Related papers: Generalizations of Heisenberg uncertainty relation
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…
Uncertainty relation is one of the fundamental building blocks of quantum theory. Nevertheless, the traditional uncertainty relations do not fully capture the concept of incompatible observables. Here we present a stronger…
We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…
The well-known Robertson-Schr\"odinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit…
We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices.…
The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role…
We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is…
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…
Heisenberg's uncertainty principle, coherence and Bell nonlocality have been individually examined through many experiments. In this Letter, we systematically characterize all of this quantumness in a unified manner. We first construct…
The concept of uncertainty quanta for a general system is introduced and applied to some important problems in physics and mathematics. EPR paradox gives new clue to the further understanding of particle correlation which turns out to be…
We investigate disordered one- and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to…
The paper contains a brief review of an approach to quantum entanglement based on analysis of dynamic symmetry of systems and quantum uncertainties, accompanying the measurement of mean value of certain basic observables. The latter are…
The Heisenberg Uncertainty Principle (HUP) limits the accuracy in the simultaneous measurements of the position and momentum variables of any quantum system. This is known to be true in the context of non-relativistic quantum mechanics.…
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…
Uncertainty relations (URs) like the Heisenberg-Robertson or the time-energy UR are often considered to be hallmarks of quantum theory. Here, a simple derivation of these URs is presented based on a single classical inequality from…
The spin-statistics theorem is generalized to include quantum entanglement. Specifically, within the context of spin entanglement, we prove that isotropic spin-correlated (ISC) states must occur in pairs. This pairing process can be…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…
The uncertainty of a quantum state is given by the composition of two components. The first is called the quantum component and is given by the probability distribution of an observable relative to the state. The second is the classical…