Neste trabalho estudamos as propriedades de emaranhamento dos estados de dois quasifótons de frequências diferentes, fazendo a aproximação de que o vácuo de quasifótons é igual ao vácuo de fótons, no caso em que não temos campo externo algum e no caso da presença de um campo magnético externo, constante e homogêneo. Estudamos também as propriedades de emaranhamento do próprio vácuo de quasifótons e dos estados de dois quasifótons no caso monocromático, sem campo externo e com o vácuo de quasifótons levado em conta exatamente. / In this work we study the properties of entanglement of the states of two quasi-photons of different frequencies, considering the approximation that the quasi-photon\'s vacuum is equal the photon\'s vacuum, in the case where we have no external field and in the case where we have an external, constant and homogeneous magnetic field. We study also the properties of entanglement of the quasi-photon\'s vacuum and of the states of two quasi-photons in the monochromatic case, without external field and with the quasi-photon\'s vacuum considered exactly.

acase@tulane.edu / In this dissertation we test our ability to implement linear entangling operations between small numbers of photons for application in quantum communication and computation. We begin by presenting a fast and highly parallelizable numerical algorithm for simulating linear optical circuits on classical hardware. Then, we apply this algorithm to three independent topics in quantum information: First, in Chapter 2, we determine the information capacity of an optical quantum channel and show that a linear encoding is generally sufficient to achieve this capacity. In Chapter 3 we introduce a computational encoding basis wherein qubits are stored in single-photon blocks and then test our ability to apply entangling operations between blocks. Finally, in Chapter 4, we use our algorithm to make progress in the long-standing problem of designing a near-perfect optical Bell state analyzer. We find a clear trend in state distinguishability as we incorporate unentangled pairs of ancilla photons. We also prove that if a measurement outcome in which all photons are bunched into only two output modes is possible, then perfect state discrimination is impossible. We then present a set of conditions that prevent this outcome. / 1 / Jake A Smith

In this thesis, I study bipartite discord between A and B in terms of the structure formed by the bipartite and tripartite entanglement found in the purified system ABC. I find that discord manifests itself only when there is both tripartite and bipartite entanglement present in the purification. This allows one to understand the asymmetry of quantum discord, D(A|B) ≠ D(B|A) in terms of entanglement monogamy. For the cases where AB has rank two and for two-mode Gaussian states, I find that discord also necessarily appears whenever there is tripartite and bipartite entanglement in ABC. As a result of this, some light is shed on a counter-intuitive property of Gaussian states: the presence of classical correlations necessarily requires the presence of quantum discord. Finally, these results are found to be closely linked to the protocol for remote activation of entanglement by a third party.

This thesis investigates three areas of the theory of graph homomorphisms: cores of graphs, the homomorphism order, and quantum homomorphisms. A core of a graph X is a vertex minimal subgraph to which X admits a homomorphism. Hahn and Tardif have shown that, for vertex transitive graphs, the size of the core must divide the size of the graph. This motivates the following question: when can the vertex set of a vertex transitive graph be partitioned into sets which each induce a copy of its core? We show that normal Cayley graphs and vertex transitive graphs with cores half their size always admit such partitions. We also show that the vertex sets of vertex transitive graphs with cores less than half their size do not, in general, have such partitions. Next we examine the restriction of the homomorphism order of graphs to line graphs. Our main focus is in comparing this restriction to the whole order. The primary tool we use in our investigation is that, as a consequence of Vizing's theorem, this partial order can be partitioned into intervals which can then be studied independently. We denote the line graph of X by L(X). We show that for all n ≥ 2, for any line graph Y strictly greater than the complete graph Kₙ, there exists a line graph X sitting strictly between Kₙ and Y. In contrast, we prove that there does not exist any connected line graph which sits strictly between L(Kₙ) and Kₙ, for n odd. We refer to this property as being ``n-maximal", and we show that any such line graph must be a core and the line graph of a regular graph of degree n. Finally, we introduce quantum homomorphisms as a generalization of, and framework for, quantum colorings. Using quantum homomorphisms, we are able to define several other quantum parameters in addition to the previously defined quantum chromatic number. We also define two other parameters, projective rank and projective packing number, which satisfy a reciprocal relationship similar to that of fractional chromatic number and independence number, and are closely related to quantum homomorphisms. Using the projective packing number, we show that there exists a quantum homomorphism from X to Y if and only if the quantum independence number of a certain product graph achieves |V(X)|. This parallels a well known classical result, and allows us to construct examples of graphs whose independence and quantum independence numbers differ. Most importantly, we show that if there exists a quantum homomorphism from a graph X to a graph Y, then ϑ̄(X) ≤ ϑ̄(Y), where ϑ̄ denotes the Lovász theta function of the complement. We prove similar monotonicity results for projective rank and the projective packing number of the complement, as well as for two variants of ϑ̄. These immediately imply that all of these parameters lie between the quantum clique and quantum chromatic numbers, in particular yielding a quantum analog of the well known ``sandwich theorem". We also briefly investigate the quantum homomorphism order of graphs.

This thesis investigates techniques for the automated optimization of quantum circuits. In the first part we develop an exponential time algorithm for synthesizing minimal depth quantum circuits. We combine this with effective heuristics for reducing the search space, and show how it can be extended to different optimization problems. We then use the algorithm to compute circuits over the Clifford group and T gate for many of the commonly used quantum gates, improving upon the former best known circuits in many cases. In the second part, we present a polynomial time algorithm for the re-synthesis of CNOT and T gate circuits while reducing the number of phase gates and parallelizing them. We then describe different methods for expanding this algorithm to optimize circuits over Clifford and T gates.

Quantum information processing devices promise to solve some problems more efficiently than their classical counterparts. The source of the speedup is the structure of quantum theory itself. In that sense, the physical units that are the building blocks of such devices are its power. The quest then is to find or manufacture a system that behaves according to quantum theory, and yet is controllable in such a way that the desired algorithms can be implemented. Candidate systems are benchmarked against general criteria to evaluate their success. In this thesis, I advance a particular system and present the progress made towards each of these criteria. The system is a three-qubit 13C solid-state nuclear magnetic resonance (NMR) based quantum processor. I report results concerning system characterization and control, pseudopure state preparation, and quantum error correction. I also report on using the system to test a central question in the foundation of quantum mechanics.

Currently, a major challenge for solid-state spin qubit systems is achieving one-qubit operations on a timescale shorter than the spin coherence time, T2*, a goal currently two orders of magnitude away. By taking advantage of the quasi-one-dimensional structure of a nanowire and the strong spin-orbit interaction of InAs, it is estimated that π-rotations can be implemented using electric dipole spin resonance on the order of 10 ns. To this end, a procedure for the fabrication of homogeneous InAs nanowire quantum dot devices is presented herein for future investigations of solid state spin qubits as a test bed for quantum computing. Both single and double quantum dot systems are formed using local gating of InAs nanowires. Single quantum dot systems were characterized through electron transport measurements in a dilution refrigerator; in one case, the charging energy was measured to be 5.0 meV and the orbital energy was measured to be 1.5-3.5 meV. The total capacitance of the single quantum dot system was determined to be approximately 30 aF. An estimate of the quantum dot geometry resulting from confinement suggests that the quantum dot is approximately 115 nm long. The coupling energy of the double quantum dot system was measured to be approximately 4.5 meV. The electron temperature achieved with our circuitry in the dilution refrigerator is estimated to be approximately 125 mK.

In this thesis, we develop a number of operational tests and tools for benchmarking the quantum nature of optical quantum communication devices. Using the laws of quantum physics, ideal quantum devices can fundamentally outperform their classical counterparts, or even achieve objectives which are classically impossible. Actual devices will not be ideal, but they may still be capable of facilitating quantum communication. Benchmarking tests, based on the presence of entanglement, can be used to verify whether or not imperfect quantum devices offer any advantage over their classical analogs. The general goal in this thesis is to provide strong benchmarking tools which simultaneously require minimal experimental resources but also offer a wide range of applicability. Another major component is the extension of existing qualitative benchmarks (`Is it quantum or classical?') to more quantitative forms (`How quantum is it?'). We provide a number of benchmarking results applicable to two main situations, namely discrete remote state preparation protocols and continuous-variable quantum device testing. The theoretical tools derived throughout this thesis are also applied to the tasks of certifying a remote state preparation experiment and a continuous-variable quantum memory.

<p>Among the various physical systems considered for scalable quantum information processing (QIP), individually trapped ions or neutral atoms have emerged as promising candidates. Recent experiments using these systems have demonstrated the basic building blocks required for a useful quantum computer. In many of these experiments, precisely tuned lasers control and manipulate the quantum bit (qubit) represented in the electronic energy levels of the ion or atom. Scaling these systems to the necessary number of qubits needed for meaningful calculations, requires the development of scalable optical technology capable of delivering laser resources across an array of ions or atoms. That scalable technology is currently not available.</p><p>In this dissertation, I will report on the development, design, characterization, and implementation of an optical beam steering system utilizing microelectromechanical systems (MEMS) technology. Highly optimized micromirrors enable fast reconfiguration of multiple laser beam paths which can accommodate a range of wavelengths. Employing micromirrors with a broadband metallic coating, our system has the flexibility to simultaneously control multiple beams covering a wide range of wavelengths. </p><p>The reconfiguration of two independent beams at different wavelengths (780 and 635 nm) across a common 5x5 array of target sites is reported along with micromirror switching times as fast as 4 us. The optical design of the system minimizes residual intensity at neighboring sites to less than 40 dB below the peak intensity. Integration of a similar system into a neutral atom QIP experiment is reported where 5 individually trapped atoms are selectively manipulated through single qubit rotations with a single laser source. This demonstration represents the first application of MEMS technology in scalable QIP laser addressing.</p> / Dissertation

In this thesis, we explore the quantum dynamics of light interactions with optically thick collections of atoms. We provide a theoretical description of several recent experiments in which some key operations necessary for the implementation of quantum communication networks are demonstrated. Collective Raman scattering from an atomic ensemble is shown to produce probabilistic entanglement between the polarization of a scattered photon and an associated collective atomic excitation. The predicted correlations agree with experimental observations. We also propose a method to use cascade transitions to produce entanglement between a photon with a frequency in the telecom range (ideal for transmission over optical fibers) and a near infrared photon (ideal for storage in an atomic ensemble), and a description of the experimental demonstration is provided. We also propose and describe the implementation of a deterministic source of single photons. In addition, we generalize the theory of dark-state polaritons in ensembles of three level Lambda atoms to account for the nuclear spin degeneracy of alkali atoms. This generalized theory provides a description of the first demonstration of single photon storage and retrieval from atomic ensembles. Additionally, in the presence of a uniform magnetic field, we predict the occurrence of collapses and revivals of the photon retrieval efficiency as a function of storage time within the ensemble. These predictions are in very good agreement with subsequent experimental observations. We also exploit the ability of photon storage to entangle remote atomic qubits.