We present an overview of the quantitative theory of single-copy entanglement in finite-
dimensional quantum systems. In particular we emphasize the point of view that different …

We study quantum circuits composed of a sequence of CNOT gates between distant qubits
of an-qubit system. We present some results concerning two important topics related to …

In this paper, we study the nature of entanglement in quantum Grover's and Shor's
algorithms. So far, the authors who have been interested in this problem have approached …

We expand on an idea of Vinberg to take a tensor space and the natural Lie algebra that
acts on it and embed their direct sum into an auxiliary algebra. Viewed as endomorphisms of …

Spin states of maximal projection along some direction in space are called (spin) coherent,
and are, in many respects, the'most classical'available. For any spin s, the spin coherent …

Given tensors T and T 0 of order k and k0 respectively, the tensor product T n T 0 is a tensor
of order k þ k0. It was recently shown that the tensor rank can be strictly submultiplicative …

The decomposition locus of a tensor is the set of rank-one tensors appearing in a minimal
tensor-rank decomposition of the tensor. For tensors lying on the tangential variety of any …

We propose a new approach to the geometry of the four-qubit entanglement classes
depending on parameters. More precisely, we use invariant theory and algebraic geometry …

In this paper we investigate the entanglement nature of quantum states generated by
Grover's search algorithm by means of algebraic geometry. More precisely we establish a …

To characterize entanglement of tripartite C d⊗ C d⊗ C d systems, we employ algebraic-
geometric tools that are invariants under stochastic local operation and classical …