Related papers: Solving a Nonlinear Eigenvalue Equation in Quantum…
We investigate how equilibrium entanglement is manifested in the nonlinear response of an $N$-qubit system. We show that in the thermodynamic limit the irreducible part of the $n$th-order nonlinear susceptibility indicates that the…
In this paper, we investigate how to reduce the number of measurement configurations needed for sufficiently precise entanglement quantification. Instead of analytical formulae, we employ artificial neural networks to predict the amount of…
The state overlap, quantified via $\tr[\rho \sigma]$, is a metric widely used to assess the closeness between two quantum states $\rho$ and $\sigma$. Although global state overlap alone does not directly capture entanglement properties, we…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…
We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement…
Making use of the master equation and effective Hamiltonian approach, we investigate the steady state entanglement in a three-qubit $XX$ model. Both symmetric and nonsymmetric qubit-qubit couplings are considered. The system (the three…
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…
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…
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…
We develop a geometric approach to quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We use the entanglement measure proposed by us for $N$-qubit pure states (PRA \textbf{77}, 062334…
Entanglement properties of purified quantum states are of key interest for two reasons. First, in quantum information theory, minimally entangled purified states define the Entanglement of Purification as a fundamental measure for the…
Quantum information theory and quantum computing are theoritical basis of quantum computers. Thanks to entanglement, quantum mechanical systems are provisioned to realize many information processing problems faster than classical…
We present a graphical framework to represent entanglement in three-qubit states. The geometry associated with each entanglement class and type is analyzed, revealing distinct structural features. We explore the connection between this…
Quantum entanglement is a key resource in quantum computing and quantum information processing tasks. However, its quantification remains a major challenge since it cannot be directly extracted from physical observables. To address this…
Quantum metrology promises measurement precision beyond the classical limit by using suitably tailored quantum states and detection strategies. However, scaling up this advantage is experimentally challenging, due to the difficulty of…
Incorporating nonlinearity into quantum machine learning is essential for learning a complicated input-output mapping. We here propose quantum algorithms for nonlinear regression, where nonlinearity is introduced with feature maps when…
Entanglement asymmetry is a measure of symmetry breaking in quantum subsystems, inspired by quantum information theory, particularly suited to study out-of-equilibrium states. We study the entanglement asymmetry of a class of excited…
We present detailed analytical calculations for an 1D Ising ring of arbitrary number of spin-1/2 particles, in order to reveal entanglement properties of the stationary states. We show that the ground state and specific eigenstates of the…