相关论文: Quantum state transformations and the Schubert cal…
We study fluctuations of the matrix coefficients for the quantized cat map. We consider the sum of matrix coefficients corresponding to eigenstates whose eigenphases lie in a randomly chosen window, assuming that the length of the window…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
The Schur-Horn theorem is a well-known result that characterizes the relationship between the diagonal elements and eigenvalues of a symmetric (Hermitian) matrix. In this paper, we extend this theorem by exploring the eigenvalue…
In this study the determinant of the average quadratic error matrix is used as the measure of state estimation efficiency. This quantity is easily computable in some cases, so it gives us a reasonable tool to find optimal measurement setup…
We propose a quantum algorithm for finding eigenvalues of non-unitary matrices. We show how to construct, through interactions in a quantum system and projective measurements, a non-Hermitian or non-unitary matrix and obtain its eigenvalues…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
We investigate entanglement properties at quantum phase transitions of an integrable extended Hubbard model in the momentum space representation. Two elementary subsystems are recognized: the single mode of an electron, and the pair of…
We continue here to study simple matrix models of quantum mechanical Hamiltonians. The eigenvalues and eigenfunctions were associated energy levels and wave functions. Whereas previously we considered the weak coupling limits of our models,…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
Recently, the quaternionic quantum walk was formulated by the first author as a generalization of discrete-time quantum walks. We treat the right eigenvalue problem of quaternionic matrices to analysis the spectra of its transition matrix.…
This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
Entropic inequalities related to the quantum mutual information for bipartite system and tomographic mutual information is studied for Werner state of two qubits. Quantum correlations corresponding to entanglement properties of the qubits…
Quantum computers have the potential to transform the ways in which we tackle some important problems. The efforts by companies like Google, IBM and Microsoft to construct quantum computers have been making headlines for years. Equally…
Quantum information is about the entanglement of states. To this starting point we add parameters whereby a single state becomes a non-vanishing section of a bundle. We consider through examples the possible entanglement patterns of…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
It is obvious that we still have not any unified framework covering a zoo of interpretations of Quantum Mechanics, as well as satisfactory understanding of main ingredients of a phenomena like entanglement. The starting point is an idea to…
Networks based on entangled quantum systems enable interesting applications in quantum information processing and the understanding of the resulting quantum correlations is essential for advancing the technology. We show that the theory of…
We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the…
It is assumed that the quantum state that may describe a macroscopic system at a given instant of time is one of the eigenstates of the reduced density matrix calculated from the wave function of the system plus its environment. This…