Related papers: Uncertainty relations for general phase spaces
We discuss exchange scenario's thermodynamic uncertainty relations for the work done on a two-qubit entangled nonequilibrium steady state obtained by coupling the two qubits and putting each of them in weak contact with a thermal bath. In…
The change of a quantum state can generally only be fully monitored through simultaneous measurements of two non-commuting observables X and Y spanning a phase space. A measurement device that is coupled to the thermal environment provides…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
This paper presents the uncertainty related to position and momentum localization of a quantum state in terms of entropic uncertainty relations. We slightly improve the inequality given in [Phys. Rev. A 74, 052101 (2006)] and introduce a…
Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the…
The canonical Robertson-Schr\"{o}dinger uncertainty relation provides a loose bound for the product of variances of two non-commuting observables. Recently, several tight forward and reverse uncertainty relations have been proved which go…
Recent theoretical and experimental studies have given raise to new aspects in quantum measurements and error-disturbance uncertainty relations. After a brief review of these issues, we present an experimental test of the error-disturbance…
In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudo-spin observables for an arbitrary non-positive Hermitian…
Following to the Weil method we generalize the Heisenberg-Robertson uncertainty relation for arbitrary two operators. Consideration is made in spherical coordinates, where the distant variable is restricted from one side, . By this reason…
We propose a new generalised formalism for estimating the quantum phase uncertainty of pure and mixed continuous-variable quantum states and compare this with the phase uncertainty given by the quantum Fisher information. In order to…
We formulate uncertainty relations for arbitrary finite number of incompatible observables. Based on the sum of variances of the observables, both Heisenberg-type and Schr\"{o}dinger-type uncertainty relations are provided. These new lower…
The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…
The Heisenberg uncertainty relation, which links the uncertainties of the position and momentum of a particle, has an important footprint on the quantum behavior of a physical system. Analogous to this principle, we propose that…
A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main…
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…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…
The well-known Robertson-Schroedinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state-dependence. Therefore, Abbott \emph{et al.} introduced a general approach to derive tight…
Uncertainty and intrinsic measurement disturbance, two fundamental concepts in quantum measurement, have conventionally been viewed as distinct and studied separately. In this work, we establish a fundamental connection between them,…
Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…
We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the…