techniques on matrix manifolds, we obtain algorithms to solve the problem. Matlab programs are written based on these algorithms and numerical examples are illustrated. The numerical results reveal new patterns leading to new insights and research problems on the topic.
We consider the optimal approximation of certain quantum states of a harmonic oscillator with the superposition of a finite number of coherent states in phase space placed either on an ellipse or on a certain lattice. These scenarios are currently ex
The correlations of certain entangled quantum states can be fully reproduced via a local model. We discuss in detail the practical implementation of an algorithm for constructing local models for entangled states, recently introduced by Hirsch et al.
Constructing local hidden variable (LHV) models for entangled quantum states is challenging, as the model should reproduce quantum predictions for all possible local measurements. Here we present a simple method for building LHV models, applicable to
The decomposition of a matrix, as a product of factors with particular properties, is a much used tool in numerical analysis. Here we develop methods for decomposing a matrix $C$ into a product $X Y$, where the factors $X$ and $Y$ are required to min
Suppose we would like to approximate all local properties of a quantum many-body state to accuracy $delta$. In one dimension, we prove that an area law for the Renyi entanglement entropy $R_alpha$ with index $alpha<1$ implies a matrix product state r