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We discuss the diagonalization of a general Hamiltonian operator for a set of coupled harmonic oscillators and determine the conditions for the existence of bound states. We consider the particular cases of two and three oscillators studied…
We study disorder induced transition between quantum Hall states and insulator state in a {\it lattice} model. We find the positions of the extended states do not change as disorder strength is varied. As a consequence, there are direct…
The notion of ladder operators is introduced for systems with continuous spectra. We identify two different kinds of annihilation operators allowing the definition of coherent states as modified "eigenvectors" of these operators. Axioms of…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…
Quantum theory's Hilbert space apparatus in its finite-dimensional version is nearly reconstructed from four simple and quantum-mechanically motivated postulates for a quantum logic. The reconstruction process is not complete, since it…
A general procedure for constructing coherent states, which are eigenstates of annihilation operators, related to quantum mechanical potential problems, is presented. These coherent states, by construction are not potential specific and…
One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with…
In this paper we explore the possibility of fundamental tests for coherent state optical quantum computing gates [T. C. Ralph, et. al, Phys. Rev. A \textbf{68}, 042319 (2003)] using sophisticated but not unrealistic quantum states. The…
Some popular mechanisms for restricting the diffusion of waves include introducing disorder (to provoke Anderson localization) and engineering topologically non-trivial phases (to allow for topological edge states to form). However, other…
We introduce deterministic state-transformation protocols between many-body quantum states which can be implemented by low-depth Quantum Circuits (QC) followed by Local Operations and Classical Communication (LOCC). We show that this gives…
Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce…
By analytically continuing the eigenvalue problem of a system of two coupled harmonic oscillators in the complex coupling constant $g$, we have found a continuation structure through which the conventional ground state of the decoupled…
Semi-classical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semi-classical (coherent) state is…
Bosonic two-ring ladders constitute an important class of atomtronic circuits, where coherent current flows not only can offer a new insight into many-body physics, but also can play the role of actual degrees of freedom, and hence allow…
The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to…
Entanglement is one of the most fascinating features arising from quantum-mechanics and of great importance for quantum information science. Of particular interest are so-called hybrid-entangled states which have the intriguing property…
We investigate the existence and the properties of fully separable (fully factorized) ground states in quantum spin systems. Exploiting techniques of quantum information and entanglement theory we extend a recently introduced method and…
We demonstrate the existence of confined states in one- and two-dimensional (1D and 2D) systems of two linearly-coupled components, with the confining harmonic-oscillator (HO) potential acting upon one component, and an expulsive anti-HO…
We perform an exact diagonalization study of the topological order in topological flat band models through calculating entanglement entropy and spectra of low energy states. We identify multiple independent minimal entangled states, which…
Based on a recently introduced operator algebra for the description of a class of integrable quantum liquids we define the ground states for all canonical ensembles of these systems. We consider the particular case of the Hubbard chain in a…