Related papers: Wigner-Araki-Yanase theorem for continuous and unb…
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation…
Recently, universally valid uncertainty relations have been established to set a precision limit for any instruments given a disturbance constraint in a form more general than the one originally proposed by Heisenberg. One of them leads to…
Two hallmarks of quantum non-demolition (QND) measurement are the ensemble-level conservation of the expectation value of the measured observable $A$ and the eventual, inevitable collapse of the system into some eigenstate of $A$. This…
We address the Riemann and Cauchy problems for systems of $n$ conservation laws in $m$ unknowns which are subject to $m-n$ constraints ($m\geq n$). Such constrained systems generalize systems of conservation laws in standard form to include…
The Wigner-Yanase skew information stands for the uncertainty about the information on the values of observables not commuting with the conserved quantity. The Wigner-Yanase skew information-based uncertainty relations can be regarded as a…
When a measurement is made on a system that is not in an eigenstate of the measured observable, it is often assumed that some conservation law has been violated. Discussions of the effect of measurements on conserved quantities often…
This paper investigates the properties of trajectories in harmonic oscillator systems equipped with a point, absolutely continuous, or singular measure. As demonstrated in [30], infinite-dimensional linear flows of countable oscillator…
We characterize a value of an observable by a `sum rule' for generally non-commuting observables and a `product rule' when restricted to a maximal commuting subalgebra of observables together with the requirement that the value is unity for…
An experiment that would measure non--commuting quantum mechanical observables without collapsing the wave function has been recently proposed by Y Aharonov and J Anandan. These authors argue that this "protected measurement" may give…
Uncertainty principle plays a vital role in quantum physics. The Wigner-Yanase skew information characterizes the uncertainty of an observable with respect to the measured state. We generalize the uncertainty relations for two quantum…
We study how convergence of an observer whose state lives in a copy of the given system's space can be established using a Riemannian metric. We show that the existence of an observer guaranteeing the property that a Riemannian distance…
In contrast to a projective quantum measurement in which the system is projected onto an eigenstate of the measured operator, in a weak measurement the system is only weakly perturbed while only partial information on the measured…
From an analysis of projective measurements, it is shown that the Wigner rule is the unique operational quasi-probability for the post-measurement state. A unique pre-measurement quasi-probability is derived from a principle of invariance…
We apply weighted Mourre commutator theory to prove the limiting absorption principle for the discrete Schr{\"o}dinger operator perturbed by the sum of a Wigner-von Neumann and long-range type potential. In particular, this implies a new…
Lueders theorem states that two observables commute if measuring one of them does not disturb the measurement outcomes of the other. We study measurements which are described by continuous positive operator-valued measurements (or POVMs)…
Takens' Embedding Theorem asserts that when the states of a hidden dynamical system are confined to a low-dimensional attractor, complete information about the states can be preserved in the observed time-series output through the delay…
In the quantum regime, the third law of thermodynamics implies the unattainability of pure states. As shown recently, such unattainability implies that a unitary interaction between the measured system and a measuring apparatus can never…
The quantum theory of indirect measurements in physical systems is studied. The example of an indirect measurement of an observable represented by a self-adjoint operator $\mathcal{N}$ with finite spectrum is analysed in detail. The…
Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are…
We develop a deterministic large-time mechanism yielding Ces{\`a}ro asymptotic observability inequalities from moving localized observations for conservative evolutions. On each observation interval, exact convexification on a compact…