Related papers: Procedures for Converting among Lindblad, Kraus an…
For a binary system specified by the density operators r0 and r1 and by the prior probabilities q0 and q1, Helstrom's theory permits the evaluation of the optimal measurement operators and of the corresponding maximum correct detection…
Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the…
We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
We present broadly applicable tools for determining the behavior of eigenvalues and eigenvectors under the addition of self-adjoint operators and under the multiplication of unitaries, in finite-dimensional Hilbert spaces. The new tools…
On account of the Abel-Galois no-go theorem for the algebraic solution to quintic and higher order polynomials, the eigenvalue problem and the associated characteristic equation for a general noise dynamics in dimension $d$ via the…
This paper deals with the optimization of trial states for the computation of dominant eigenvalues of operators and very large matrices. In addition to preliminary results for the energy spectrum of van der Waals clusters, we review results…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
We perform quantum process tomography (QPT) for both discrete- and continuous-variable quantum systems by learning a process representation using Kraus operators. The Kraus form ensures that the reconstructed process is completely positive.…
The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semi-classical…
Determining the state of a system and measuring properties of its evolution are two of the most important tasks a physicist faces. For the first purpose one can use tomography, a method that after subjecting the system to a number of…
The global behavior of dynamical systems can be studied by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with the system. Two important operators which are frequently used to gain insight into the…
While quantum master equations (QMEs) are the primary workhorse in quantum information science, quantum optics, spectroscopy, and quantum thermodynamics, bringing an arbitrary $N$-level QME into Lindbladian form and verifying complete…
Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…
The kinetic energy of a multi-particle system is described by the one-particle kinetic energy density matrix $\tau(x, y)$. Alongside the one-particle density matrix $\gamma(x, y)$, it is one of the key objects in the quantum-mechanical…
Due to the significant progress made in the implementation of quantum hardware, efficient methods and tools to design corresponding algorithms become increasingly important. Many of these tools rely on functional representations of certain…
The formalism of subdynamics is extended to the functional approach of quantum systems, and used for the Friedrichs model, in which diagonal singularities in states and observables are included. We compute in this approach the generalized…
Markovian dynamics of open quantum systems are described by the L-GKS equation, known also as the Lindblad equation. The equation is expressed by means of left and right matrix multiplications. This formulation hampers numerical…
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a quantum process. QPT is a major quantum information processing tool, since it especially allows one to experimentally characterize the actual behavior of…
In the broad range of studies related to quantum graphs, quantum graph spectra appear as a topic of special interest. They are important in the context of diffusion type problems posed on metric graphs. Theoretical findings suggest that…