Related papers: Heisenberg's uncertainty principle for simultaneou…
It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a "weak-measurement", this disturbance can be reduced. One…
The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension…
The quantification of the "measurement uncertainty" aspect of Heisenberg's Uncertainty Principle---that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two…
We introduce and characterize two different measures which quantify the level of synchronization of interacting continuous variable quantum systems. The two measures allow to extend to the quantum domain the notions of complete and phase…
Joint measurements of non-commuting observables are characterized by unavoidable measurement uncertainties that can be described in terms of the error statistics for input states with well-defined values for the target observables. However,…
Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation.…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
It is well known that jointly measurable observables cannot lead to a violation of any Bell inequality - independent of the state and the measurements chosen at the other site. In this letter we prove the converse: every pair of…
Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields…
We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality…
Quantum mechanics predicts the joint probability distributions of the outcomes of simultaneous measurements of commuting observables, but the current formulation lacks the operational definition of simultaneous measurements. In order to…
Incompatible observables underlie pillars of quantum physics such as contextuality and entanglement. The Heisenberg uncertainty principle is a fundamental limitation on the measurement of the product of incompatible observables, a `joint'…
The quantum mechanical measurement problem is the difficulty of dealing with the indefiniteness of the pointer observable at the conclusion of a measurement process governed by unitary quantum dynamics. There has been hope to solve this…
In this study, we investigate quantum nonseparability between an observed system and a measuring apparatus, or multiple measuring apparatuses. We show that the physical meaning of the outcome of the measuring apparatus obtained by weak…
Quantum theory famously entails the existence of incompatible measurements; pairs of observables which cannot be simultaneously measured to arbitrary precision. Incompatibility is widely regarded to be a uniquely quantum phenomenon, linked…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
When you measure an observable, A, in Quantum Mechanics, the state of the system changes. This, in turn, affects the quantum-mechanical uncertainty in some non-commuting observable, B. The standard Uncertainty Relation puts a lower bound on…
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…