Quantum entanglement rapidly becomes unwieldy to calculate as the number of particles

and the dimension of the spaces associated to those particles increase. One meaningful approach

which simplifies that analysis is the restriction to subsets of states which obey some physically

relevant symmetry. In this thesis, entanglement properties of totally permutation-symmetric,

translationally invariant, and party-site symmetric states are examined, as well as those of small

bond-dimensional matrix product states.

This paper is about the politics of claiming credit. Effectively taking the credit for some desirable outcome is an essential element of politics. In tightly controlled, closed, polities, both mythic and real, leaders control the mass media in order to present a coherent, consistent, self-serving and state-serving narrative that ascribes responsibility and blame. This paper explores the disparities in success at claiming credit, with the intent of explaining why some challengers end up deriving credit both in the short and long term for their efforts, while others do not. I begin by looking at the question of the outcomes of social movements, briefly reviewing the relevant literature, which focuses predominantly on public policy. I move to the literature on public policy, examining the difficulties in assessing success or failure of policies. I then identify a number of variables, including goals, political positioning, coalition politics, and constituencies, that explain why some movements have a harder time claiming credit than others. I conclude by suggesting that the positioning of institutional actors, and the degree of their identification with a social movement, is critical to the movement's capacity to claim success.

The content and the process of making policy serve as both stimuli and outcomes of social movements. Understanding these relationships, that is, how policy and citizen movements affect each other, is essential to understanding the functioning of contemporary democratic politics and indeed, the democratic process more broadly. Although scholars of both social movements and of public policy have acknowledged the importance of the others' work, they have not gone much beyond acknowledgment. Unfortunately, this leaves fundamental issues in the study of political participation and influence underdeveloped theoretically and understudied empirically. In this paper, I offer a dialogic model of the mutual influence of protest and policy, which emphasizes the interaction of activist efforts and the policy process, and the dynamics of political coalitions inside and outside established political institutions. Focused attention to the theoretical and practical problems of understanding the relationship between policy and movements.

This dissertation provides a study of complex networks within a hyperbolic latent space model. We present, to our knowledge, the first theoretical analysis of popular link prediction indices on graphs in hyperbolic space. In network and graph analysis, nodes with different degrees are usually handled differently. For instance, when two individuals are both connected to a celebrity, it is often considered less likely that they know each other compared to a scenario in which they are both connected to an ordinary person. In this dissertation, we explore the reason behind this heuristic and analyze some popular link prediction indices through a hyperbolic graph model. Specifically, in this model, we identify the optimal weighted scheme for the common neighbor index and extend our findings to the shortest path index and some other indices, thereby introducing modifications to these methods. Empirical results demonstrate that our findings hold true not only in theory, i.e., for simulated data, but also in real-world networks. Moreover, we also explore different embedding methods to recover the underlying hyperbolic geometry from resulting graphs. By comparing different methods, we found that ordinal embedding effectively recovers the latent geometry of networks. Building on this, we proposed a modified ordinal embedding method that integrates the insights from our theoretical analysis. This enhancement further improves our ability to capture and represent the underlying hyperbolic structure of complex networks. This dissertation aims to enhance the understanding of complex networks, offering new perspectives and tools to analyze them effectively. Through a blend of theoretical rigor and practical experimentation, we provide a comprehensive study that contributes to the broader field of network science.

We propose a novel approach to holographic quantum error-correcting codes by replacing perfect tensors with alternative tensors at each node with a small probability. Specifically, we employ repetition tensors as alternatives. The boundary states of our models capture key features of conformal field theory states, particularly the power law of the two-point function and logarithmic entanglement, which are precisely obeyed in many cases. The noisy holographic quantum error-correcting codes on trees and tilings of two-dimensional hyperbolic space preserve the bulk/boundary duality in AdS/CFT, and their boundary states exhibit the features of conformal field theory accordingly.

Quantum computing is a system of computation that exploits the quantum-mechanical nature of reality at nano-scales in order to perform certain operations in a way that can scale better than is possible with classical computing. While the hardware side

of quantum computing is still in its infancy, many quantum algorithms - sets of instructions to run on a quantum computer in order to complete particular tasks - have been designed and analyzed. One of the most famous of these is Grover’s algorithm, an algorithm for searching a database. Two types of generalizations of Grover’s algorithm have been studied: spatial search algorithms (algorithms for searching discrete spaces) and “analog” search algorithms (algorithms performed by the evolution of physical systems). We develop and analyze algorithms that are generalizations of both those generalizations – an analog search algorithm for searching continuous, rather than discrete, spaces.

Activists often claim that science is on their side, even when scientists themselves seem to disagree. This dissertation explores when, why, and how activists make science claims in political venues. When science is used to challenge a movement, activists must demonstrate that their claims are scientific to a broader public—including people with little knowledge of the relevant research. To do so, activists seek out scientific resources as proof that their claims are scientifically sound. How activists form their claims is shaped by the movement’s access to mainstream scientific resources: the experts, publications, and statements that are seen as credible by mainstream scientific institutions. These institutions function as scientific gatekeepers, determining what does and does not qualify as science. Thus, resources approved by these sources can reassure lay audiences that a claim is backed by real science.

When movements enjoy mainstream scientific resources, activists rely on these resources to make their case. When movements lack scientific resources, they must find or create new resources that support their stance. But critically, what is considered mainstream science can change over time. Thus, activists can cultivate new mainstream resources. If these attempts fail, activists will create alternative scientific resources: experts, publications, and associations that are not recognized by scientific gatekeepers, but may be seen as scientific by lay people. Since movements can develop their own scientific resources, they are unlikely to concede. Instead, the use of science by one movement encourages the creation of new scientific resources by its opponents.

I explore these dynamics using the case of LGBT conversion therapy. Critically, the position of scientific gatekeepers on conversion therapy has changed over the past sixty years. As a result, both sides have been in the position of enjoying mainstream scientific resources, and of lacking these resources. Thus, the case illuminates how activists deploy scientific resources, develop new resources, and adapt their strategies in response to changing scientific and political contexts.

Encoding the state of physical systems, the many-body wavefunction lives in a Hilbert space that conveniently offers a tensor factor to each constituent of the system. Consequentially, the wavefunction inherits structural properties such as entanglement, a new type of quantum correlation across the tensor factors. Entanglement can be quantified by forming polynomials in the wavefunction that remain invariant under local operations, which in turn naturally imply the properties we intuit about entanglement. It follows from the Tarski-Seidenberg theorem that these polynomial entanglement measures must obey polynomial constraints. It is among these constraints that the core features separating quantum correlations from classical correlations are illuminated, such as their monogamous nature. The smallest non-trivial system which exhibits entanglement monogamy tradeoffs governed by polynomial constraints is three qubits, for which we find novel constraints that are stronger than the previously known constraints, and which may as well be a complete description of three-qubit entanglement since the number of degrees of freedom matches the number of entanglement measures. A remarkable redundancy known in three qubits is that any party's total entanglement decomposes exactly into bipartite and tripartite type entanglement; we find that this behavior is merely part of the GHZ family tradition, and that any party within the n-qubit GHZ SLOCC equivalence class also has total entanglement which decomposes exactly into all k-partite type entanglements, thus providing insight into strong versions of monogamy relations. Refocusing back to tripartite systems, we then suppose arbitrarily many degrees of freedom into our subsystems, which appear to refuse all temptations of polygamy. Up to this point we have only been considering idealized isolated systems as it is known that monogamy relations aren't sensitive to the total purity, however we then find entanglement constraints which are violated by globally mixed states, ultimately suggesting that environments can enable entanglement to grow beyond what is otherwise allowed. Finally, we address the dynamical behavior of entanglement under several key interactions, and characterize the couplings according to their ability to generate entanglement.

Coalitions and collaborations can improve organizations’ chances of affecting political change. However, competition for resources, incongruent collective identities, ideological disputes, incompatible organizational structures, and interpersonal conflict often prevent social movement organizations from working together. This dissertation explores how social movement organizations overcome these traditional barriers and come together to form coalitions and maintain alliances. I used both qualitative and quantitative methods to understand how the American pro-Israel movement has formed and maintained coalitions among diverse groups with contrasting religious and political values. Advanced statistical analyses of an original dataset of 968 national American Jewish organizations coupled with comparative historical analysis of American Evangelical and Jewish support for Israel highlighted how social movement organizations can overcome traditional barriers that frequently limit inter-organizational alliances. I found that that despite numerous barriers, coalitions and alliances can be formed and maintained when situated in an amenable context, they have appropriate access to resources, and organizational leaders act as brokers and organizational entrepreneurs. Changes to the broader political and national context enabled coalition formation and growth by both increasing the incentives for individual organizations and changing the structure of the organizational field to create new opportunities for alliances. Sufficient access to monetary and organizational resources encouraged groups to overcome traditional barriers, like competition and ideological disputes. The deliberate choices of various organizations leaders to capitalize on opportunities and skillfully deploy resources facilitated the growth and maintenance of a vast network of inter-organizational collaborations among Jewish organizations. Furthermore, organizational entrepreneurs and brokers helped facilitate collaborations between adversarial organizations. I integrated specialized knowledge from Jewish Studies, Political Science, and Sociology to advance our understanding of organizational processes and political advocacy. This dissertation expands our current sociological understanding of social movement coalitions and collaborations, especially underdeveloped theories of adversarial collaborative movements.