Related papers: Position Uncertainty in the Heisenberg Uncertainty…
We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…
Reports on experiments recently performed in Vienna [Erhard et al, Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg's error-disturbance relation. In…
While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's Uncertainty Principle," Heisenberg originally formulated his ideas in terms of a relationship between…
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…
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…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…
Our investigation of the results of the neutron spin experiment by Ehhart et al. demonstrates that their results cannot be understood in accordance with common sense. For example, their results obtained with different measurement errors are…
The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant, hbar/2, as demonstrated…
We point out that the Gaussian wave-packet formalism can serve as a concrete realization of the joint measurement of position and momentum, which is an essential element in understanding Heisenberg's original philosophy of the uncertainty…
The idea to base the uncertainty relation for photons on the electromagnetic energy distribution in space enabled us to derive a sharp inequality that expresses the uncertainty relation [Phys. Rev. Lett. {\bf 108}, 140401 (2012)]. An…
Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be sharply determined simultaneously. Standard-deviation and entropic formulations capture the spread of the probability distribution but say…
Heisenberg's intuition was that there should be a tradeoff between measuring a particle's position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two…
Heisenberg's uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: although…
We derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems. The relations are formulated in terms of a directly operational…
The uncertainty principle generally prohibits determination of certain pairs of quantum mechanical observables with arbitrary precision and forms the basis of indeterminacy in quantum mechanics. It was Heisenberg who used the famous…
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A…
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…
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by $N$ linear combinations of position and momentum observables. The state-independent bounds depend on their…
In the study of Heisenberg's error-disturbance relation, it is commonly believed that the non-unitary change of states hinders us from deducing the information encoded in original states about subsequently measured observable. However, we…
It is generally accepted that the disturbance interpretation cannot explain Heisenberg's uncertainty relation DxDp=h. In this paper a clear distinction will be made between the notions of state preparation and measurement, noting that the…