Related papers: Representability for Quantum Theory beyond Particl…
We compare approaches to evaluation of decoherence at low temperatures in two-state quantum systems weakly coupled to the environment. By analyzing an exactly solvable model, we demonstrate that a non-Markovian approximation scheme yields…
The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in…
Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of…
The momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In…
This paper derives and demonstrates a new, purely density-based ab initio approach for calculation of the energies and properties of many-electron systems. It is based upon the discovery of relationships that govern the "mechanics" of the…
We show that in classical mechanics, as well as in nonrelativistic quantum mechanics the equation of the relative motion for a two-body bound system at rest can be replaced by individual dynamical equations of the same kind as the first…
Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…
If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single…
Two important classes of quantum structures, namely orthomodular posets and orthomodular lattices, can be characterized in a classical context, using notions like partial information and points of view. Using the formalism of representation…
A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state…
What is the quantum system? Consider the wavefunction of the electron, what we call single particle wave-function and assume that it contains N wave packets. If we pass all the wave packets through an electric field, all are deflected, as…
Neural-network state representations of quantum many-body systems are attracting great attention and more rigorous quantitative analysis about their expressibility and complexity is warranted. Our analysis of the restricted Boltzmann…
We represent generalized density matrices of a $d$-complex dimensional quantum system as a subcone of a real pointed cone of revolution in $\mathbb{R}^{d^2}$, or indeed a Minkowskian cone in $\mathbb{E}^{1,d^2-1}$. Generalized pure states…
Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum…
This paper is concerned with the pure-state $N$-representability problem for systems under a magnetic field. Necessary and sufficient conditions are given for a spin-density $2 \times 2$ matrix $R$ to be representable by a Slater…