Related papers: Convex Hulls of Varieties and Entanglement Measure…

Quantifying entanglement in composite systems is a fundamental challenge, yet exact results are only available in few special cases. This is because hard optimization problems are routinely involved, such as finding the convex decomposition…

We show a powerful method to compute entanglement measures based on convex roof constructions. In particular, our method is applicable to measures that, for pure states, can be written as low order polynomials of operator expectation…

Convex roof extensions are widely used to create entanglement measures in quantum information theory. The aim of the article is to present some tools which could be helpful for their treatment. Sections 2 and 3 introduce into the subject.…

We provide a general construction of convex roof measures of coherence. This construction is based on arbitrary coherence measures of pure states in the framework of resource theory of coherence. Convex roof measures of coherence bound from…

We describe an algorithm for computing the convex hull of a finite collection of points in the affine building of SL_d(K), for K a field with discrete valuation. These convex hulls describe the relations among a finite collection of…

An algorithm is proposed that serves to handle full rank density matrices, when coming from a lower rank method to compute the convex-roof. This is in order to calculate an upper bound for any polynomial SL invariant multipartite…

We consider two properties of the set of quantum states as a convex topological space and some their implications concerning the notions of a convex hull and of a convex roof of a function defined on a subset of quantum states. By using…

To quantify the entanglement is one of the most important topics in quantum entanglement theory. In [arXiv: 2006.12408], the authors proposed a method to build a measure from the orginal domain to a larger one. Here we apply that method to…

We show that the quantification of entanglement of any rank-2 state with any polynomial entanglement measure can be recast as a geometric problem on the corresponding Bloch sphere. This approach provides novel insight into the properties of…

We develop a numerical methodology for the computation of entanglement measures for mixed quantum states. Using the well-known Schr\"odinger-HJW theorem, the computation of convex roof entanglement measures is reframed as a search for…

A relevant problem regarding entanglement measures is the following: Given an arbitrary mixed state, how does a measure for multipartite entanglement change if general local operations are applied to the state? This question is nontrivial…

Characterization of the multipartite mixed state entanglement is still a challenging problem. Since due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement…

Gudder, in a recent paper, defined a candidate entanglement measure which is called the entanglement number. The entanglement number is first defined on pure states and then it extends to mixed states by the convex roof construction. In…

Quantum entanglement is a unique correlation phenomenon in quantum mechanics, and the measurement of quantum entanglement plays an important role in quantum computing and quantum communication. Many mainstream entanglement criteria and…

The primary goal in the study of entanglement as a resource theory is to find conditions that determine when one quantum state can or cannot be transformed into another via local operations and classical communication. This is typically…

We investigate the lower bound obtained from experimental data of a quantum state $\rho$, as proposed independently by G\"uhne et al. and Eisert et al. for mixed states of three qubits. The measure we consider is the convex-roof extended…

We extend the concept of the negativity, a good measure of entanglement for bipartite pure states, to mixed states by means of the convex-roof extension. We show that the measure does not increase under local quantum operations and…

In this manuscript, we present a coherence measure based on the quantum optimal transport cost in terms of convex roof extended method. We also obtain the analytical solutions of the quantifier for pure states. At last, we propose an…

New measures of multipartite entanglement are constructed based on two definitions of multipartite information and different methods of optimizing over extensions of the states. One is a generalization of the squashed entanglement where one…

I calculate the mixed threetangle $\tau_3[\rho]$ for the reduced density matrices of the four-qubit representant states found in Phys. Rev. A {\bf 65}, 052112 (2002). In most of the cases, the convex roof is obtained, except for one class,…