Related papers: Bounds to unitary evolution

The limited distinctness of physical systems is roughly expressed by uncertainty relations. Here we show distinctness is a finite resource we can exactly count to define basic physical quantities, limits to the resolution of space and time,…

We derive a sharp bound as the quantum speed limit (QSL) for the minimal evolution time of quantum open systems in the non-Markovian strong-coupling regime with initial mixed states by considering the effects of both renormalized…

Quantum speed limits set the maximal pace of state evolution. Two well-known limits exist for a unitary time-independent Hamiltonian: the Mandelstam-Tamm and Margolus-Levitin bounds. The former restricts the rate according to the state…

We give a new derivation of the minimal velocity estimates for unitary evolutions with some optimal bounds.

In a recent paper [J. Math. Phys. 47 082303 (2006)], Quantum Energy Inequalities were used to place simple geometrical bounds on the energy densities of quantum fields in Minkowskian spacetime regions. Here, we refine this analysis for…

The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…

At the lower edge of the energy continuum the birth of an isolated quantum bound state is studied as caused by an infinitesimally small change of the interaction. In our model a single, asymptotically free massive quantum particle is…

Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…

We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states,…

We look for upper bounds of the relative energy difference of two pure quantum states with a fixed fidelity between them or upper bounds of the fidelity for a fixed relative energy difference. The results depend on the concrete families of…

The speed limit provides an upper bound for the dynamical evolution time of a quantum system. Here, we introduce the notion of quantum acceleration limit for unitary time evolution of quantum systems under time-dependent Hamiltonian. We…

We consider methods for obtaining local lower bounds on characteristics of quantum (correspondingly, classical) systems, i.e. lower bounds valid in the trace norm $\epsilon$-neighborhood of a given state (correspondingly, probability…

We derive generalizations of the energy-time uncertainty relation for driven quantum systems. Using a geometric approach based on the Bures length between mixed quantum states, we obtain explicit expressions for the quantum speed limit…

We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…

A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…

Phase estimation, due to Kitaev [arXiv'95], is one of the most fundamental subroutines in quantum computing. In the basic scenario, one is given black-box access to a unitary $U$, and an eigenstate $\lvert \psi \rangle$ of $U$ with unknown…

Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…

Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…

Two thought experiments are analyzed, revealing that the quantum state of the universe does not contain definitive evidence of the wavefunction collapse. The first thought experiment shows that unitary quantum evolution alone can account…

An explicit expression for the finite-volume energy shift of shallow three-body bound states for non-identical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of…