Related papers: Maximally Localized States in Quantum Mechanics wi…
This paper presents the uncertainty related to position and momentum localization of a quantum state in terms of entropic uncertainty relations. We slightly improve the inequality given in [Phys. Rev. A 74, 052101 (2006)] and introduce a…
Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions on states under which it is possible to infer the expectation values of all…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
Localization properties of quasi-one dimensional quantum wire nanostructures are investigated using the transfer matrix-Lyapunov exponent technique. We calculate the localization length as a function of the effective mean-field mobility…
The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincar\'e symmetry of field theory can be extended to the larger conformal symmetry. We use…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
We show that the von Neumann--Lueders collapse rules in quantum mechanics always select the unique state that maximises the quantum relative entropy with respect to the premeasurement state, subject to the constraint that the…
We consider a particle governed by a one-dimensional Hamiltonian in which artificial periodic spin-orbit coupling and Zeeman lattice have incommensurate periods. Using best rational approximations to such quasiperiodic Hamiltonian, the…
We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a…
Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to reconstruct the density matrix of a physical system from measurement results. One strategy to deal with positivity and unit trace…
State estimation for discrete-time linear systems with quantized measurements is addressed. By exploiting the set-theoretic nature of the information provided by the quantizer, the problem is cast in the set membership estimation setting.…
The resistivity minima of the quantum Hall effect arise due to the localization of the electron states at the Fermi energy, when it is positioned between adjacent Landau levels. In this paper we calculate the localization length $\xi$ of…
The first result in this paper provides a very general $\epsilon$-removal argument for the multilinear restriction estimate. The second result provides a refinement of the multilinear restriction estimate in the case when some terms have…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…
We challenge the widespread belief, originated by Newton and Wigner (Rev. Mod. Phys, 21, 400 (1949)) that the incorporation of special relativity into quantum mechanics implies that a massive particle cannot be localized within an…
We discuss the interdependence of resource state, measurement setting and temporal order in measurement-based quantum computation. The possible temporal orders of measurement events are constrained by the principle that the randomness…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
Correlations and measures of entanglement in ground state wavefunctions of relativistic quantum field theories are spatially localized over length scales set by the mass of the lightest particle. We utilize this localization to design…
This paper proposes a new high-order generalized uncertainty principle, which can modify the momentum operator and position operator simultaneously. Moreover, the new form of GUP is consistent with the viewpoint of the existence of the…