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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…
We describe libhmm, a C++20 library for Hidden Markov Model parameter estimation, sequence decoding, and model selection. libhmm addresses two gaps in existing software: the absence of a well-maintained, zero-dependency C++ HMM library…
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…
In this paper we study the problem of calculating the convex hull of certain affine algebraic varieties. As we explain, the motivation for considering this problem is that certain pure-state measures of quantum entanglement, which we call…
Multipartite entanglement underpins quantum technologies but its study is limited by the lack of universal measures, unified frameworks, and the intractability of convex-roof extensions. We establish an axiomatic framework and introduce the…
We explore the dual problem of the convex roof construction by identifying it as a linear semi-infinite programming (LSIP) problem. Using the LSIP theory, we show the absence of a duality gap between primal and dual problems, even if the…
Experimentally quantifying entanglement and coherence are extremely important for quantum resource theory. However, because the quantum state tomography requires exponentially growing measurements with the number of qubits, it is hard to…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
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.…
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…
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…
For paving the way to novel applications in quantum simulation, computation, and technology, increasingly large quantum systems have to be steered with high precision. It is a typical task amenable to numerical optimal control to turn the…
Multiparameter quantum metrology is essential for a wide range of practical applications. However, simultaneously achieving the ultimate precision for all parameters, as prescribed by the quantum Cram\'er-Rao bound (QCRB), remains a…
Most particle induced X-ray emission (PIXE) data analysis codes are not focused on handling multilayered samples. We have developed an open-source library called "LibCPIXE", for PIXE data analysis. It is written in standard C and implements…
Mixed-integer programming (MIP) is a well-established framework for computer-aided molecular design (CAMD). By precisely encoding the molecular space and score functions, e.g., a graph neural network, the molecular design problem is…
Mixed state entanglement measures can act as a versatile probes of many-body systems. However, they are generally hard to compute, often relying on tricky optimizations. One measure that is straightforward to compute is the logarithmic…
We establish the profound equivalence between measures of genuine multipartite entanglement(GME) and their corresponding coherence measures. Initially we construct two distinct classes of measures for genuine multipartite entanglement…
There exists, in general, a convex set of quantum state estimators that maximize the likelihood for informationally incomplete data. We propose an estimation scheme, catered to measurement data of this kind, to search for the exact…
A C++ library, named ZKCM, has been developed for the purpose of multiprecision matrix calculations, which is based on the GNU MP and MPFR libraries. It is especially convenient for writing programs involving tensor-product operations,…
Peak estimation of hybrid systems aims to upper bound extreme values of a state function along trajectories, where this state function could be different in each subsystem. This finite-dimensional but nonconvex problem may be lifted into an…