Related papers: Uncertainty relations for time averaged weak value…
For nonequilibrium steady states, we identify observables whose fluctuations satisfy a general symmetry and for which a new reciprocity relation can be shown. Unlike the situation in recently discussed fluctuation theorems, these…
Weak measurements with imaginary weak values are reexamined in light of recent experimental results. The shift of the meter, due to the imaginary part of the weak value, is derived via the probability of postselection, which allows…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
We show how a number of well-known uncertainty principles for the Fourier transform, such as the Heisenberg uncertainty principle, the Donoho--Stark uncertainty principle, and Meshulam's non-abelian uncertainty principle, have little to do…
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…
We study the time evolution of the reduced Wigner function for a class of quantum Brownian motion models. We derive two generalized uncertainty relations. The first consists of a sharp lower bound on the uncertainty function, $U = (\Delta…
Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not…
We propose tests of the weak equivalence principle (WEP) using a torsion balance, in which superposition of energy eigenstates are created in a controllable way for the test masses. After general considerations on the significance of tests…
The weak value of an observable is experimentally accessible by weak measurements as theoretically analyzed by Aharonov et al. and recently experimentally demonstrated. We introduce a weak operator associated with the weak values and give a…
Some of the possible consequences of a generalized uncertainty principle (which emerges in the context of string theory and quantum gravity models as a consequence of fluctuations of the background metric) are analyzed considering the case…
This paper is generally concerned with understanding how the uncertainty principle arises in formulations of quantum mechanics, such as the decoherent histories approach, whose central goal is the assignment of probabilities to histories.…
Collective effects in deformed atomic nuclei present possible avenues of study on the non-spherical distribution of neutrons and the violation of the local Lorentz invariance. We introduce the weak quadrupole moment of nuclei, related to…
Quantum weak measurement, measuring some observable quantities within the selected subensemble of the entire quantum ensemble, can produce many interesting results such as the superluminal phenomena. An outcome of such a measurement is the…
An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal…
Quantum mechanics presents peculiar properties that, on the one hand, have been the subject of several theoretical and experimental studies about its very foundations and, on the other hand, provide tools for developing new technologies,…
Weak values and Kirkwood--Dirac (KD) quasiprobability distributions have been independently associated with both foundational issues in quantum theory and advantages in quantum metrology. We propose simple quantum circuits to measure weak…
We investigate the sequential composition of weak values in the framework of time-symmetric quantum mechanics. Specifically, we consider a forward'' weak measurement from a preselected state $\ket{\psi}$ to a post-selected state…
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…
We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With $X_n$ denoting position at time $n$, we show that $X_n/n$ converges weakly as $n \to \infty$ to a certain distribution which is…
In quantum theory, a physical observable is represented by a Hermitian operator as it admits real eigenvalues. This stems from the fact that any measuring apparatus that is supposed to measure a physical observable will always yield a real…