In this Bachelor’s thesis the following question is answered: Does the inequality posed in the article Klyachko et al [2008] cover the real part of the Bloch surface of a 3D quantum system when used as in Kochen and Specker [1967]? The Klyachko inequality relies on using five measurements to show contextuality of a subset of states on the real part of the Bloch surface. These can now be used in several configurations as present in the Kochen-Specker contextuality proof, by simply rotating the measurements. We show here that these new inequalities will have subsets of violation that eventually cover the entire real part of the Bloch surface. This can be extended to show that all states of a spin 1 system are non-contextual, so that we have recovered a state-independent contextuality proof by using the Klyachko inequality several times. In the final part, an interpretation of this is given and also some recommendations for further research that should be done in the field.

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We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This procedure is called (n,1,p) quantum random access code (QRAC) where p > 1/2 is its success probability. It is known that (2,1,0.85) and (3,1,0.79) QRACs (with no classical counterparts) exist and that (4,1,p) QRAC with p > 1/2 is not possible. We extend this model with shared randomness (SR) that is accessible to both parties. Then (n,1,p) QRAC with SR and p > 1/2 exists for any n > 0. We give an upper bound on its success probability (the known (2,1,0.85) and (3,1,0.79) QRACs match this upper bound). We discuss some particular constructions for several small values of n. We also study the classical counterpart of this model where n bits are encoded into 1 bit instead of 1 qubit and SR is used. We give an optimal construction for such codes and find their success probability exactly---it is less than in the quantum case. Interactive 3D quantum random access codes are available on-line at http://home.lanet.lv/~sd20008/racs

We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This procedure is called (n,1,p) quantum random access code (QRAC) where p > 1/2 is its success probability. It is known that (2,1,0.85) and (3,1,0.79) QRACs (with no classical counterparts) exist and that (4,1,p) QRAC with p > 1/2 is not possible. We extend this model with shared randomness (SR) that is accessible to both parties. Then (n,1,p) QRAC with SR and p > 1/2 exists for any n > 0. We give an upper bound on its success probability (the known (2,1,0.85) and (3,1,0.79) QRACs match this upper bound). We discuss some particular constructions for several small values of n. We also study the classical counterpart of this model where n bits are encoded into 1 bit instead of 1 qubit and SR is used. We give an optimal construction for such codes and find their success probability exactly---it is less than in the quantum case. Interactive 3D quantum random access codes are available on-line at http://home.lanet.lv/~sd20008/racs

Orientador: Flávio Caldas da Cruz / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-30T22:47:31Z (GMT). No. of bitstreams: 1 Depetri_WilliamIunes_M.pdf: 11907943 bytes, checksum: 4f7cedccb63e0fd32bea356921cb78f6 (MD5) Previous issue date: 2016 / Resumo: Pentes de frequência ópticos têm sido desenvolvidos para medias de precisão e metrologia, mas tabém vêm ganhando interesse para espectroscopia de precisão de banda larga. Pentes ópticos no infravermelho médio são muito atraentes para espectroscopia molecular, dado que eles permitem acesso a fortes bandas vibracionais de gases na chamada "região de digital molecular". Pentes ópticos são uma tecnologia bem desenvolvida no infravermelho próximo, dado a disponibilidade de lasers de Ti:Safira e Er-fiber, e apesar de desenvolvimentos recentes, sua extensão para o infravermelho médion depende de conversão não-linear de frequência. Aqui, pretendemos estudar a greração de pentes ópticos no infravermelho médio via geração de diferença de frequência e amplificação paramétrica óptica do espectro de um oscilador de femtosegundo no infravermelho próximo. Neste trabalho, analizamos numericamente difereça de frequência e amplificação paramétrica para a geração de pentes de frequência ópticos no infravermelho médio resolvendo no domínio do tempo as equações acopladas para o campo elétrico em mistura de três ondas para pulsos ultracurtos. Uma abordagem tradicional é a utilização de quasi-phase matching em cristais periodicamente polados, o que pode ser bastante eficiente, porém apresenta limitações na largura de banda. Nóis investigamos cristais periódicos com um período fixo, e cristais aperiódicos, ou chirped, tanto com chirp contínuo como discreto. Nós comparamos as configurações nas quais a amplificação paramétrica é otimizada ou não, explorando uma analogia entre conversãpo não-linear em sistemas de dois níveis. Nossos resultados são apresentados como gráficos temporais da propagação dos pulsos, seus respectivos espectros e potências ao longo dos cristais, e comparados com resultados experimentais, com o intuito de ajudar experimentos futuros / Abstract: Optical frequency combs (OFC) have been developed for precision measurements and metrology, but have also gained interest for broadband precision spectroscopy. OFC in the mid-infrared (MIR) are very attractive for molecular spectroscopy, since they allow to access the strong vibrational bands of gases in the so-called molecular fingerprint region. OFC are a well-developed technology in the near-infrared, due to the avilability of Ti:Saphire or Er-fiber lasers, and spite of recent developments, their extension into the MIR relies on nonlinear frequency conversion. Here we intend to study the generation of MIR OFC via difference frequency generation (DFG) and optical parametric amplification (OPA) of spectral portions of a near-infrared femtosecond oscillator. In this work, we numerically analyze DFG and OPA for the generation of optical frequency combs in the mid-infrared by solving the time-domain coupled wave equations for the electric fields in three-wave mixing for ultrashort pulses. A traditional approach is to use quasi-phase matching in periodically poled crystals, which can be quite efficient but may have bandwidth limitations.We investigate periodically poled crystals with a single-grating and aperiodic or chirped crystal with either continuous or discrete chirp. We compare the configurations in which a strong pump pulse has higher or smaller wavelength compared to the signal, cases in which the parametric amplification is enhanced or not. We also analyze these results in the context of adiabatic frequency conversion, which explores an analogy between nonlinear conversion and two-level systems. Our results are presented as time plots for the propagation of the pulses, their corresponding spectra and powers along the crystals and are compared to experimental results, and also intended to support further experiments / Mestrado / Física / Mestre em Física / 132987/2014-7 / CNPQ

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