Revisiting entanglement within the Bohmian approach to quantum mechanics

We revisit the concept of entanglement within the Bohmian approach to quantum mechanics. Inspired by Bohmian dynamics, we introduce two partial measures for the amount of entanglement corresponding to a pure state of a pair of quantum particles. One of these measures is associated with the statistical correlations exhibited by the joint probability density of the two Bohmian particles in configuration space. The other partial measure corresponds to the correlations associated with the phase of the joint wave function, and describes the non-separability of the Bohmian velocity field. The sum of these two components is equal to the total entanglement of the joint quantum state, as measured by the linear entropy of the single-particle reduced density matrix.Fil: Zander, Claudia. University of Pretoria; SudáfricaFil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Bioinvestigaciones (Sede Junín); Argentin

Classical & quantum dynamics of information and entanglement properties of fermion systems

Due to their great importance, both from the fundamental and from the practical points of view, it is imperative that the various facets of the concepts of information and entanglement are explored systematically in connection with diverse physical systems and processes. These concepts are at the core of the emerging field of the Physics of Information. In this Thesis I investigate some aspects of the dynamics of information in both classical and quantum mechanical systems and then move on to explore entanglement in fermion systems by searching for novel ways to classify and quantify entanglement in fermionic systems. In Chapter 1 a brief review of the different information and entropic measures as well as of the main evolution equations of classical dynamical and quantum mechanical systems is given. The conservation of information as a fundamental principle both at the classical and quantum levels, and the implications of Landauer's theorem are discussed in brief. An alternative and more intuitive proof of the no-broadcasting theorem is also provided. Chapter 2 is a background chapter on quantum entanglement, where the differences between the concept of entanglement in systems consisting of distinguishable subsystems and the corresponding concept in systems of identical fermions are emphasized. Different measures of entanglement and relevant techniques such as majorization, are introduced. To illustrate some of the concepts reviewed here I discuss the entanglement properties of an exactly soluble many-body model which was studied in paper (E) of the publication list corresponding to the present Thesis. An alternative approach to the characterization of quantum correlations, based on perturbations under local measurements, is also briefly reviewed. The use of uncertainty relations as entanglement indicators in composite systems having distinguishable subsystems is then examined in some detail. Chapter 3 is based on papers (A) and (B) of the list of publications. Extended Landauer-like principles are developed, based amongst others on the conservation of information of divergenceless dynamical systems. Conservation of information within the framework of general probabilistic theories, which include the classical and quantum mechanical probabilities as particular instances, is explored. Furthermore, Zurek's information transfer theorem and the no-deleting theorem are generalized. Chapter 4 is based on articles (C) and (D) mentioned in the publication list, and investigates several separability criteria for fermions. Criteria for the detection of entanglement are developed based either on the violation of appropriate uncertainty relations or on inequalities involving entropic measures. Chapter 5 introduces an approach for the characterization of quantum correlations (going beyond entanglement) in fermion systems based upon the state disturbances generated by the measurement of local observables. Chapter 6 summarizes the conclusions drawn in the previous chapters. The work leading up to this Thesis has resulted in five publications in peer reviewed science research journals.Thesis (PhD)--University of Pretoria, 2012.Physicsunrestricte

Information measures, entanglement and quantum evolution

Due to its great importance, both from the fundamental and from the practical points of view, it is imperative that the concept of entanglement is explored. In this thesis I investigate the connection between information measures, entanglement and the “speed” of quantum evolution. In Chapter 1 a brief review of the different information and entanglement measures as well as of the concept of “speed” of quantum evolution is given. An illustration of the quantum no-cloning theorem in connection with closed timelike curves is also provided. The work leading up to this thesis has resulted in the following three publications and in one conference proceeding: (A) C. Zander and A.R. Plastino, “Composite systems with extensive Sq (power-law) entropies”, Physica A 364, (2006) pp. 145-156 (B) S. Curilef, C. Zander and A.R. Plastino, “Two particles in a double well: illustrating the connection between entanglement and the speed of quantum evolution”, Eur. J. Phys. 27, (2006) pp. 1193-1203 (C) C. Zander, A.R. Plastino, A. Plastino and M. Casas, “Entanglement and the speed of evolution of multi-partite quantum systems”, J. Phys. A: Math. Theor. 40 (11), (2007) pp. 2861-2872 (D) A.R. Plastino and C. Zander, “Would Closed Timelike Curves Help to Do Quantum Cloning?”, AIP Conference Proceedings: A century of relativity physics, ERE 841, (2005) pp. 570-573. Chapter 2 is based on (A) and is an application of the Sq (powerlaw) entropy. A family of models for the probability occupancy of phase space exhibiting an extensive behaviour of Sq and allowing for an explicit analysis of the thermodynamic limit is proposed. Chapter 3 is based on (B). The connection between entanglement and the speed of quantum evolution as measured by the time needed to reach an orthogonal state is discussed in the case of two quantum particles moving in a one-dimensional double well. This illustration is meant to be incorporated into the teaching of quantum entanglement. Chapter 4 is based on (C). The role of entanglement in time evolution is investigated in the cases of two-, three- and N-qubit systems. A clear correlation is seen between entanglement and the speed of evolution. States saturating the speed bound are explored in detail. Chapter 5 summarizes the conclusions drawn in the previous chapters.Dissertation (MSc)--University of Pretoria, 2007.PhysicsMScUnrestricte

Entropic entanglement criteria for fermion systems

Entanglement criteria for general (pure or mixed) states of systems consisting of N identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system and the entropy of the one-particle, reduced density matrix.This abstract was presented at the ‘Studentesimposium in die Natuurwetenskappe 2011’, presented under the protection of the Suid- Afrikaanse Akademie vir Wetenskap en Kuns. The symposium was held at the University of South Africa on 27–28 October 2011.http://www.satnt.ac.zaam2013ai201

CAP-reform and the provision of non-commodity outputs in Brandenburg

This paper presents an attempt to model the response of selected farms to decoupled direct payments and the associated impact on the provision of a defined set of non-commodity outputs (NCO’s) using a combined modelling approach consisting of the AgriPoliS and MODAM models. AgriPoliS focuses on the socio-economic dimension of multifunctionality at the individual farm and regional levels and explicitly models heterogeneous farms (in size, location and efficiency) within a competitive and dynamic environment. The linear-programming model MODAM allows a detailed representation of production processes and their impact on the environmental dimension of multifunctionality at the farm level. We simulate the impact of a uniform area payment and a fully decoupled single farm payment. Our case study region is the district Ostprignitz-Ruppin in Brandenburg. Results show that the decoupling schemes create a trade-off between the NCO’s and that adjustment reactions differ between farms depending on their legal form, size, and production.decoupling, multifunctionality, non-commodity outputs, modelling, simulation, policy analysis, ecological indicators, Agricultural and Food Policy, Land Economics/Use,

Positive operator valued measures and the quantum Monty Hall problem

A quantum version of the Monty Hall problem, based upon the Positive Operator Valued Measures (POVM) formalism, is proposed. It is shown that basic normalization and symmetry arguments lead univocally to the associated POVM elements, and that the classical probabilities associated with the Monty Hall scenario are recovered for a natural choice of the measurement operators.Facultad de Ciencias Exacta

Revisiting entanglement within the Bohmian approach to quantum mechanics

We revisit the concept of entanglement within the Bohmian approach to quantum mechanics. Inspired by Bohmian dynamics, we introduce two partial measures for the amount of entanglement corresponding to a pure state of a pair of quantum particles. One of these measures is associated with the statistical correlations exhibited by the joint probability density of the two Bohmian particles in configuration space. The other partial measure corresponds to the correlations associated with the phase of the joint wave function, and describes the non-separability of the Bohmian velocity field. The sum of these two components is equal to the total entanglement of the joint quantum state, as measured by the linear entropy of the single-particle reduced density matrix.http://www.mdpi.com/journal/entropyam2018Physic

Landauer's principle and divergenceless dynamical systems

Landauer's principle is one of the pillars of the physics of information. It constitutes one of the foundations behind the idea that "information is physical". Landauer's principle establishes the smallest amount of energy that has to be dissipated when one bit of information is erased from a computing device. Here we explore an extended Landauerlike principle valid for general dynamical systems (not necessarily Hamiltonian) governed by divergenceless phase space flows.Facultad de Ciencias Exacta

Multiqubit systems: highly entangled states and entanglement distribution

Texto completo arXiv:0803.3979v1.-- PACS: 03.67.Lx Quantum computation architectures and implementations 03.67.Mn Entanglement measures, witnesses, and other characterizations 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.).-A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multi-qubits states. In particular, our present results are compared with those recently reported by Brown et al. [J. Phys. A: Math. Gen. 38 (2005) 1119]. The statistical distribution of entanglement values for the aforementioned multi-qubit systems is also exploredThis work was partially supported by the MEC grant FIS2005-02796 (Spain) and FEDER (EU) and by CONICET (Argentine Agency). The financial assistance of the National Research Foundation (NRF; South African Agency) toward this research is hereby acknowledged. Opinions expressed and conclusions arrived at, are those of the authors and are not necessarily to be attributed to the NRF. A Borras acknowledges support from the FPU grant AP-2004- ´ 2962 (MEC-Spain)Peer reviewe

Case Study - Germany, Sustainable Agriculture and Soil Conservation (SoCo Project)

This Technical Note 'Case Study ¿ Germany' is part of a series of case studies within the ¿Sustainable Agriculture and Soil Conservation¿ (SoCo) project. Ten case studies were carried out in Belgium, Bul-garia, the Czech Republic, Denmark, France, Germany, Greece, Italy, Spain and the United Kingdom between spring and summer 2008. The selection of case study areas was designed to capture differences in soil degradation processes, soil types, climatic conditions, farm structures and farming prac-tices, institutional settings and policy priorities. A harmonised methodological approach was pursued in order to gather insights from a range of contrasting conditions over a geographically diverse area. The case studies were carried out by local experts to reflect the specificities of the selected case studies.JRC.DDG.J.5-Agriculture and Life Sciences in the Econom