<p>Quantum entanglement is employed as a resource throughout quantum information science. However, before entanglement can be put to intelligent use, the issues of its production and detection must be considered. This thesis proposes four schemes for producing the bound entangled Smolin state. Three of these schemes produce the Smolin state by means of general quantum gates acting on different initial states - an all-zero state, a GHZ-state and two combined Bell states. The fourth scheme is based on one-qubit operations acting on two-photon states produced by SPDC. Furthermore, a maximum overlap entanglement witness detecting entanglement in the Smolin state is derived. This witness is measurable in three measurement settings with the maximal noise tolerance p=2/3. Lastly, simplified entanglement witnesses for the 4-, 6- and 8-qubit unitary invariant states are derived. These witnesses are measurable in three measurement settings with noise tolerances p=0.1802..., p=0.1502... and p=0.0751..., respectively.</p>

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Entanglement are the non-local correlations permitted by quantum theory, believed to play a fundamental role in a quantum computer. We have investigated these correlations in a number of theoretical models for condensed matter systems. Such systems are likely candidates for quantum computing, and experimentally feasible for instance as superconducting qubits. At quantum critical points the ground state of these systems is very complicated, and the entanglement is usually larger than at non-critical points. This entanglement can be used to identify the critical points through what we denote the entanglement signature, even for very small systems. From another perspective, it seems that the entanglement is an essential tool to find an unknown ground state, since this gives rise to a simple decomposition of the state.

The group theory allows one to study different branches of physics using the same set of commutation relations. It is shown that a formulation of the polarization optics that depends on the representations of the Lorentz group is possible. The set of four Stokes parameters, which is a standard tool of polarization optics, can be used to form a four-vector that is physically unrelated but mathematically equivalent to the space-time four-vector of the special relativity. By using the Stokes parameters, it is also possible to generate four-by-four matrix representations of the ordinary optical filters that are traditionally represented with the two-by-two Jones matrices. These four-by-four matrices are treated as the entities of the Lorentz group. They are like the Lorentz transformations applicable to the four-dimensional polarization space. Besides, optical decoherence process can be formulated within the framework of the SO(3,2) de Sitter group. The connection between the classical and quantum mechanical descriptions of the polarization of light allows the extension of the Stokes parameters to the quantum domain. In this respect, the properties of the polarization of the two-photon system can also be studied within the framework of the Lorentz group.

While there are exemplary studies on the relationships between social networks and media such as television and the Internet, less is known about the social network consequences of mobile phone use during life-stage transitions. This study investigates the roles that mobile phones play in supporting the relationships of young people as they transition to and through their first-year of university in Toronto, Canada. Focussing on information practices during a transition that tests the resilience of support networks, this study queried the extent to which mobile phones play a role in keeping relationships intact, enabling students to maintain a sense of social cohesion and belonging. Data were collected from November 2007 to September 2008 through a longitudinal research design. Socio-technical concepts and network analysis techniques were applied to analyze the ways in which mobile communication is embedded in the everyday social life of young people aged 17-34. Set within the culturally-specific context of urban Canada, the data provided substantial evidence that mobile phones foster social cohesion within intimate relations but provide a more tenuous platform from which to nurture new relationships. First-year undergraduates have integrated the mobile phone into the way they engage with their social networks to a considerable degree, with commuter students experiencing additional tensions in negotiating relationships from home and on-campus. Findings showed that mobile phones were the devices of choice to mitigate feelings of loneliness, with deleterious consequences for the development of new relationships. Furthermore, the mobile phone was a key contributor to a rising sense of empowerment and autonomy for young adults as they negotiated identity transformations during their rite of passage into adulthood. Issues of trust and reciprocity in forming new relationships were mediated through a continuum of social media of which the mobile phone was the most intimate. Evidence of continuous access to social networks has broader implications for how mechanisms for coping with being alone and disconnection are acquired in this generation. Finally, observations of ritualistic interaction practices involving mobile phones may be theorized as small-scale evidence of larger societal shifts from collective constructs of community to that of networked individuals.

While there are exemplary studies on the relationships between social networks and media such as television and the Internet, less is known about the social network consequences of mobile phone use during life-stage transitions. This study investigates the roles that mobile phones play in supporting the relationships of young people as they transition to and through their first-year of university in Toronto, Canada. Focussing on information practices during a transition that tests the resilience of support networks, this study queried the extent to which mobile phones play a role in keeping relationships intact, enabling students to maintain a sense of social cohesion and belonging. Data were collected from November 2007 to September 2008 through a longitudinal research design. Socio-technical concepts and network analysis techniques were applied to analyze the ways in which mobile communication is embedded in the everyday social life of young people aged 17-34. Set within the culturally-specific context of urban Canada, the data provided substantial evidence that mobile phones foster social cohesion within intimate relations but provide a more tenuous platform from which to nurture new relationships. First-year undergraduates have integrated the mobile phone into the way they engage with their social networks to a considerable degree, with commuter students experiencing additional tensions in negotiating relationships from home and on-campus. Findings showed that mobile phones were the devices of choice to mitigate feelings of loneliness, with deleterious consequences for the development of new relationships. Furthermore, the mobile phone was a key contributor to a rising sense of empowerment and autonomy for young adults as they negotiated identity transformations during their rite of passage into adulthood. Issues of trust and reciprocity in forming new relationships were mediated through a continuum of social media of which the mobile phone was the most intimate. Evidence of continuous access to social networks has broader implications for how mechanisms for coping with being alone and disconnection are acquired in this generation. Finally, observations of ritualistic interaction practices involving mobile phones may be theorized as small-scale evidence of larger societal shifts from collective constructs of community to that of networked individuals.

This thesis considers entanglement, an important resource for quantum information processing tasks, while taking into account the theory of relativity. Not only is this a more complete description of quantum information, but it is necessary to fully understand quantum information processing tasks done by systems in arbitrary motion. It is shown that accelerated measurements on the vacuum of a free Dirac spinor field results in an entangled state for an inertial observer. The physical mechanism at work is the Davies-Unruh effect. The entanglement produced increases as a function of the acceleration, reaching maximal entanglement in the asymptotic limit of infinite acceleration. The dynamics of entanglement between two Unruh-DeWitt detectors, one stationary and the other undergoing non-uniform acceleration, was studied numerically. In the ultraweak coupling limit, the entanglement decreases as a function of time for the parameters considered and decreases faster than if the moving detector had had a uniform acceleration.

This thesis is divided into two parts. In Part I we introduce a new formalism for quantum strategies, which specify the actions of one party in any multi-party interaction involving the exchange of multiple quantum messages among the parties. This formalism associates with each strategy a single positive semidefinite operator acting only upon the tensor product of the input and output message spaces for the strategy. We establish three fundamental properties of this new representation for quantum strategies and we list several applications, including a quantum version of von Neumann's celebrated 1928 Min-Max Theorem for zero-sum games and an efficient algorithm for computing the value of such a game. In Part II we establish several properties of a class of quantum operations that can be implemented locally with shared quantum entanglement or classical randomness. In particular, we establish the existence of a ball of local operations with shared randomness lying within the space spanned by the no-signaling operations and centred at the completely noisy channel. The existence of this ball is employed to prove that the weak membership problem for local operations with shared entanglement is strongly NP-hard. We also provide characterizations of local operations in terms of linear functionals that are positive and "completely" positive on a certain cone of Hermitian operators, under a natural notion of complete positivity appropriate to that cone. We end the thesis with a discussion of the properties of no-signaling quantum operations.

This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational purposes, it has been used to explain and control the dynamics in various physical systems. In order to use the quantum walk to its fullest potential, it is important to know and optimize the properties purely due to quantum dynamics and in presence of noise. Various studies of its dynamics in the absence and presence of noise have been reported. We propose new approaches to optimize the dynamics, discuss symmetries and effect of noise on the quantum walk. Making use of its properties, we propose the use of quantum walk as an efficient new tool for various applications in physical systems and quantum information processing. In the first and second part of this dissertation, we discuss evolution process of the quantum walks, propose and demonstrate the optimization of discrete-time quantum walk using quantum coin operation from SU(2) group and discuss some of its properties. We investigate symmetry operations and environmental effects on dynamics of the walk on a line and an $n-$cycle highlighting the interplay between noise and topology. Using the properties and behavior of quantum walk discussed in part two, in part three we propose the application of quantum walk to realize quantum phase transition in optical lattice, that is to efficiently control and redistribute ultracold atoms in optical lattice. We also discuss the implementation scheme. Another application we consider is creation of spatial entanglement using quantum walk on a quantum many body system.

Quantum entanglement is employed as a resource throughout quantum information science. However, before entanglement can be put to intelligent use, the issues of its production and detection must be considered. This thesis proposes four schemes for producing the bound entangled Smolin state. Three of these schemes produce the Smolin state by means of general quantum gates acting on different initial states - an all-zero state, a GHZ-state and two combined Bell states. The fourth scheme is based on one-qubit operations acting on two-photon states produced by SPDC. Furthermore, a maximum overlap entanglement witness detecting entanglement in the Smolin state is derived. This witness is measurable in three measurement settings with the maximal noise tolerance p=2/3. Lastly, simplified entanglement witnesses for the 4-, 6- and 8-qubit unitary invariant states are derived. These witnesses are measurable in three measurement settings with noise tolerances p=0.1802..., p=0.1502... and p=0.0751..., respectively.