Related papers: Lower Bounds on Coherent State Rank
There are a number of approximation algorithms for NP-hard versions of low rank approximation, such as finding a rank-$k$ matrix $B$ minimizing the sum of absolute values of differences to a given $n$-by-$n$ matrix $A$,…
Consensus-based optimization (CBO) is a versatile multi-particle optimization method for performing nonconvex and nonsmooth global optimizations in high dimensions. Proofs of global convergence in probability have been achieved for a broad…
We investigate questions related to the set $\mathcal{SEP}_d$ consisting of the linear maps $\rho$ acting on $\mathbb{C}^d\otimes \mathbb{C}^d$ that can be written as a convex combination of rank one matrices of the form $xx^*\otimes yy^*$.…
The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work we show the existence of an infinite number of such states for some…
We obtain, using the Birman-Schwinger method, a series of necessary conditions for the existence of at least one bound state applicable to arbitrary central potentials in the context of nonrelativistic quantum mechanics. These conditions…
We have developed a formalism that includes both quasibound states with real energies and quantum resonances within the same theoretical framework, and that admits a clean and unambiguous distinction between these states and the states of…
The interdependence of position and momentum, as highlighted by the Heisenberg uncertainty principle, is a cornerstone of quantum physics. Yet, position-momentum correlations have received little systematic attention. Motivated by recent…
We extend the framework of quantum pushforward designs to the approximate setting, where averaging is achieved only up to finite precision. Using Schatten $p$-norms and Lipschitz continuity arguments, we derive bounds on the approximation…
The construction of physically relevant low dimensional state models, and the design of appropriate measurements are key issues in tackling quantum state tomography for large dimensional systems. We consider the statistical problem of…
We discuss parameter dependent polynomial ordinary differential equations that model chemical reaction networks. By classical quasi-steady state (QSS) reduction we understand the following familiar heuristic: Set the rate of change for…
A general scenario for an $N$-sequential conclusive state discrimination introduced recently in Loubenets and Namkung [arXiv:2102.04747] can provide a multipartite quantum communication realizable in the presence of a noise. In the present…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight…
Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the…
The problem of computing a representation for a real polynomial as a sum of minimum number of squares of polynomials can be casted as finding a symmetric positive semidefinite real matrix (Gram matrix) of minimum rank subject to linear…
The Morse potential quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to…
We discuss the estimation of the distance of a given mixed many-body quantum state to the set of fully separable states, applied to the concrete scenario of collective spin states. Concretely, we discuss lower bounds to distances from the…
We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value $r$. In this scenario two notions of informationally complete measurements emerge:…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density…