It is possible to prepare classical optical beams which cannot be characterized by a tensor product of vectors describing each of their degrees of freedom. Here we report the experimental creation of such a non-separable, tripartite GHZ-like state of path, polarization and transverse modes of a classical laser beam. We use a Mach-Zehnder interferometer with an additional mirror and other optical elements to perform measurements that violate Mermin's inequality. This demonstration of a classical optical analogue of tripartite entanglement paves the path to novel optical applications inspired by multipartite quantum information protocols. PACS numbers:A composite quantum system is said to be entangled when it is not fully described by the state of its components [1]. Besides indicating a departure from classical physics, entangled states represent an important resource for a number of quantum information protocols [2]. In classical optics, the mode structure associated with different degrees of freedom of the wave field can also be described by complex vector spaces. As examples, an arbitrary polarization can be written as a complex superposition of circularly polarized beams, and the spatial configuration of a paraxial beam can be decomposed in terms of Laguerre-Gaussian beams. These degrees of freedom can be represented on two independent Poincaré spheres [3], in complete analogy with the Bloch sphere used to represent qubit states [2]. Intriguingly, also in classical optics there are field configurations which cannot be described as a tensor product of definite modes of each individual degree of freedom of the system [4]. These non-separable structures display a classical analogue of quantum entanglement [5][6][7][8]. One example are vector vortex beams, which are non-separable superpositions of transverse modes and polarization states of a laser beam [9][10][11]. This analogy was used to demonstrate the topological phase acquired by entangled states evolving under local unitary operations [12]. Recently, it has attracted a growing interest due both to the fundamental aspects involved, but also for potential applications to classical optical information processing [13][14][15][16][17][18][19][20]. Nonseparable structures have also proved their utility in the quantum optical domain [22][23][24][25][26][27][28][29][30][31][32][33]. Analogously to its quantum counterpart, classical entanglement has been characterized via the violation of Bell-like inequalities [34][35][36].Composite quantum systems may have more than two parts. For tripartite systems, Mermin [37] simplified an earlier argument by Greenberger, Horne and Zeilinger * Corresponding author.[38], to show that any local hidden-variable theory for tripartite systems must satisfy (1) where Z, Y, Z represent the Pauli operators. This inequality is violated by the so-called GHZ-Mermin state:for which ZZZ = +1 and ZXX = XZX = XXZ = −1, resulting in M = 4, the maximum algebraic violation of Mermin's inequality (1). In [39], Spreeuw proposed a scheme in which t...

We investigate the generation of entanglement between two non interacting qubits coupled to a common reservoir. An experimental setup was conceived to encode one qubit on the polarization of an optical beam and another qubit on its transverse mode. The action of the reservoir is implemented as conditional operations on these two qubits, controlled by the longitudinal path as an ancillary degree of freedom. An entanglement witness and the two-qubit concurrence are easily evaluated from direct intensity measurements showing an excellent agreement with the theoretical prediction.

We propose an all-optical experiment to quantify non-Markovianity in an open quantum system through quantum coherence of a single quantum bit. We use an amplitude damping channel implemented by an optical setup with an intense laser beam simulating a single-photon polarization. The optimization over initial states required to quantify non-Markovianity is analytically evaluated. The experimental results are in a very good agreement with the theoretical predictions.

Um importante fenômeno físico, com várias aplicações tecnológicas,é o conhecido efeito Doppler. Face a sua importância, esseé um tema comum em praticamente todos os livros de ensino médio e superior. Não obstante,é um tema de difícil abordagem experimental, principalmente em escolas que não possuem um laboratório didático bem equipado. Neste trabalho, apresentamos um experimento didático, que permita a medida da frequência Doppler para ondas sonoras. Para tal, utilizamos como recursos didáticos aparelhos que fazem parte do cotidiano dos alunos, a saber, tablets, smartphones e softwares livres. Acreditamos que a utilização destes aparelhos torna a proposta de "baixo custo"e acessível a grande parte das escolas brasileiras. Palavras-chave: Efeito Doppler, experimento de baixo custo, tablets e smartphones.An important physical phenomena, with many technology applications, is the Doppler effect. In view of its importance, this is a common subject in high school or college books. However, it is a subject of difficult experimental approach, mainly in schools that do not have a well equipped teaching laboratory. In this paper, we present a didactic experimental, that enable the measure of Doppler effect for sound waves. We use as didactic resources devices that are part of daily life of students, namely, tablets and smartphones. We believe that the use of these devices makes this a "low cost" proposal and accessible of the most Brazilians schools. Keywords: Doppler effect, low cost experiment, tablets and smartphones. IntroduçãoNosúltimos anos o ensino de física vem enfrentando um de seus maiores desafios: sua prática para uma geração de estudantes imersos na tecnologia e na facilidade de acessoà informação. A sala de aula atual na disciplina de física em qualquer segmento de ensino pode ser considerada a materialização do desafio citado. Neste sentido, abordagens que envolvam tecnologias de informação e comunicação (TIC's) tem grandes chances de despertar o interesse e, sobretudo, facilitar o diálogo entre professores e alunos [1,2]. Atualmente, muitos trabalhos têm explorado novas tecnologias para auxiliarà aprendizagem no ensino de física, podemos citar, trabalhos de modelagem computacional [3][4][5], simulação * Endereço de correspondência: wagner.balthazar@ifrj.edu.br.e experimentos virtuais [6][7][8][9], softwares [10-12] e vídeo-análise [13,14]. O uso de smartphones e tablets como instrumentos de medidas associadosà experimentação também tem sido investigados [15][16][17][18]. Esses recursos didáticos, quando utilizados em sala de aula, podem contribuir para enriquecer a abordagem didática e o processo ensino-aprendizagem.Os Parâmetros Curriculares Nacionais do Ensino Médio [19] trazem diretrizes para o ensino das ciências que valorizam a compreensão da natureza e as tecnologias, visando a inserção do educando na sociedade de forma a promover um exercício crítico da cidadania. Assim, temas que envolvem aplicações tecnológicas importantes são mais potencialmente significativos para os alunos. O efeito Doppler (ED...

We experimentally observed the violation of Kujula-Dzhafarov noncontextuality inequalities by non-separable spin-orbit laser modes. Qubits are encoded on polarization and transverse modes of an intense laser beam. A spin-orbit non-separable mode was produced by means of a radial polarization converter (S-plate). The results show that contextuality can be investigated by using spin-orbit modes in a simple way, corroborating recent works stating that such system can emulate singlephoton experiments. Additionally, an improvement in the non-separable mode preparation allowed us to observe a greater violation of the Clauser-Horne-Shimony-Holt inequality for such system. The results are in very good agreement with the theoretical predictions of quantum mechanics. arXiv:1807.05567v1 [quant-ph]