Related papers: Bound state eigenfunctions need to vanish faster t…
Quantum speed limit (QSL) is the lower bound on the time required for a state to evolve to a desired final state under a given Hamiltonian evolution. Three well-known QSLs exist Mandelstam-Tamm (MT), Margolus-Levitin (ML), and dual ML…
We show that if the Wigner function of a (possibly mixed) quantum state decays toward infinity faster than any polynomial in the phase space variables $x$ and $p$, then so do all of its derivatives, i.e., it is a Schwartz function on phase…
Recently it was shown in [New J. Phys. 8, 330 (2006)] that the three dimensional Heisenberg uncertainty principle might be signifficantly sharpened if the relevant quantum state describes the particle in a central potential. I extend that…
The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non--relativistic quantum mechanics. The long--range part of pair potentials is assumed to be pure Coulomb and no restriction…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
A definition of asymptotic flatness at spatial infinity in $d$ dimensions ($d\geq 4$) is given using the conformal completion approach. Then we discuss asymptotic symmetry and conserved quantities. As in four dimensions, in $d$ dimensions…
We study a quasi-Floquet state of a $\delta$-kicked rotor with absorbing boundaries focusing on the nature of the dynamical localization in open quantum systems. The localization lengths $\xi$ of lossy quasi-Floquet states located near the…
An entanglement measure for a bipartite quantum system is a state functional that vanishes on separable states and that does not increase under separable (local) operations. It is well-known that for pure states, essentially all…
We delineate the scope of research on the completeness of eigenstates in quantum mechanics. Based on the limit of the potential function at infinity, the proof of completeness is divided into eight cases, and theoretical proofs or numerical…
Let $\Omega\subset\mathbb{R}^{n}$ be a smooth bounded domain and $m\in C(\overline{\Omega})$ be a sign-changing weight function. For $1<p<\infty$, consider the eigenvalue problem $$ \left\{ \begin{array} [c]{ll} -\Delta_{p}u=\lambda…
Analyzing Heisenberg--Robertson (HR) and Schr\"{o}dinger uncertainty relations we found, that there can exist a large set of states of the quantum system under considerations, for which the lower bound of the product of the standard…
The auxiliary q-rules of quantum mechanics developed in other papers are applied to the problem of the location of material objects, both macroscopic and microscopic. All objects tend to expand in space due to the uncertainty in their…
In certain circumstances, the uncertainty, $\Delta S [\phi]$, of a quantum observable, $S$, can be bounded from below by a finite overall constant $\Delta S>0$, \emph{i.e.}, $\Delta S [\phi] \geq \Delta S$, for all physical states $\phi$.…
Integrable systems possess stable families of quasiparticles, which are composite objects (bound states) of elementary excitations. Motivated by recent quantum computer experiments, we investigate bound-state transport in the spin-$1/2$…
The speed limits on entanglement are defined as the maximal rate at which entanglement can be generated or degraded in a physical process. We derive the speed limits on entanglement, using the relative entropy of entanglement and…
Using Foster-Lyapunov techniques we establish new conditions on non-extinction, non-explosion, coming down from infinity and staying infinite, respectively, for the general continuous-state nonlinear branching processes introduced in Li et…
We provide an upper bound on the quasi-relative entropy in terms of the trace distance. The bound is derived for two cases: 1) any operator monotone decreasing function and full rank mixed qubit or classical states; 2) a large class of…
In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is…
Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and…