Related papers: State-extended uncertainly relations and tomograph…
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…
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of…
We give an introduction to Gaussian states and operations. A discussion of the entanglement properties of bipartite Gaussian states in terms of its covariance matrix follows. It is explained how entanglement can be witnessed using feasible…
We experimentally verify uncertainty relations for mixed states in the tomographic representation by measuring the radiation field tomograms, i.e. homodyne distributions. Thermal states of single-mode radiation field are discussed in…
Recently, it has been argued that quantum mechanics is a complete theory, and that different quantum states do necessarily correspond to different elements of reality, under the assumptions that quantum mechanics is correct and that…
Quantum entanglement and nonlocality are inequivalent notions: There exist entangled states that nevertheless admit local-realistic interpretations. This paper studies a special class of local-hidden-variable theories, in which the linear…
We introduce the concept of selective quantum state tomography or SQST, a tomographic scheme that enables a user to estimate arbitrary elements of an unknown quantum state using a fixed measurement record. We demonstrate how this may be…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…
Two basic properties of the set of all probability measures on the set of quantum states and their corollaries are considered. Several applications of these properties to analysis of functional constructions widely used in quantum…
We discuss the uncertainty relations in quantum mechanics on noncommutative plane. In particular, we show that, for a given state at most one out of three basic nontrivial uncertainty relations can be saturated. We consider also in some…
Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the…
We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
The quantum mechanics of closed systems such as the universe is formulated using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for sets of alternative histories that are…
Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of "mixed state" for any nonlinear version of quantum theory are introduced: (i) >genuine mixture< corresponds to operational "mixing" of…
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
The positive vector optical tomogram fully describing the quantum state of spin 1/2 particle without any redundancy is introduced. Reciprocally the vector symplectic tomogram and vector quasidistributions $\vec W({\mathbf q},{\mathbf p})$,…
Quantum tomography is an important tool for obtaining information about the quantum state from experimental data. In this study, we conduct a comparative analysis of various quantum tomography protocols, including protocols based on highly…
The study of Gaussian states has arisen to a privileged position in continuous variable quantum information in recent years. This is due to vehemently pursued experimental realisations and a magnificently elegant mathematical framework. In…
The uncertainty principle is one of the features of quantum theory. Fine-grained uncertainty relations (FGURs) are a contemporary interpretation of this principle. Each FGUR is derived from a scenario where multiple measurements of a…