In this thesis we demonstrate experimentally the implementation of quantum processes and simulation of complex dynamics, through the manipulation of a quantum system. Pairs of entangled photons generated by spontaneous parametric down conversion (SPDC) were used as the quantum system. The entangled state in the transversal path has been manipulated using programmable spatial light modulators (SLM). A nonlinear crystal with phase matching type I and a continuouslaser beam with wavelength in the violet region were used for the generation of twin photons in entangled path states that allow us to vary the Hilbert space dimension. Three quantum protocols were experimentally studied in this thesis: minimum Deutsch algorithm, entanglement concentration and simulation of dissipative dynamics. In the Deutsch algorithm implementation were used twin photons generated by SPDC and a double slit to encode a spatial qubit were used. The second photon was used as a trigger to prepare a conditional state of the first. The SLM was used as the oracle mentioned in the algorithm, i. e., it is responsible for implementing the balancedand constant functions. The entanglement concentration protocol for two-qutrit states was also implemented. Partially entangled path states were generated using SPDC along with a SLM that modules amplitude only. A second SLM phase modulator inside a Sagnac interferometer was used to implement the protocol using the method known as Procustean. The third protocol demonstrated experimentally was the simulation of two dissipative dynamics in qudits: dephasing and amplitude. One of the photons passes through a noisy channel, implemented using a SLM, and the transmitted state is characterized allowing us to identify the noisy channel properties.
In this thesis we demonstrate experimentally the implementation of quantum processes and simulation of complex dynamics, through the manipulation of a quantum system. Pairs of entangled photons generated by spontaneous parametric down conversion (SPDC) were used as the quantum system. The entangled state in the transversal path has been manipulated using programmable spatial light modulators (SLM). A nonlinear crystal with phase matching type I and a continuouslaser beam with wavelength in the violet region were used for the generation of twin photons in entangled path states that allow us to vary the Hilbert space dimension. Three quantum protocols were experimentally studied in this thesis: minimum Deutsch algorithm, entanglement concentration and simulation of dissipative dynamics. In the Deutsch algorithm implementation were used twin photons generated by SPDC and a double slit to encode a spatial qubit were used. The second photon was used as a trigger to prepare a conditional state of the first. The SLM was used as the oracle mentioned in the algorithm, i. e., it is responsible for implementing the balancedand constant functions. The entanglement concentration protocol for two-qutrit states was also implemented. Partially entangled path states were generated using SPDC along with a SLM that modules amplitude only. A second SLM phase modulator inside a Sagnac interferometer was used to implement the protocol using the method known as Procustean. The third protocol demonstrated experimentally was the simulation of two dissipative dynamics in qudits: dephasing and amplitude. One of the photons passes through a noisy channel, implemented using a SLM, and the transmitted state is characterized allowing us to identify the noisy channel properties.
We report an experimental implementation of the minimal Deutsch algorithm in an optical setting. In this version, a redundancy is removed from the most famous form of the algorithm. The original version involves manipulation of two qubits, while in its minimal version, only one qubit is used. Our qubit is encoded in the transversal spatial modes of a spontaneous parametric down-converted signal photon, with the aid of a double slit, with the idler photon playing a crucial role in creating a heralded single-photon source. A spatial light modulator (SLM) is programmed to physically generate one-bit functions necessary to implement the algorithm's minimal version, which shows that the SLM can be used in future implementations of quantum protocols.
In this work we implement the Deutsch-Jozsa algorithm with one qubit by removing a redundancy on it, which reduces the size of the register and simpli es the function evaluation. In order to do this, we used a pair of photons produced by down convertion, where one of them is used as triguer and the other passes trougth a double slit; as result its output is in a superposition of paths, i.e., one qubit. Using a spatial light modulator (SLM) that puts phases on the paths of the photons, and detecting in coincidence, we demonstrate the Deutsch-Jozsa algorithm with photons, and using only one qubit.
During the past thirty years the field of Quantum Information has beenvery successful in proposing protocols and algorithms that involve two-level quantum systems known as qubits. It has been shown that cryptographic keys can be distributed securely using quantum resources and that quantum algorithms can solve tasks such as the factoring of large numbers with an exponential speedup over classical algorithms. Most implementations, however, are restricted to proof-of-concept experiments using few qubits, due to the difficulty of scaling the physical systems utilized. Quantum systems with more than two levels, called qudits, present themselves as an alternative way of obtaining a space with large dimensionality without recurring to a large number of qubits. This reduces the number of particles necessary for implementing protocols in a scale that is relevant for practical applications. Additionally, pairs of entangled qudits are more robust agains noise than their qubit counterparts and are also more adequate for experiments that test the non-local and contextual behavior of nature, as predicted by its description using Quantum Mechanics. In this thesis we present the construction and characterization of a source of states of four qudits. We used a pulsed laser as pump for type-II Spontaneous Parametric Down Conversion (SPDC) to occur on a PPKTP, a KTiOPO4 (KTP) crystal with a periodic ferroelectric domain inversion, a technique called periodic poling. In type-II SPDC a pair of photons, also called biphoton, is generated in which one has horizontal polarization while the other hasvertical polarization. Due to the use of a pulsed pump beam and the highdown-conversion efficiency of our PPKTP, the probability that a single pump pulse will originate two pairs of photons is high. In order to generate qudits we used the multiple-slit implementation, meaning that a multiple slit was placed between the PPKTP and the detectors, encoding discrete qudit states onto the continuous transverse mode of the biphoton. Using double, triple and quadruple slits we produced, respectively, qubit, qutrit and ququart states. A system of lenses placed between the PPKTP and the slits manipulated the amplitude of the transverse biphoton state impinging on the slits and, thus, the quantum correlations between qudits after the slits. By projecting either the near or far field of the crystal onto the slits, the lenses changed the characteristics of the biphoton amplitude function and allowed us to obtain either states with very high entanglement, in the case of the near field, or very low entanglement, in the case of the far field. A lens in the f-f configuration between the plane of the slits and the plane of the detectors projected the far field of the slits, so we could observe conditional interference patterns. We detected the photons in coincidence asa function of the position of two detectors These were used to generate maps of coincidences between two photons with different polarization and for two photons with the same polarization. The first case contains contributions from photons of a single pair and from photons from two different pairs, while the second case contains contributions from different pairs only. In order to isolate the single pair contribution on different-polarization coincidences, we removed the background component from photons of different pairs, given by the same-polarization coincidences. Besides serving to isolate the singlepair signal, same-polarization coincidences confirm the existence two-pair events and give us information about the purity of the reduced state of a single photon, which is related to the degree of entanglement in a biphoton. We conclude that manipulating the biphoton transverse amplitude is a promising technique for generating qudit states while controlling their entanglement and correlation properties, especially if more exotic transverse amplitudes are explored, such as Hermite-Gaussian pump beams or amplitudes engineered with a spatial light modulator. The use of high-efficiency SPDC sources allows for states of more than one biphoton, engineered using transverse amplitude manipulation, to be employed in many different protocolsin Quantum Information, serving as sources of heralded pure or mixedstates, or playing an important role in tests of the non-local and contextual nature of physical systems, as predicted by Quantum Mechanics.
The goal of this thesis is to study the generation, characterization and evolution of photonic and atomic quantum states generated by spontaneous parametric down conversion (SPDC) and by a cold atomic beam of rubidium. Photons generated by SPDC are entangled in transversal path after passing through mutiple slits. Two qubit and two qutrit states are generated and their density operator are obtained by minimum quantum state tomography. An discussion about the amount of entanglement and the quality of the experimentally obtained density operator is performed. Through the interaction between a cold atomic beam with a light beam inside a cavity in the quantum electrodynamics regime and in the presence of a external magnetic eld, a superposition of the magnetic sublevels of the ground state of 85Rb is generated detecting a photon with horizontal polarization. Measuring the intensity correlation function by a homodyne process a conditional quantum beat of the ground state superposition is observed. Through a quantum feedback protocol, an study of evolution and how to preserve coherence is done.
We experimentally perform the simulation of open quantum dynamics in single-qudit systems. Using a spatial light modulator as a dissipative optical device, we implement dissipative-dynamical maps onto qudits encoded in the transverse momentum of spontaneous parametric down-converted photon pairs. We show a well-controlled technique to prepare entangled qudits states as well as to implement dissipative local measurements; the latter realize two specific dynamics: dephasing and amplitude damping. Our work represents a new analogy-dynamical experiment for simulating an open quantum system.
In this thesis, we explore the properties of photons generated by parametric down-conversion (PDC) and entangled in continuous variables of transverse momentum, with the aim of using this degree of freedom for developing a new method for generating en-tangled states in discrete and multidimensional spaces. Such states have a great potential for applications in fundamental problems of quantum mechanics as well as in quantum information protocols. Our study is based on the theory of angular spectrum transfer from the laser beam tothe two-photon state, proposed and demonstrated by Monken, Souto Ribeiro and P Ladua [Phys. Rev. A 57, 3123 (1998)]. Using it, we investigate theoretically the evolution of the quantum state of photon pairs when they propagate from the crystal and are transmitted through linear optical systems like lenses and apertures. The two-photon state is calculated when there is only one optical system in the path of each photon and we also discuss the generalization of the method employed in the calculation, for more complex experiments. With the two-photon state obtained, we propose a method for generating entangledstates of qubits (two-dimensional quantum systems) and qudits (D-dimensional quantum systems), using the transverse momentum of photons from PDC. The method is based on the selection of specific transverse spatial modes of each photon, by using an array of D-slits (D . 2) in the path of these photons. In this method we have the control of the dimension, D, of each qudit and also the degree of entanglement between them, by manipulating the transverse laser beam profile, which is due to the transfer of angular spectrum. In order to test the theory, we make an experiment for a specific case, which has a great interest in practical applications of entanglement: we demonstrate the generation of maximally entangled states of qudits with D = 4 and D = 8. The quantum character of the correlations is assured qualitatively by measuring two-photon interference patterns with conditional fringes. We also investigate the propagation of these entangled states of qudits through free space and with a simple experiment we show that they can be distributed for distant and spatially separated parts, keeping the correlations. Finally, we perform an experiment for quantifying entanglement in this type of state that we are producing. In this work, we restrict ourselves to the simplest case of two qubits. We prepare different states by manipulating the transverse laser beam profile and their degree of entanglement is measured in two ways: (i) through the degree ofconditionality of the two-photon interference patterns and (ii) through the measurement of marginal probability. We discuss the extension of the method (i) for two-qudit states.