Related papers: Uncertainty relations for time averaged weak value…
We give a short review of known exact inequalities that can be interpreted as "energy-time" and "frequency-time" uncertainty relations. In particular we discuss a precise form of signals minimizing the physical frequency-time uncertainty…
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
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…
We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a…
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.…
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…
By use of window functions, time-frequency analysis tools like Short Time Fourier Transform overcome a shortcoming of the Fourier Transform and enable us to study the time- frequency characteristics of signals which exhibit transient os-…
We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral…
We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for…
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…
We discuss neutrino oscillations in the framework of the quantum field theory without introducing the concept of neutrino weak eigenstates. The external particles are described by wave packets and the different mass eigenstate neutrinos…
Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the…
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone--von Neumann theorem, the solutions of the dynamical equations, the Schr\"odinger equation (1) for states or the Heisenberg…
This paper gives various asymptotic formulae for the transition probability associated with discrete time quantum walks on the real line. The formulae depend heavily on the `normalized' position of the walk. When the position is in the…
The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective…
The Heisenberg-Robertson uncertainty relation quantitatively expresses the impossibility of jointly sharp preparation of incompatible observables. However it does not capture the concept of incompatible observables because it can be trivial…
We show that the weak value of any observable in pre- and post-selected states can be expressed as the sum of the average of the observable in the pre-selected state and an anomalous part. We argue that at a fundamental level the anomalous…
Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
Weak values of quantum observables are a powerful tool for investigating quantum phenomena. Some methods for measuring weak values in the laboratory require weak interactions and postselection, while others are deterministic, but require…