相关论文: A Non-Convex Optimization Strategy for Computing C…

We present two ready-to-use numerical algorithms to evaluate convex-roof extensions of arbitrary pure-state entanglement monotones. Their implementation leaves the user merely with the task of calculating derivatives of the respective…

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 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…

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…

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…

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 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…

We investigate the evolution of entanglement in the Fenna-Matthew-Olson (FMO) complex based on simulations using the scaled hierarchy equation of motion (HEOM) approach. We examine the role of multipartite entanglement in the FMO complex by…

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 present a multipartite entanglement measure for $N$-qubit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for several important classes of $N$-qubit…

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 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…

Explicit expressions for the concurrence of all positive and trace-preserving ("stochastic") 1-qubit maps are presented. We construct the relevant convex roof patterns by a new method. We conclude that two component optimal decompositions…

I present an exact solution for the convex roof of the square root of the threetangle for all states within the Bloch sphere. The working horse that optimal decompositions contain as many states from the zero-polytope as possible which can…

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 provide a proof that entanglement of any density matrix which block diagonal in subspaces which are disjoint in terms of the Hilbert space of one of the two potentially entangled subsystems can simply be calculated as the weighted…

Entanglement forging based variational algorithms leverage the bi-partition of quantum systems for addressing ground state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous…

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…

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…