Related papers: Significant Conditions on the Two-electron Reduced…
We show that the Two-Higgs-Doublet Model (2HDM) constrained by the two-loop-order requirement of cancellation of quadratic divergences is consistent with the existing experimental constraints. The model allows to ameliorate the little…
The Pauli exclusion principle is fundamental to understanding electronic quantum systems. It namely constrains the expected occupancies $n_i$ of orbitals $\varphi_i$ according to $0 \leq n_i \leq 2$. In this work, we first refine the…
Numerical approximation of quantum states via convex combinations of states with positive partial transposes (bi-PPT state) in multipartite systems constitutes a fundamental challenge in quantum information science. We reformulate this…
In this work, we use an extension of the quantization condition, given in Ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The…
Density Matrix Renormalization Group (DMRG) algorithm has been extremely successful for computing the ground states of one-dimensional quantum many-body systems. For problems concerned with mixed quantum states, however, it is less…
We present classification of Q-conditional symmetries for the two-dimensional nonlinear wave equations and the reductions corresponding to these nonlinear symmetries. Classification of inequivalent reductions is discussed.
Unitary metaplectic representations of the group $SL_2(\mathbb{Z}_{2^n})$ are necessary to describe the evolution of $2^n$-dimensional quantum systems, such as systems involving $n$ qubits. It is shown that in order for the metaplectic…
We propose an efficient quantum state tomography method inspired by compressed sensing and threshold quantum state tomography that can drastically reduce the number of measurement settings to reconstruct the density matrix of an $N$-qudit…
We study the separability of bipartite quantum systems in arbitrary dimensions based on the Bloch representation of density matrices. We present two separability criteria for quantum states in terms of the matrices $T_{\alpha\beta}(\rho)$…
Reconstruction of density matrices is important in NMR quantum computing. An analysis is made for a 2-qubit system by using the error matrix method. It is found that the state tomography method determines well the parameters that are…
This paper is devoted to studies of non-negative, non-trivial (classical, punctured, or distributional) solutions to the higher order Hardy-H\'enon equations \[ (-\Delta)^m u = |x|^\sigma u^p \] in $\mathbf R^n$ with $p > 1$. We show that…
In this paper we consider two-loop two-, three- and four-point diagrams with elliptic structure in the case of two different masses $m$ and $M$. The latter diagrams generally arise within NRQCD matching procedures and are relevant for…
Within the framework of Relativistic Schroedinger Theory (an alternative form of quantum mechanics for relativistic many-particle systems) it is shown that a general N-particle system must occur in one of two forms: either as a ``positive''…
The $N$-representability problem is the problem of determining whether or not there exists $N$-particle states with some prescribed property. Here we report an affirmative solution to the fermion $N$-representability problem when both the…
In our recent work \cite{StojnicHopBnds10} we looked at a class of random optimization problems that arise in the forms typically known as Hopfield models. We viewed two scenarios which we termed as the positive Hopfield form and the…
We treat a system (a molecule or a solid) in which electrons are coupled linearly to any number and type of harmonic oscillators and which is further subject to external forces of arbitrary symmetry. With the treatment restricted to the…
Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for…
Just as any state of a single qubit or 2-level system can be obtained from any other state by a rotation operator parametrized by three real Euler angles, we show how any state of an n-qubit or 2^n-level system can be obtained from any…
We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be…
We revisit the relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q. Renyi's…