Related papers: Uncertainty relations for time averaged weak value…
Using the quantum transition path time probability distribution we show that time averaging of weak values leads to unexpected results. We prove a weak value time energy uncertainty principle and time energy commutation relation. We also…
A quantum transition can be seen as a result of interference between various pathways(e.g. Feynman paths) which can be labelled by a variable $f$. An attempt to determine the value of f without destroying the coherence between the pathways…
Weak values have been shown to be helpful especially when considering them as the outcomes of weak measurements. In this paper we show that in principle, the real and imaginary parts of the weak value of any operator may be elucidated from…
We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging…
The Schr{\"o}dinger inequality is known to underlie the Kennard-Robertson inequality, which is the standard expression of quantum uncertainty for the product of variances of two observables $A$ and $B$, in the sense that the latter is…
Weak measurements have an increasing number of applications in contemporary quantum mechanics. They were originally described as a weak interaction that slightly entangled the translational degrees of freedom of a particle to its spin,…
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…
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…
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…
The arrival time probability distribution is defined by analogy with the classical mechanics. The difficulty of requirement to have the values of non-commuting operators is circumvented using the concept of weak measurements. The proposed…
A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that ``strange'' weak values for projection operators (such as values less than zero) always…
The theory of weak measurement, proposed by Aharonov and coworkers, has been applied by Steinberg to the long-discussed traversal time problem. The uncertainty and ambiguity that characterize this concept from the perspective of von Neumann…
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…
The time derivative of a physical property often gives rise to another meaningful property. Since weak values provide empirical insights that cannot be derived from expectation values, this paper explores what physical properties can be…
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…
The time evolution of the two-time conditional probability of the classical stochastic process is described in an analogous form of the quantum mechanical wave equations. By using it, we emulate the same strange behaviors as those of the…
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…
Constructing an ontology for quantum theory is challenging, in part due to unavoidable measurement back-action. The Aharonov-Albert-Vaidman weak measurement formalism provides a method to predict measurement results (weak values) in a…
Parks introduced a formulation of time dependent weak values in 2008, which is the formalism we use in this paper. In this paper we extend notions from time dependent weak values to show that Hamiltonians associated with weak value…
What does it take for real-deterministic c-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of real-deterministic c-valued variables out of the weak values…