Related papers: Uncertainty Relation of Functions for Kernel-based…
The Kinetic Uncertainty Relation (KUR) bounds the signal-to-noise ratio of stochastic currents in terms of the number of transitions per unit time, known as the dynamical activity. This bound was derived in a classical context, and can be…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=exp[i phi] VU. Its most important application is to constrain how much a quantum state can be localised simultaneously in two…
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…
In quantum thermodynamics, entropy production is usually defined in terms of the quantum relative entropy between two states. We derive a lower bound for the quantum entropy production in terms of the mean and variance of quantum…
Thermodynamic Uncertainty Relations (TURs) set universal bounds linking current fluctuations to entropy production in nonequilibrium steady states. Their multidimensional generalization (MTUR) introduces matrix inequalities connecting…
Uncertainty relations for Hermitian operators have been confirmed through many experiments. However, previous experiments have only tested the special case of non-Hermitian operators, i.e., uncertainty relations for unitary operators. In…
The thermodynamics and kinetics of a nonequilibrium classical system fundamentally constrain the precision of an observable regarding the celebrated thermodynamic uncertainty relation (TUR) and the kinetic uncertainty relation (KUR). They…
Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an…
The Robertson's formulation of the uncertainty relation is the most widely accepted form of the Heisenberg uncertainty relation (HUR). It gets modified when we consider it for entangled particles. But this formulation does not consider the…
In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schr\"odinger field theory, obtaining the Schr\"odinger…
The kinetic uncertainty relation (KUR) is a trade-off relation between the precision of an observable and the mean dynamical activity in a fixed time interval for a time-homogeneous and continuous-time Markov chain. In this letter, we…
The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in…
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better…
A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the…
The notion of a $U$-statistic for an $n$-tuple of identical quantum systems is introduced in analogy to the classical (commutative) case: given a selfadjoint `kernel' $K$ acting on $(\mathbb{C}^{d})^{\otimes r}$ with $r<n$, we define the…
We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum…
Some of the possible consequences of a generalized uncertainty principle (which emerges in the context of string theory and quantum gravity models as a consequence of fluctuations of the background metric) are analyzed considering the case…
Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…