相关论文: Schroedinger uncertainty relation and its minimiza…
Contractive states for a free quantum particle were introduced by Yuen [Yuen H P 1983 Phys. Rev. Lett. 51, 719] in an attempt to evade the standard quantum limit for repeated position measurements. We show how appropriate families of two-…
A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…
We discuss two topics that are usually considered to be exclusively "quantum": the Schroedinger equation, and the uncertainty principle. We show (or rather recall) that the Schroedinger equation can be derived from Hamilton's equations…
We prove the equivalence (under some conditions) of two sets of coherent states built for the one-dimensional infinite square well: the so-called generalized and Gaussian Klauder coherent states. We then derive an approximate close…
We study the relation between two evolution pictures that are currently considered for totally constrained theories. Both descriptions are based on Rovelli's evolving constants approach, where one identifies a (possibly local) degree of…
Nonclassicality cannot be a single-observable property since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior from the joint measurement of…
This paper reviews and suggests a resolution of the problem of definite outcomes of measurement. This problem, also known as "Schrodinger's cat," has long posed an apparent paradox because the state resulting from a measurement appears to…
Heisenberg uncertainty relation in quantum mechanics sets the limit on the measurement precision of non-commuting observables, which prevents us from measuring them accurately at the same time. In some applications, however, the information…
A complete set of solutions |z,u,v>_{sa} of the eigenvalue equation (ua^2+va^{dagger 2})|z,u,v> = z|z,u,v> ([a,a^{dagger}]=1) are constructed and discussed. These and only these states minimize the Schr\"{o}dinger uncertainty inequality for…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…
Some focusing coupled Schrodinger equations are investigated. First, existence of ground state is obtained. Second, global and non global existence of solutions are discussed via potential-well method. Finally, strong instability of…
We consider in the whole plane the Hamiltonian coupling of semilinear Schroedinger equations which have critical growth in the sense of Moser. We prove that the (nonempty) set S of ground state solutions is compact up to translations.…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
We consider the uncertainty bound on the sum of variances of two incompatible observables in order to derive a corresponding steering inequality. Our steering criterion when applied to discrete variables yields the optimum steering range…
In our previous work we have found a lower bound for the multipartite uncertainty product of the position and momentum observables over all separable states. In this work we are trying to minimize this uncertainty product over a broader…
In a setting of noncommutative space with minimal length we confirm the general assertion that the more nonclassical an input state for a beam splitter is, the more entangled its output state becomes. By analysing various nonclassical…
The Vlasov-Schr\"odinger-Poisson system is a kinetic-quantum hybrid model describing quasi-lower dimensional electron gases. For this system, we construct a large class of 2D kinetic/1D quantum steady states in a bounded domain as…
It is generally believed that classical regime emerges as a limiting case of quantum theory. Exploring such quantum-classical correspondences in a more transparent manner is central to the deeper understanding of foundational aspects and…
We derive a class of inequalities, from the uncertainty relations of the SU(1,1) and the SU(2) algebra in conjunction with partial transposition, that must be satisfied by any separable two-mode states. These inequalities are presented in…
Eigenfunctions and eigenvalues of the free magnetic Schr\"odinger operator, describing a spinless particle confined to an infinite layer of fixed width, are discussed in detail. The eigenfunctions are realized as an orthonormal basis of a…