Related papers: Random and free positive maps with applications to…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
The selection of random subspaces plays a role in quantum information theory analogous to the role of random strings in classical information theory. Recent applications have included protocols achieving the quantum channel capacity and…
We construct a new class of positive indecomposable maps in the algebra of `d x d' complex matrices. These maps are characterized by the `weakest' positivity property and for this reason they are called atomic. This class provides a new…
We give an exact solution to the nonlinear optimization problem of approximating a Hermitian matrix by positive semi-definite matrices. Our algorithm was then used to judge whether a quantum state is entangled or not. We show that the exact…
Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely…
Based on the random matrix model, we can build statistical models using massive datasets across the power grid, and employ hypothesis testing for anomaly detection. First, the aim of this paper is to make the first attempt to apply the…
Given a PPT state $A=\sum_{i=1}^nA_i\otimes B_i \in M_k\otimes M_k$ and a vector $v\in\Im(A)\subset\mathbb{C}^k\otimes\mathbb{C}^k$ with tensor rank $k$, we provide an algorithm that checks whether the positive map $G_A:M_k\rightarrow M_k$,…
We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite…
Quantum entanglement is an important resource in many modern technologies, like quantum computation or quantum communication and information processing. Therefore, most interest is given to detect and quantify entangled states. Entanglement…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
We initiate the systematic study of resource theories of quantum channels, i.e. of the dynamics that quantum systems undergo by completely positive maps, in abstracto: Resources are in principle all maps from one quantum system to another,…
We introduce and study bipartite quantum states that are invariant under the local action of the cyclic sign group. Due to symmetry, these states are sparse and can be parameterized by a triple of vectors. Their important semi-definite…
Quantum entanglement is usually revealed via a well aligned, carefully chosen set of measurements. Yet, under a number of experimental conditions, for example in communication within multiparty quantum networks, noise along the channels or…
We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions $N$ and $M$. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish,…
We investigate two models of measuring devices designed to detect a non-relativistic free particle in a given region of spacetime. These models predict different probabilities for a free quantum particle to enter a spacetime region $R$ so…
This thesis focuses on the experimental creation and detection of a variety of quantum correlations using nuclear magnetic resonance hardware. Quantum entanglement, being most common and counter-intuitive, is one of the main type considered…
Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation and one-way…
We use open quantum system techniques to construct one-parameter semigroups of positive maps and apply them to study the entanglement properties of a class of 16-dimensional density matrices, representing states of a 4x4 bipartite system.
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…