Related papers: Universally valid uncertainty relations in general…
One unique feature of quantum mechanics is the Heisenberg uncertainty principle, which states that the outcomes of two incompatible measurements cannot simultaneously achieve arbitrary precision. In an information-theoretic context of…
Distance to Uncontrollability is a crucial concept in classical control theory. Here, we introduce Quantum Distance to Uncontrollability as a measure how close a universal quantum system is to a non-universal one. This allows us to provide…
We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
Uncertainty relation usually is one of the most important features in quantum mechanics, and is the backbone of quantum theory, which distinguishes from the rule in classical counterpart. Specifically, entropy-based uncertainty relations…
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. 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…
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…
It has been shown recently that the framework of quantum sampling, as introduced by Bouman and Fehr, can lead to new entropic uncertainty relations highly applicable to finite-key cryptographic analyses. Here we revisit these so-called…
We formulate a general complementarity relation starting from any Hermitian operator with discrete non-degenerate eigenvalues. We then elucidate the relationship between quantum complementarity and the Heisenberg-Robertson's uncertainty…
We describe how to obtain information on a quantum-mechanical system by coupling it to a probe and detecting some property of the latter, using a model introduced by von Neumann, which describes the interaction of the system proper with the…
We discuss some of the issues to be addressed in arriving at a definitive noncommutative Riemannian geometry that generalises conventional geometry both to the quantum domain and to the discrete domain. This also provides an introduction to…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
In this letter, the number-phase entropic uncertainty relation and the number-phase Wigner function of generalized coherent states associated to a few solvable quantum systems with nondegenerate spectra are studied. We also investigate time…
Introductory courses on quantum mechanics usually include lectures on uncertainty relations, typically the inequality derived by Robertson and, perhaps, other statements. For the benefit of the lecturers, we present a unified approach --…
Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty…
We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the Poincar\'e algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial…
Uncertainty relations express the fundamental incompatibility of certain observables in quantum mechanics. Far from just being puzzling constraints on our ability to know the state of a quantum system, uncertainty relations are at the heart…
We study universal uncertainty relations and present a method called joint probability distribution diagram to improve the majorization bounds constructed independently in [Phys. Rev. Lett. 111, 230401 (2013)] and [J. Phys. A. 46, 272002…
Heisenberg's uncertainty relation for measurement noise and disturbance states that any position measurement with noise epsilon brings the momentum disturbance not less than hbar/2epsilon. This relation holds only for restricted class of…