Related papers: The Quantum Eigenvalue Problem and Z-Eigenvalues o…
We study tensor products of infinite dimensional representations (not corepresentations) of the $\mathrm{SU}(2)$ quantum group. Eigenvectors of certain self-adjoint elements are obtained, and coupling coefficients between different…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…
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…
Traditionally, quantum entanglement has played a central role in foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can exhibit results at odds with classical behavior. These…
Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and…
The complex-valued quantum mechanics considers quantum motion on the complex plane instead of on the real axis, and studies the variations of a particle complex position, momentum and energy along a complex trajectory. On the basis of…
The phenomenon of quantum entanglement is fundamental to the implementation of quantum computation, and requires at least two qubits for its demonstration. However, both Deutsch algorithm and Grover's search algorithm for two bits do not…
We study the behavior of eigenvalues of matrix P_N + Q_N where P_N and Q_N are two N -by-N random orthogonal projections. We relate the joint eigenvalue distribution of this matrix to the Jacobi matrix ensemble and establish the universal…
The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as…
This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum…
In this work we discuss about the problem of an electrically charged particle placed on the symmetry axis of an electrically charged ring in a quantum viewpoint. This problem should be an expanded version of the usual quantum ring and…
This paper introduces the notion of tubular eigenvalues of third-order tensors with respect to T-products of tensors and analyzes their properties. A focus of the paper is to discuss relations between tubular eigenvalues and two alternative…
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…
The entangled quantum states play a key role in quantum information. The association of the quantum state vector with each individual physical system in an attributive way is a source of many false paradoxes and inconsistencies. The…
We consider the quantum optics of a single photon interacting with a system of two level atoms. This leads to the study of a nonlinear eigenproblem for a system of nonlocal partial differential equations. Two classes of solutions to these…
The eigenvalue hypothesis claims that any quantum Racah matrix for finite-dimensional representations of $U_q(sl_N)$ is uniquely determined by eigenvalues of the corresponding quantum $\cal{R}$-matrices. If this hypothesis turns out to be…
The pairwise entanglement of an arbitrary atomic pair randomly extracted from a laser-driven dense multiqubit sample in the presence of quantum dissipation due to spontaneous emission is considered. The dipole-dipole interaction between the…
We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the…
We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a…