Related papers: Bounding Polynomial Entanglement Measures for Mixe…
The structural study of entanglement in multipartite systems is hindered by the lack of necessary and sufficient operational criteria able to discriminate among the various entanglement properties of a given mixed state. Here, we pursue a…
We discuss the estimation of the distance of a given mixed many-body quantum state to the set of fully separable states, applied to the concrete scenario of collective spin states. Concretely, we discuss lower bounds to distances from the…
For a general tripartite system in some pure state, an observer possessing any two parts will see them in a mixed state. By the consequence of Hughston-Jozsa-Wootters theorem, each basis set of local measurement on the third part will…
Entanglement measures quantify nonclassical correlations present in a quantum system, but can be extremely difficult to calculate, even more so, when information on its state is limited. Here, we consider broad families of entanglement…
It is known that $\rho^{AB}$ as a bipartite reduced state of the 3-qubit GHZ state is separable, but part $A$ and part $B$ indeed ``share tripartite entanglement'' in the GHZ state. Namely, whether a state can ``share'' more entanglement is…
We use the linear programming algorithm introduced by Akulin et al. [V. M. Akulin, G. A. Kabatiansky, and A. Mandilara, Phys. Rev. A 92, 042322 (2015)] to perform best separable approximation on two-qutrit random density matrices. We…
We investigate optimal separable approximations (decompositions) of states rho of bipartite quantum systems A and B of arbitrary dimensions MxN following the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261 (1998)].…
Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and…
The advent of quantum computers promises exponential speed ups in the execution of various computational tasks. While their capabilities are hindered by quantum decoherence, they can be exactly simulated on classical hardware at the cost of…
In this work, we study the asymptotic behavior of protocols that localize entanglement in large multi-qubit states onto a subset of qubits by measuring the remaining qubits. We use the maximal average n-tangle that can be generated on a…
We study the tripartite entanglement for a class of mixed states defined by the mixture of GHZ and W states, \rho=p|GHZ><GHZ|+(1-p)|W><W|. Based on the Caratheodory theorem and the periodicity assumption, the possible optimal decomposition…
We propose that the entanglement of mixed states is characterised properly in terms of a probability density function $\mathcal{P}(\mathcal{E})$. There is a need for such a measure since the prevalent measures (such as \textit{concurrence}…
An important problem in quantum information theory is the quantification of entanglement in multipartite mixed quantum states. In this work, a connection between the geometric measure of entanglement and a distance measure of entanglement…
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…
The thesis includes the original results of our articles [30, 37, 40, 42, 51, 53, 75]. A method is developed to compute analytically entanglement measures of three-qubit pure states. Owing to it closed-form expressions are presented for the…
Understanding and classifying multipartite entanglement is fundamental to quantum information processing. This work focuses on absolutely maximally entangled (AME) states, a class of highly entangled states characterized by their maximal…
We present optimal measuring strategies for the estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general…
The combinatorial basis of entropy by Boltzmann can be written $H= {N}^{-1} \ln \mathbb{W}$, where $H$ is the dimensionless entropy of a system, per unit entity, $N$ is the number of entities and $\mathbb{W}$ is the number of ways in which…
In the standard geometric approach to a measure of entanglement of a pure state, $\sin^2\theta$ is used, where $\theta$ is the angle between the state to the closest separable state of products of normalized qubit states. We consider here a…