Related papers: Products of weak values: uncertainty relations, co…
In the conventional formulation, it is broadly accepted that simultaneous measurability and commutativity of observables are equivalent. However, several objections have been claimed that there are cases in which even nowhere commuting…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
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…
Weak values arise experimentally as conditioned averages of weak (noisy) observable measurements that minimally disturb an initial quantum state, and also as dynamical variables for reduced quantum state evolution even in the absence of…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
Weak values are average quantities,therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as…
In this note, we consider the implications of the Heisenberg uncertainty principle (HUP) when computing uncertainties that affect the main dynamical quantities, from the perspective of special relativity. Using the well-known formula for…
From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, $\mean{\Delta \hat{q}^2}\mean{\Delta…
Recently, a new interesting concept of reverse uncertainty relation is introduced. Different from the normal uncertainty relation, the reverse one indicates that one cannot only prepare quantum states with joint small uncertainty, but also…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
It is argued that a weak value of an observable is a robust property of a single pre- and post-selected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affects other systems…
Analyzing Heisenberg--Robertson (HR) and Schr\"{o}dinger uncertainty relations we found, that there can exist a large set of states of the quantum system under considerations, for which the lower bound of the product of the standard…
Weak value is increasingly acknowledged as an important research tool for probing quantum pre- and post-selected ensembles, where some extraordinary phenomena occur. We generalize this concept to the broader notion of "weak potential" which…
In the weak measurement formalism of Y. Aharonov et al. the so-called weak value A_w of any observable A is generally a complex number. We derive a physical interpretation of its value in terms of the shift in the measurement pointer's mean…
In the Copenhagen interpretation the Heisenberg uncertainty relation is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint…
The formalism of weak measurement in quantum mechanics has revealed profound connections between measurement theory, quantum foundations, and signal processing. In this paper, we develop a pointer-free derivation of superoscillations,…
Weak measurements introduced by Aharonov, Albert and Vaidman (AAV) can provide informations about the system with minimal back action. Weak values of product observables (commuting) or higher moments of an observable are informationally…
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'…
Uncertainty relations are among the unique fingerprints of quantum physics, being direct expression of non-commutativity and complementarity. Entropic uncertainty relations arise in quantum information theory as the most natural expression…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…