Related papers: Generalized Uncertainty Relation Between an Observ…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time-fluctuations of an observable \mathcal{A} are typically exponentially small in the system size. We consider here…
An exact invariant operator of time-dependent coupled oscillators is derived using the Liouville-von Neumann equation. The unitary relation between this invariant and the invariant of two uncoupled simple harmonic oscillators is…
There are several theoretical indications that the quantum gravity approaches may have predictions for a minimal measurable length, and a maximal observable momentum and throughout a generalization for Heisenberg uncertainty principle. The…
Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is…
The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with…
We study entanglement dynamics in quantum Brownian motion (QBM) models. Our main tool is the Wigner function propagator. Time evolution in the Wigner picture is physically intuitive and it leads to a simple derivation of a master equation…
The second-order moment quantum fluctuations or uncertainties are mass-dependent, and the incompatibility between the quantum uncertainty principle and the equivalence principle is at the second-order moment (variation) level, but not the…
We uncover the quantum fluctuation-response inequality, which, in the most general setting, establishes a bound for the mean difference of an observable at two different quantum states, in terms of the quantum relative entropy. When the…
Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate…
Sharp uncertainty relations restricting the values of variances in the position space and in the momentum (wavevector) space are derived. They have the same form $\Delta r\Delta k\ge 5/2$ in the classical theory of light beams, in the…
As the fundamental tool in quantum information science, the uncertainty principle is essential for manifesting nonclassical properties of quantum systems. Plenty of efforts on the uncertainty principle with two observables have been…
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…
This paper is concerned with two questions in the decoherent histories approach to quantum mechanics: the emergence of approximate classical predictability, and the fluctuations about it necessitated by the uncertainty principle. We…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
Lower bounds on fluctuations of thermodynamic currents depend on the nature of time: discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master…
The uncertainty principle is one of the characteristic properties of quantum theory, where it signals the incompatibility of two types of measurements. In this paper, we argue that measurements of time-of-arrival $T_x$ at position $x$ and…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising…
A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…