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This chapter presents key quantum mechanics principles essential for understanding quantum computation. The postulates of quantum mechanics, mixed states, and density matrices are introduced, along with the Stern–Gerlach experiment’s role in illustrating quantum behavior. Topics such as quantum coherence, entanglement, and the EPR paradox are covered to clarify the fundamental distinctions between classical and quantum systems. Measurement is explored with an emphasis on positive operator-valued measures (POVM), a key concept in understanding quantum state collapse. These principles provide a foundation for studying quantum computation and are essential for understanding qubit behavior, quantum information processing, and subsequent algorithmic structures.
This chapter introduces quantum computation by comparing classical and quantum computers. Core concepts including qubits, superposition, and entanglement are introduced, setting the stage for deeper exploration. Various quantum computing models are summarized, with a focus on the circuit and topological models. The chapter explains why quantum computing is necessary, especially for tasks beyond classical computing’s limits. It discusses existing quantum platforms and provides an overview of their capabilities and limitations. The chapter also offers a brief historical perspective, touches on computational energy efficiency, and forecasts a quantum future where quantum and classical computing work in tandem. This groundwork provides essential insights into quantum computation’s potential and upcoming chapters’ explorations of algorithmic and theoretical principles.
Why is Robinson Crusoe’s island insect-free, when evidence suggests that Defoe was aware of their importance to thriving ecosystems? Following Amitav Ghosh’s arguments in The Great Derangement, the chapter explores how human-insect entanglement would have impacted a character like Crusoe. On the one hand, a variety of insects would have proved debilitating as they invaded his body and his dwelling space. Crusoe’s sense of sovereignty would have been sorely compromised by many pernicious creatures. On the other hand, insects would also have made his island livable. Insects not only pollinate and make human agriculture possible, but they also remove rotting flesh and other decaying matter. However, including insects in the representation would mitigate any novelistic purpose committed to the construction of a mythic, self-determining, self-enclosed, and autonomous hero like Crusoe. In this omission of entanglement, the world of the human becomes the place where the insect is not.
How are insects both visible and invisible? To return to the eighteenth century is to see the moment when they were assigned to entomological science but not to literary forms like the realist novel. The results of this dual movement include the separation of man from animal and human from non-human, leading us to think of ourselves as distinct from the natural world. This book addresses how the rise of the novel, contemporaneous with emerging entomology, shaped a sense of the “real,” as well as the “real” human conditions of terrestrial existence. The theoretical underpinnings for the argument include animal studies, material ecocriticism, and critical insect studies, with recourse to critics such as Jane Bennett. Key concepts include horizontal thinking, vibrant materiality, entanglement, symbiosis, and holobiont. The chapter closes with the words of Ed Yong, acknowledging the vital natural networks in which we find ourselves.
Discover the foundations of classical and quantum information theory in the digital age with this modern introductory textbook. Familiarise yourself with core topics such as uncertainty, correlation, and entanglement before exploring modern techniques and concepts including tensor networks, quantum circuits and quantum discord. Deepen your understanding and extend your skills with over 250 thought-provoking end-of-chapter problems, with solutions for instructors, and explore curated further reading. Understand how abstract concepts connect to real-world scenarios with over 400 examples, including numerical and conceptual illustrations, and emphasising practical applications. Build confidence as chapters progressively increase in complexity, alternating between classic and quantum systems. This is the ideal textbook for senior undergraduate and graduate students in electrical engineering, computer science, and applied mathematics, looking to master the essentials of contemporary information theory.
This chapter explores the early life of the unique Jewish-Arab, Hebrew-Arabic journal Mifgash-Liqa’, meaning “Encounter” or “Meeting” in both languages. Originally founded in 1964 by Sephardi writer Yehuda Burla, Yemenite Jewish writer Mordechai Tabib, and Palestinian Israeli scholar Mahmud Abbasi, it was revived by Palestinian Israeli poet and translator Muhammad Hamza Ghanayim fourteen years after its first discontinuation in 1970. In the 1980s, Mifgash-Liqa’ witnessed more profound literary, cultural, and artistic encounters between Israel’s Hebrew and Arabic speakers and with the Arab World, in an era when Mizrahi and Palestinian Israelis were finding their voices.
The chapter argues that, beyond providing publication opportunities for marginalized writers in Israel, Mifgash-Liqa’ aimed to create Israeli literature through translation and by blurring the boundary between Hebrew and Arabic literature. Examples include The Israeli Monologue by Salman Natour and A Locked Room by Shimon Ballas. Borrowing Juelietta Singh’s notion of “entanglement,” the chapter highlights an inclusiveness that abandons the desire for mastery over oneself or others. The journal’s editorials and texts embody the call for a radically different imagination, for coexistence in a yet unforeseeable future, for possibilities beyond identity politics, for what it means to be Israeli.
Chapter 14 is entirely devoted to the electron spin and an introduction to quantum entanglement. The first part deals with the groundbreaking discovery of spin, its introduction into quantum formalism, and some of its most important effects on atomic spectra, notably the anomalous Zeeman effect. Historically, spin has been considered as an angular momentum that particles can have by the mere fact of their existence, which is called "intrinsic" and does not require any explanation. To address this shortcoming, Section 4 presents a possible explanation for the origin of electron spin as a result of its interaction with the vacuum field. Section 5 introduces the entangled system of two particles with spin, which provides an opportunity to discuss, necessarily schematically, the Schrödinger cat and the Einstein-Podolsky-Rosen thought experiment, as well as the Bell inequalities.
Buildings frequently change over their lifespans as they are adapted to new needs and affected by damage and decay, yet our approaches to architectural history often fail to account for the material and cultural effects of interventions on existing structures or to pursue the critical questions they raise about temporality and urban environments. The book’s Introduction orients readers to diachronic approaches to architectural history, that is, beyond the moment of initial construction, oriented to the perspective of historical actors. In recognizing moments of architectural revision and rebuilding as inflection points, it stresses the importance of accounting for architectural fabrics composed of variously dated elements and of examining the ways that architectural change shapes audience perception of the site’s history and their own era’s relationship to it. Close examination of two exceptionally long-lasting structures, the Pantheon in Rome and the Hagia Sophia/Ayasofia in Constantinople/Istanbul present a compelling contrast to most modern forms of architectural restoration and illustrate central themes of the book. The chapter situates study of historical architecture within current approaches to cultural time and to material culture and places architectural change in dialogue with text-based approaches to Roman temporality.
Like a puppy playing with the long stick which is the risk-uncertainty conundrum, we chew energetically on the risk end, letting the uncertainty end drag in the dust. The stick is shaped, I argue, by Newtonian humanism. It combines the scientific and humanist stances that have co-evolved in modern times, constituting a commonsensical, internally inconsistent, worldview. And that view bends the analysis of the political world toward controllable risk, sidestepping or silencing unruly uncertainty.
In this seminal study, Peter J. Katzenstein drags the analysis of world politics from the Newtonian humanism of the nineteenth century into a new post-Newtonianism of the twenty-first. The key concept is entanglement. By examining differences in context, process, and language, Katzenstein specifies how risk and uncertainty intertwine. Three deeply researched case studies – finance and political economy, nuclear crisis politics and war, and global warming and AI – support his original arguments. A chapter on power further illustrates the risk-uncertainty conundrum. Entanglements in World Politics calls for humility and eclectic pragmatism, emphasizing the unity of knowledge of the natural and humanistic sciences and the complementarities of science and religion. Katzenstein's engaging writing and innovative approach make this a must-read for anyone interested in the complexities of global politics. This book is also available as Open Access on Cambridge Core.
Urban historians have become increasingly attentive to the various flows of peoples, resources and ideas that connected and at times disconnected urban spaces worldwide. This chapter on the history of urban revolutions, rebellions and riots draws on these debates. It aims to make sense of the way in which local occurrences of violence and discontent turned into events of national or transnational significance in late nineteenth- and twentieth-century Europe. As globally entangled sites of capitalist accumulation, knowledge production and migration, European cities played a pre-eminent role in the diffusion of protests and the emergence of new forms of insurgent citizenship. In order to explore this role, the chapter highlights four ‘transnational circuits’ that impacted on urban repertoires of contention: 1) activist networks, 2) mass media, 3) the circulation of expert knowledge, and 4) (post-)colonial migration. Attending to the way that different political conflicts were or were not embedded in such transnational circuits, it points to similarities and simultaneities, as well as differences and disconnections between urban agencies in Europe and beyond.
This chapter discusses light–matter interactions from a semiclassical point of view. By expanding the electromagnetic field into a Taylor series we derive the multipolar interaction potential and particle-field Hamiltonian. Then, using the Green function formalism, we calculate the fields of an oscillating dipole and, based on Poynting’s theorem, derive a general expression for the rate of energy dissipation in an arbitrary environment. This expression leads to the concept of local density of states (LDOS) and provides a direct link to spontaneous emission and atomic decay rates. The rate of energy dissipation of an oscillating dipole is also used to derive the absorption cross-section in terms of the polarizability. By accounting for radiation reaction and scattering losses, we obtain a compact expression for the dynamic polarizability. Dipole radiation and atomic decay rates can be enhanced via LDOS engineering, and the enhancement factor is referred to as the Purcell factor. We show that if the LDOS gets enhanced in a certain frequency range, it must be reduced in other frequency ranges, a feature described by the LDOS sum rule. After discussing the properties of a single dipole, we continue with analyzing the interaction between multiple dipoles. We derive the interaction potential and calculate the energy transfer rate between dipoles. For short distances we recover the famous Förster energy transfer formula. If the interaction energy becomes sufficiently large, we enter the regime of strong coupling, which gives rise to hybridized and delocalized modes, level splittings, and entanglement.
The chapter sets out to examine Nairobi as a site of cultural imagination. It argues that since its founding by the British colonialists, Nairobi has featured prominently as a site of “rest” for its many immigrant communities but also for the local Kenyans from its rural hinterlands. The chapter further examines how writers of African fiction have tapped into its rich tapestry, turning it into a powerful archive and a rich source of literary imagination. The chapter shows how Nairobi has become a site where the antinomies of the new nation-state play themselves out, as it gets mobilized by writers of fiction to figure a number of competing cultural and social imaginaries within Kenya and the East African region more broadly. By drawing attention to a set of fictional works on Nairobi, the chapter allows us to literally take a “walk” through the streets of Nairobi and to absorb its full significance as a layered site of archival imagination. It offers a glimpse of Nairobi as a bottomless resource for archive-building – a site of endless potential for literary imagination.
The modern study of the Peloponnesian War has suffered from a double blind spot. On the one hand, the traditional study of political history based on events has shown little interest in the great development in the study of ancient Greek economic, social and cultural history. On the other hand, social, economic and cultural history has shown little interest in the study of events like the Peloponnesian War. In this chapter I want to discuss an alternative framework that can incorporate the full wealth provided by Thucydides and bridge the gap between economic, social and cultural history based on static analysis and political history based on dry narrative. The key for accomplishing this task is the concept of entanglement. The Peloponnesian War can be understood as a history of three different kinds of entanglements. The first entanglement is that between different levels: local communities, micro-regions, macro-regions and the Panhellenic world. The second entanglement concerns a series of processes put into motion by certain key factors: violence, honour, wealth and political discourse. The third entanglement concerns the variety of actors involved in the Peloponnesian War: state apparatuses, alliances, empires, potentates, factions, networks, exiles, mobile humans, the enslaved.
The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.
Chien-Shiung Wu (1912–1997) is often referred to as “the Chinese Marie Curie” even though she conducted most of her research in the US. She is best known for her discovery of the non-conservation of parity for weakly interacting particles – a finding for which she is widely regarded as having been passed over for the 1957 Nobel Prize in Physics. Seven years earlier, though, in a one-page letter to Physical Review, Wu and her graduate student also quietly reported what has come to be understood as the first conclusive evidence of entangled photons. Twenty years later, as quantum foundations research emerged from shadow, Wu revisited her 1949 experiment with a more refined approach. Wu shared the new results with Stuart Freedman, a collaborator of John Clauser. Clauser et al. would rigorously critique Wu’s experiments through at least 1978. In 2022, the Nobel Committee honored Clauser, Alain Aspect, and Anton Zeilinger, each of whom had produced increasingly convincing proof of entanglement beginning in the 1970s. Wu’s foundational work from almost seventy years earlier, however, was not mentioned. This chapter aims to help bring Wu’s entangled photons back into the light.
This response to “Horizontal Threads: Towards an Entangled Spatial History of the Romanov Empire,” reflects on shifting approaches to the structure of empires and the power of entanglement as an analytical tool for making sense of the incorporationist work of empire.
Chapter 6 is the first chapter in the second part of the book, titled “Entangled Timescales of the Visual Arts.” Chapter 6 explains the meaning of this title by focusing on an important feature of complex systems, namely, that they consist of interacting processes on different time scales, from very short to very long. These processes are entangled, that is, they occur in continuous interaction and are interdependent. These entangled processes form the basis for important complexity features of the arts, such as self-organization, emergence, novelty and creativity, attractors, critical states, variability, and so on.
The study of the quantum–classical correspondence has been focused on the quantum measurement problem. However, most of the discussion in the preceding chapters is motivated by a broader question: Why do we perceive our quantum Universe as classical? Therefore, emergence of the classical phase space and Newtonian dynamics from the quantum Hilbert space must be addressed. Chapter 6 starts by re-deriving decoherence rate for non-local superpositions using the Wigner representation of quantum states. We then discuss the circumstances that, in some situations, make classical points a useful idealization of the quantum states of many-body systems. This classical structure of phase space emerges along with the (at least approximately reversible) Newtonian equations of motion. Approximate reversibility is a non-trivial desideratum given that the quantum evolution of the corresponding open system is typically irreversible. We show when such approximately reversible evolution is possible. We also discuss quantum counterparts of classically chaotic systems and show that, as a consequence of decoherence, their evolution tends to be fundamentally irreversible: They produce entropy at the rate determined by the Lyapunov exponents that characterize classical chaos. Thus, quantum decoherence provides a rigorous rationale for the approximations that led to Boltzmann’s H-theorem.
Chapter 5 explores the consequences of decoherence. We live in a Universe that is fundamentally quantum. Yet, our everyday world appears to be resolutely classical. The aim of Chapter 5 is to discuss how preferred classical states, and, more generally, classical physics, arise, as an excellent approximation, on a macroscopic level of a quantum Universe. We show why quantum theory results in the familiar “classical reality” in open quantum systems, that is, systems interacting with their environments. We shall see how and why, and to what extent, quantum theory accounts for our classical perceptions. We shall not complete this task here—a more detailed analysis of how the information is acquired by observers is needed for that, and this task will be taken up in Part III of the book. Moreover, Chapter 5 shows that not just Newtonian physics but also equilibrium thermodynamics follows from the same symmetries of entanglement that led to Born’s rule (in Chapter 3).