Related papers: Quantum integrability of quadratic Killing tensors
We give a sufficient condition for quantising integrable systems.
In a previous work we have introduced the concept of quasi-integrable quantum system. In the present one we determine sufficient conditions under which, given an integrable classical system, it is possible to construct a quasi-integrable…
We propose in this work a concept of integrability for quantum systems, which corresponds to the concept of noncommutative integrability for systems in classical mechanics. We determine a condition for quantum operators which can be a…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…
We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…
We use an isomorphism between the space of valence two Killing tensors on an n-dimensional constant sectional curvature manifold and the irreducible GL(n+1)-representation space of algebraic curvature tensors in order to translate the…
The efficient certification of classically intractable quantum devices has been a central research question for some time. However, to observe a "quantum advantage", it is believed that one does not need to build a large scale universal…
The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the reduction procedure. The reduced coherent states for the…
Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…
Quantum metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…
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…
Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers. This naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to…
Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction…
We present the classification of quadratically integrable systems of the cylindrical type with magnetic fields in quantum mechanics. Following the direct method used in classical mechanics by [F Fournier et al 2020 J. Phys. A: Math. Theor.…
Killing tensor fields have been thought of as describing hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Many problems in classical mechanics can be…
In this paper we discuss maximal superintegrability of both classical and quantum St\"ackel systems. We prove a sufficient condition for a flat or constant curvature St\"ackel system to be maximally superintegrable. Further, we prove a…
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar…