An Improved Lotka–Volterra Model Using Quantum Game Theory

Human decision-making does not conform to the independent decision-making hypothesis from classical decision-making theory. Thus, we introduce quantum decision-making theory into the Lotka–Volterra model (L–V model), to investigate player population dynamics while incorporating the initial strategy, game payoffs and interactive strategies in an open social system. Simulation results show that: (1) initial strategy, entanglement intensity of strategy interaction, and payoffs impact population dynamics; (2) In cooperative coexistence, game players mutually exceed the initial environmental capacity in an open system, but not in competitive coexistence; (3) In competitive coexistence, an initial strategy containing an entanglement intensity of strategies plays a vital role in game outcomes. Furthermore, our proposed model more realistically delineates the characteristics of population dynamics in competitive or cooperative coexistence scenarios

Multi-photon entanglement and applications in quantum information

Since the awareness of entanglement was raised by Einstein, Podolski, Rosen and Schrödinger in the beginning of the last century, it took almost 55 years until entanglement entered the laboratories as a new resource. Meanwhile, entangled states of various quantum systems have been investigated. Sofar, their biggest variety was observed in photonic qubit systems. Thereby, the setups of today's experiments on multi-photon entanglement can all be structured in the following way: They consist of a photon source, a linear optics network by which the photons are processed and the conditional detection of the photons at the output of the network. In this thesis, two new linear optics networks are introduced and their application for several quantum information tasks is presented. The workhorse of multi-photon quantum information, spontaneous parametric down conversion, is used in different configurations to provide the input states for the networks. The first network is a new design of a controlled phase gate which is particularly interesting for applications in multi-photon experiments as it constitutes an improvement of former realizations with respect to stability and reliability. This is explicitly demonstrated by employing the gate in four-photon experiments. In this context, a teleportation and entanglement swapping protocol is performed in which all four Bell states are distinguished by means of the phase gate. A similar type of measurement applied to the subsystem parts of two copies of a quantum state, allows further the direct estimation of the state's entanglement in terms of its concurrence. Finally, starting from two Bell states, the controlled phase gate is applied for the observation of a four photon cluster state. The analysis of the results focuses on measurement based quantum computation, the main usage of cluster states. The second network, fed with the second order emission of non-collinear type II spontaneous parametric down conversion, constitutes a tunable source of a whole family of states. Up to now the observation of one particular state required one individually tailored setup. With the network introduced here many different states can be obtained within the same arrangement by tuning a single, easily accessible experimental parameter. These states exhibit many useful properties and play a central role in several applications of quantum information. Here, they are used for the solution of a four-player quantum Minority game. It is shown that, by employing four-qubit entanglement, the quantum version of the game clearly outperforms its classical counterpart. Experimental data obtained with both networks are utilized to demonstrate a new method for the experimental discrimination of different multi-partite entangled states. Although theoretical classifications of four-qubit entangled states exist, sofar there was no experimental tool to easily assign an observed state to the one or the other class. The new tool presented here is based on operators which are formed by the correlations between local measurement settings that are typical for the respective quantum state.Fast 55 Jahre vergingen bis die Entdeckung des Phänomens der Verschränkung durch Einstein, Podolski, Rosen und Schrödinger Ende des zwanzigsten Jahrhunderts Einzug in die Labore hielt. Mittlerweile wurde eine Vielfalt von verschränkten Zuständen untersucht; die größte davon in Systemen photonischer Qubits. Alle modernen Experimente zu viel-Photonen Verschränkung lassen sich in drei wesentliche Bestandteile untergliedern: Eine Photonenquelle, ein Netzwerk aus linearen optischen Komponenten welches die Photonen verarbeitet, und eine bedingte Detektion der Photonen am Ausgang des Netzwerks. Die vorliegende Arbeit führt zwei neue Netzwerke ein und präsentiert deren Anwendungen in verschiedenen Problemstellungen der Quanteninformation. Als Photonenquelle dient hierbei der Prozeß der spontanen parametrischen Fluoreszenz in unterschiedlichen Konfigurationen. Das erste Netzwerk ist ein neuartiges Kontroll-Phasengatter das sich gegenüber früheren Realisierungen vor allem durch seine hohe Stabilität auszeichnet. Wie anhand mehrerer Beispiele gezeigt wird, eignet es sich besonders für den Einsatz in mehr-Photonen Experimenten. Mit Hilfe des Gatters werden alle vier Bell Zustände in einem Teleportations- und "entanglement swapping" Experiment unterschieden. Ein ähnlicher experimenteller Aufbau erlaubt ferner die direkte Messung der Verschränkung zweier Kopien eines Zustands in Form der "Concurrence". Ausgehend von zwei Bell Zuständen wird das Gatter darüberhinaus zur Beobachtung eines Vier-Photonen "Cluster Zustands" verwendet. Die Analyse der Ergebnisse konzentriert sich dabei auf die Hauptanwendung von Cluster Zuständen, das meßbasierte Quantenrechnen. Das zweite Netzwerk bildet, zusammen mit der Emission zweiter Ordnung der parametrischen Fluoreszenz als Input, eine einstellbare Quelle verschiedenster Zustände. Während die Beobachtung eines Zustands bisher einen individuell maßgeschneiderten Versuchsaufbau benötigte, können mit dem neuen Netzwerk viele verschiedene Zustände innerhalb desselben Aufbaus beobachtet werden. Dies erfordert lediglich die Veränderung eines einzelnen, leicht zugänglichen experimentellen Parameters. Die so erzeugten Zustände besitzen eine Reihe nützlicher Eigenschaften und spielen eine zentrale Rolle in vielen Anwendungen. Hier werden sie zur Lösung eines vier-Parteien Quanten "Minority" Spiels verwendet. Es wird gezeigt, dass die Quanten Version des Spiels durch den Einsatz von vier-Qubit Verschränkung sein klassisches Pendant an Möglichkeiten deutlich übertrifft. Mit Hilfe experimenteller Daten beider Netzwerke wird eine neue Methode der Unterscheidung vier-Qubit verschränkter Zustände vorgestellt. Obwohl theoretische Klassifizierungen verschränkter Zustände existieren, gab es bisher keine einfache experimentelle Methode einen beobachteten Zustand der einen oder anderen Klasse zuzuordnen. Das hier vorgestellte Konzept ermöglicht eine experimentelle Klassifizierung basierend auf Operatoren die aus zustandsabhängigen Korrelationsmessungen bestimmt werden

Generation and Manipulation of Entanglement in Quantum Optical Systems

In this thesis, several new procedures for the generation and manipulation of entangled states in quantum optical systems are introduced. Each is evaluated in terms of realistic models of the imperfect apparatus of any real laboratory implementation. The first half of the thesis considers entanglement generation in Cavity QED, introducing several proposals for the creation of maximally entangled two-qubit states. The second half of the thesis focuses on the manipulation of entangled states of light pulses. In particular, an entanglement distillation procedure for Gaussian states is introduced. This combines a Procrustean protocol for the generation of highly entangled non-Gaussian states, with a "Gaussification" procedure, which allows more highly entangled approximately Gaussian states to be distilled from a non-Gaussian supply.Comment: PhD Thesis (December 2004), Imperial College London, 165 page

Detectores cuánticos y correlaciones de vacío en espacio y tiempo: resultados teóricos y propuestas de simulación

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Teórica I, leída el 27/11/2014Depto. de Física TeóricaFac. de Ciencias FísicasTRUEunpu

Multiphoton Quantum Optics and Quantum State Engineering

We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromnagnetic field, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.Comment: 198 pages, 36 eps figure

Operational Approaches to Quantum Correlations and Particle Creation in Field Theory

In this thesis we examine a variety of question regarding several quantum information-theoretic concepts as they manifest in the context of relativistic quantum fields. In particular, we study the qualitative and quantitative structure of entanglement (as well as more generalized quantum correlations) in field theory. Primarily we study the nature of vacuum entanglement, but consider spatial correlations in more general field states as well. We also discuss several novel aspects of particle creation phenomena, which generally go hand in hand with the presence of field entanglement. Such investigations are important from two perspectives. First, we gain enlightening new insight into the nature of quantum fields and, therefore, into the fundamental constituents of the matter contained in our universe. Second, we are able to consider the possibility of utilizing the relativistic nature of quantum fields as a resource for quantum technological tasks such as entanglement distribution, information processing, and metrology. As a general guiding principle, here we approach such questions from an operational perspective. That is, we focus less on the mathematical facts derivable from a given theory and instead attempt to answer in what concretely physical ways such facts manifest themselves. For example, in what ways can vacuum entanglement actually be experimentally detected and measured, at least in principle? Such an approach allows us to circumvent otherwise problematic interpretational issues. It also lends itself more naturally to the proposal of real world experiments regarding, and utilizations of, the physics being investigated. In this thesis we utilize two models of detection as applied to field theory. The first is one that we will develop from scratch and use to great effect in a number of studies; this is the non-perturbative oscillator detector. In this context, a ``detector" is simply some quantum system that is allowed to interact in some way with a quantum field. The response of this system then gives us information about the field properties. Typically such studies are done perturbatively, which presents several severe limitations on what may be investigated. We develop an alternative model, in which the detector is identified as a quantum harmonic oscillator, that allows non-perturbative solutions. We go on to apply this model to a variety of studies. We start by the examining the Unruh effect in a cavity setting. Not only are we able to examine the thermalization behavior of such a detector (which is stronger than what can be achieved perturbatively), we also demonstrate that the Unruh response is largely independent of the cavity boundary conditions, indicating a surprising amount of generality and universality to the phenomenon. We also consider the spacelike extraction of spatial entanglement by a set of such detectors. This includes the harvesting of genuine tripartite entanglement out of the vacuum, as well as the observation that the extractable quantum discord (a generalized measure of quantum correlations) can be greatly amplified by thermal fluctuations in the field, in opposite behavior to entanglement. This calls into question the nature of quantum discord, but also suggests at the possibility of actually using environmental noise as a quantum computational resource. Next, we use the oscillator detector model to great effect by proposing a method of reliably and sustainably generating and distributing entanglement via a cavity field. This protocol is inherently non-perturbative, and we refer to it as entanglement farming. Lastly, we modify the farming scenario to discover a very sensitive resonance effect that generates a large difference in the protocol output due to a minute change in system parameters, including the length of cavity being used. We put this forth as a potential method of quantum seismic metrology. The second model that we will consider simply involves performing projective measurements onto a given set of field modes. We will find, however, that such an approach allows us to solve previously intractable problems. In particular, we apply this procedure to the physically sensible choice of localized, positive frequency field modes. Using this model we perform two different studies. In the first, we consider the response of an observer accelerating not through the vacuum state but rather a thermal state. Such a setting has not been (properly) studied previously, due to the computational challenges involved. By applying the localized projective measurement model we are able determine that such an observer sees both an Unruh response from acceleration and a response from the field thermality and that, critically, these responses are distinguishable. We then go on to examine the degradation of quantum correlations between two observers due to the acceleration of one of the observers. This is a prototypical scenario of interest and, by applying realistic measurement assumptions, we obtain results qualitatively different from many previous works on the issue. In addition to these models, we question the nature of vacuum entanglement and particle creation by considering an operationally straightforward procedure that greatly demystifies these phenomena and puts them on to solid, physically concrete grounds. This operation is that of very quickly introducing a boundary condition onto one's field, for example by creating a mirror. The real particles generated in this process will then be quantum entangled with each other, even if they are created at spatially separate locations, and this entanglement derives exactly from the previously present vacuum entanglement. Not only does this realization provide an operationally satisfying interpretation of vacuum entanglement, it also suggests a straightforward procedure for its experimental verification. In all of this, the computational framework that we will rely upon is that of Gaussian quantum mechanics. This is a restriction of continuous variable quantum mechanics that, while limited in its applicability, provides extremely powerful computational tools in the cases that it may be used. The scenarios of interest in this thesis fall within this category and lend themselves naturally to a Gaussian approach. With this we are able to perform, near trivially, many otherwise intractable studies