Related papers: Improvement of Uncertainty Relations for Mixed Sta…
We prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable…
We suggest to use the photon homodyne detection experimental data for checking the Heisenberg and Schr\"{o}dinger-Robertson uncertainty relations, by means of measuring optical tomograms of the photon quantum states.
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…
The uncertainty relation lies at the heart of quantum theory and behaves as a non-classical constraint on the indeterminacies of incompatible observables in a system. In the literature, many experiments have been devoted to the test of the…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
A pair of uncertainty relations relevant for quantum states of multislit interferometry is derived, based on the mutually commuting "modular" position and momentum operators and their complementary counterparts, originally introduced by…
In the history of quantum mechanics, various types of uncertainty relationships have been introduced to accommodate different operational meanings of Heisenberg uncertainty principle. We derive an optimized entropic uncertainty relation…
The canonical commutation relation is a cornerstone of quantum theory and underlies the Heisenberg uncertainty principle. Although uncertainty relations have been extensively tested, direct verifications of the underlying commutation…
It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…
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…
The well-known Robertson-Schr\"odinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit…
Uncertainty principle is one of the fundamental principles of quantum mechanics. Exploring such uncertainty relations in pre- and postselected (PPS) systems, where weak measurements on post-selected states have been used as a powerful tool…
The uncertainty relation formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable so that their product should be no less than…
In this paper, we compute uncertainty relations for non-commutative space and obtain a better lower bound than the standard one obtained from Heisenberg's uncertainty relation. We also derive the reverse uncertainty relation for product and…
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…
Uncertainty relation is one of the fundamental building blocks of quantum theory. Nevertheless, the traditional uncertainty relations do not fully capture the concept of incompatible observables. Here we present a stronger…
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…
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…
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…
Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum…