Related papers: The $A_m^{(1)}$ Q-system
Spin-mechanics studies interactions between spin systems and mechanical vibrations in a nanomechanical resonator and explores their potential applications in quantum information processing. In this tutorial, we summarize various types of…
We introduce a scheme to perform quantum-information processing that is based on a hybrid spin-photon qubit encoding. The proposed qubits consist of spin-ensembles coherently coupled to microwave photons in coplanar waveguide resonators.…
We apply quantum control techniques to control a large spin chain by only acting on two qubits at one of its ends, thereby implementing universal quantum computation by a combination of quantum gates on the latter and swap operations across…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
We present the characterizations of symbol correspondences for mechanical systems that are symmetric by $SU(3)$, which we refer to as \emph{quark systems}. The quantum quark systems are the unitary irreducible representations of $SU(3)$ of…
We show that quantum optical systems preserving the total number of excitations admit a simple classification of possible resonant transitions (including effective), which can be classified by analizying the free Hamiltonian and the…
We develop the classical and quantum theory of a spinning particle moving in a Mobius strip. We first propose a Lagrangian for such a system and then we proceed to quantize the system via the constraint Hamiltonian system formalism. Our…
For an $n$-qubit system, a rational function on the space of mixed states which is invariant with respect to the action of the group of local symmetries may be viewed as a detailed measure of entanglement. We show that the field of all such…
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
Semiconductor quantum dots (QDs) offer a platform to explore the physics of quantum electronics including spins. Electron spins in QDs are considered good candidates for quantum bits in quantum information processing, and spin control and…
Quantum technologies offer ways to solve certain tasks more quickly, efficiently, and with greater precision than their classical counterparts. Yet substantial challenges remain in the construction of sufficiently error-free and scalable…
Beisert et al. have identified an integrable SU(2,2) quantum spin chain which gives the one-loop anomalous dimensions of certain operators in large N QCD. We derive a set of nonlinear integral equations (NLIEs) for this model, and compute…
The alternative to the standard formulation of the quark-parton model is proposed. Our relativistically covariant approach is based on the solution of the master equations relating the structure and distribution functions, which…
We present a general study of the large family of exact integrable quantum chains with multispin interactions introduced recently in \cite{AP2020}. The exact integrability follows from the algebraic properties of the energy density…
We introduce a discrete Q-function of N qubit system projected into the space of symmetric measurements as a tool for analyzing general properties of quantum systems in the macroscopic limit. For known states the projected Q-function helps…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
We analyse the $n$-dimensional superintegrable Kepler-Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. We identify the elements for each sub-structure…
Collective spins of large atomic samples trapped inside optical resonators can carry quantum information that can be processed in a way similar to quantum computation with continuous variables. It is shown here that by combining the…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
In this paper, we investigate a family of one-dimensional multi-component quantum many-body systems. The interaction is an exchange interaction based on the familiar family of integrable systems which includes the inverse square potential.…