Related papers: A Simple Derivation of Schroedinger Uncertainty Re…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the…
The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schr\"{o}dinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily…
The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty…
The Schr\"odinger-like equations for the marginal and conditional probability amplitudes resulting from the exact factorization of the wavefunction of a two-component system are derived in a form that is invariant to gauge and coordinate…
We investigate the Peres-Horodecki positive partial transpose (PPT) criterion in the context of conserved quantities and derive a condition of in- separability for a composite bipartite system depending only on the dimen- sions of its…
We highlight overlap as one of the simplest inequalities in linear space that yields a number of useful results. One obtains the Cauchy-Schwarz inequality as a special case. More importantly, a variant of it is seen to work desirably in…
The state-extended uncertainty relations generalizing the Robertson Schrodinger inequality are presented in the form appropriate for the experimental check by homodyne photon state detection. The method of qubit portrait of qudit states…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…
We study sum uncertainty relations for arbitrary finite $N$ quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial…
In this article, I show how the Aharonov-Vaidman identity $A \left \vert \psi\right \rangle = \left \langle A \right \rangle \left \vert \psi\right \rangle + \Delta A \left \vert \psi^{\perp}_A \right \rangle$ can be used to prove relations…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
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…
Heisenberg's uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: although…
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A…
In this paper we give log-convexity properties for solutions to discrete Schr\"odinger equations with different discrete versions of Gaussian decay at two different times. For free evolutions, we use complex analysis arguments to derive…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
We analyze general uncertainty relations and we show 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…
The representations of the kernels of the transmutation operator and of its inverse relating the one-dimensional Schr\"odinger operator with the second derivative are obtained in terms of the eigenfunctions of a corresponding…
We shall give a new Schr\"odinger type uncertainty relation for a quantity representing a quantum uncertainty, introduced by S.Luo in \cite{Luo1}. Our result improves the Heisenberg uncertainty relation shown in \cite{Luo1} for a mixed…