Related papers: Error-disturbance relations in mixed states
In this work, we derive Robertson-Heisenberg like uncertainty relation for two incompatible observables in a pre- and post-selected (PPS) system. The newly defined standard deviation and the uncertainty relation in the PPS system have…
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,…
The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
Being one of the centroidal concepts in quantum theory, the fundamental constraint imposed by Heisenberg uncertainty relations has always been a subject of immense attention and challenging in the context of joint measurements of general…
Defining and measuring the error of a measurement is one of the most fundamental activities in experimental science. However, quantum theory shows a peculiar difficulty in extending the classical notion of root-mean-square (rms) error to…
In this paper the uncertainty principle is found via characteristics of continuous and nowhere differentiable functions. We prove that any physical system that has a continuous and nowhere differentiable position function is subject to an…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
Universally valid uncertainty relations are proven in a model independent formulation for inherent and unavoidable extra noises in arbitrary joint measurements on single systems, from which Heisenber's original uncertainty relation is…
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for…
A universally valid uncertainty relation proposed by Ozawa is re-investigated under for the generalized equation of motion with some boundary condition. Necessary conditions for violation (lessening) of the Heisenberg-type uncertainty…
Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…
In this comment on the work of F. Buscemi, M.J.W. Hall, M. Ozawa and M.M. Wilde [PRL 112, 050401, 2014, arXiv:1310.6603], we point out a misrepresentation of measures of error and disturbance introduced in our recent work [PRL 111, 160405,…
The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We…
The uncertainty relations, pioneered by Werner Heisenberg nearly 90 years ago, set a fundamental limitation on the joint measurability of complementary observables. This limitation has long been a subject of debate, which has been reignited…
Heisenberg introduced his famous uncertainty relations in a seminal 1927 paper entitled "The Physical Content of Quantum Kinematics and Mechanics". He motivated his arguments with a gedanken experiment, a gamma ray microscope to measure the…
Heisenberg formulated a noise-disturbance principle stating that there is a tradeoff between noise and disturbance when a measurement of position and a measurement of momentum are performed sequentially, and another principle imposing a…
Position measurements are examined under the assumption that object position x_t and probe position X_t just after the measurement are expressed by a linear combination of positions x_0 and X_0 just before the measurement. The Heisenberg…
Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…