entanglement

Semidefinite hierarchies for diagonal unitary invariant bipartite quantum states

  • Jonas Britz
  • Monique Laurent
    • Categories Semi-definite Programming Tags , , , , , , , , ,

    We investigate questions about the cone \(\mathrm{SEP}_n\) of separable bipartite states, consisting of the Hermitian matrices acting on \(\mathbb{C}^n\otimes\mathbb{C}^n\) that can be written as conic combinations of rank one matrices of the form \(xx^*\otimes yy^*\) with \(x,y\in\mathbb{C}^n\). Bipartite states that are not separable are said to be entangled. Detecting quantum entanglement is a fundamental task … Read more

    Bounding the separable rank via polynomial optimization

  • Sander Gribling
  • Monique Laurent
  • Andries Steenkamp
    • Categories Convex and Nonsmooth Optimization, Global Optimization Tags , , , , ,

    We investigate questions related to the set $\mathcal{SEP}_d$ consisting of the linear maps $\rho$ acting on $\mathbb{C}^d\otimes \mathbb{C}^d$ that can be written as a convex combination of rank one matrices of the form $xx^*\otimes yy^*$. Such maps are known in quantum information theory as the separable bipartite states, while nonseparable states are called entangled. In … Read more

    Numerical estimation of the relative entropy of entanglement

  • Shmuel Friedland
  • Gilad Gour
  • Yuriy Zinchenko
    • Categories Applications - Science and Engineering, Basic Sciences Applications Tags , , ,

    We propose a practical algorithm for the calculation of the relative entropy of entanglement(REE), defined as the minimum relative entropy between a state and the set of states with positive partial transpose. Our algorithm is based on a practical semi-definite cutting plane approach. In low dimensions the implementation of the algorithm in MATLAB provides an … Read more