Managing knowledge networks (KN) within organizations has taken on enhanced importance in recent years because of the decline of middle management and other changes in formal organizational structures, the growth of information technologies, and our increasingly competitive global economy. KN can be manifested in a variety of forms: project teams, research groups, advice networks, professional communities, communities of practice, support groups, and so on. Individuals increasingly find that they must determine for themselves what choices they will make, distilling the information they have gathered in their personal networks to knowledge that results in strategies they can pursue as they act in an ever more complex world. The awareness of the operation of KN is, quite literally, an important survival tool for individuals. In turn, resulting individual learning and actions determine how organizations adapt to rapidly changing environments and innovate to meet new challenges.

I have been conducting network analysis, innovation, and information research for over three decades now (Susskind et al. 2005). This book represents a culmination of this work: a bringing together of what have been complementary, although separate, strands of research. As such it draws on my books and research articles in these diverse areas, hopefully resulting in a useful synthesis of ideas applied to the increasingly critical problem of understanding the role of KN in contemporary organizations. My first book, Organizational Communication Structure, placed network analysis within broader intellectual traditions relating it directly to formal, spatial, and cultural approaches to structure.

Network analysis is a highly systematic means of examining the overall configuration of relationships within an organization. The most common form of graphic portrayal of networks contains nodes, shown by circles in Figure 3.1, which represent social units (e.g., people, groups), and relationships (reflected in the lines) of various sorts between them. These elements of graphic representations are essential to most network analysis definitions: “In general, the term ‘network’ is taken to mean a set of units (or nodes) of some kind and the relations of specific types that occur among them” (Alba 1982, p. 42, italics in original).

Because of its generality, network analysis has been used by almost every social science to study specific problems. Network analysis has been the primary means of studying communication structure in organizations for over three decades (Farace, Monge, and Russell 1977) and has become increasingly popular in management and organizational sociology as well (Borgatti and Foster 2003). In fact, so much attention has been paid to network analysis that a comprehensive review, particularly related to data gathering methods (Box 3.1) and computer programs (Box 3.2), of all material linked to it is beyond the scope of this chapter.

Naturally our focus here is on issues fundamental to KN, which will be developed in much more detail in subsequent chapters. Social networking technology is viewed as a key feature of contemporary business approaches to how knowledge spreads within a company (Cross, Parker, and Sasson 2003; Waters 2004). Since networks provide organizations with access to knowledge, resources, and technologies, they are a key source of competitive advantage (Inkpen and Tsang 2005).

Every day we see the consequences of poorly made decisions, especially in our political life. The term groupthink has come to symbolize the very human, group processes (e.g., cohesiveness, conformity) that conspire against “good,” rational decision making. Janis (1971), in tracing the decision making of the US foreign policy establishment regarding Vietnam, the Cuban missile crises, and the Bay of Pigs, found one recurring theme – how group processes and the limits of human decision making restricted the range of information that was sought and the consideration of a range of alternatives once information was obtained.

The information context of the modern organization is rapidly evolving. Information technologies, including data bases, new telecommunications systems, and software for synthesizing information, make a vast array of information available to an ever expanding number of organizational members. Management's exclusive control over knowledge is steadily declining, in part because of the downsizing of organizations and the decline of the number of layers in organizational hierarchies. These trends make our understanding of informal communication networks, particularly those focusing on interpersonal relationships, the human side of knowledge management (KM), increasingly critical for understanding organizations. Knowledge is inherently social, with knowledge networks (KN) linked to innovation, learning, and performance (Swan 2003).

At a fundamental level, technology may be defined as organizational actions employed to transfer inputs into outputs. It can be viewed not just in the narrow sense of focusing on machines needed to produce physical goods, but in the broader sense of any systematic set of techniques which leads to organizational outputs. Naturally an understanding of technology is fundamental to our understanding of organizations, but little is known about the precise impact of technology, particularly IT given the unique attributes of information discussed in Chapter 2, on KN.

Technology has a number of potential impacts. Most importantly, it determines the human composition of organizations. The diversity of skills needed in the contemporary organization increases the heterophily of its members and generally heterophily can be associated with a variety of communication problems (Rogers 1983). Different occupations also have different knowledge needs (Case 2007). Engineers, for example, are much more likely than scientists to be interested in information that is directly and narrowly relevant to their jobs (Allen 1977). Second, technological factors also have a significant impact on the spatial environment of organizations, something we shall discuss in detail in the next chapter. Third, technology has a direct impact on the structural design of organizations.

Formal structure is one of the fundamental tools for managing knowledge in organizations. Some have viewed formal structure as one instantiation of networks, with relationships defined by asymmetry and work-related content transmitted in written channels. But, as we will soon see, there is much more to the study of formal structure.

Creativity and innovation processes often determine how rapidly private and governmental organizations change to survive in an increasingly competitive world. As Schumpeter (1943) classically observed, creative destruction, replacing the old with the new, is a fundamental component of capitalist economic systems. A stagnant organization that cannot react to evolving environmental conditions will eventually find itself no longer competitive in an increasingly complex and technologically sophisticated economy. Economic prosperity increasingly depends on the development of new products and services. Innovation may be the ultimate service provided by KM organizations.

This chapter deals with the subject of quantum error correction and the related codes (QECC), which can be applied to noisy quantum channels and quantum memories with the purpose of preserving or protecting the information integrity. I first describe the basics of quantum repetition codes, as applicable to bit-flip and phase-flip quantum channels. Then I consider the 9-qubit Shor code, which has the capability of diagnosing and correcting any combination of bit-flip and phase-flip errors, up to one error of each type. Furthermore, it is shown that the Shor code is, in fact, capable of fully restoring qubit integrity under a continuum of bit or phase errors, a property that has no counterpart in the classical world of error-correction codes. But the exploration of QECC does not stop here! We shall discover the elegant Calderbank–Shor–Steane (CSS) codes, which have the capability of correcting any number of errors t, both bit-flip and phase-flip. As an application of the CSS code, I then describe the 7-qubit Hadamard–Steane code, which can correct up to one error on single qubits. A corresponding quantum circuit, based on an original generator-matrix example, is presented.

Quantum repetition code

In Chapter 11, we saw that the simplest form of error-correction code (ECC) is the repetition code, based on the principle of majority logic. The background assumption is that in a given message sequence, or bit string, the probability of a bit error is sufficiently small for the majority of bits to be correctly transmitted through the channel.

Because of the reader's interest in information theory, it is assumed that, to some extent, he or she is relatively familiar with probability theory, its main concepts, theorems, and practical tools. Whether a graduate student or a confirmed professional, it is possible, however, that a good fraction, if not all of this background knowledge has been somewhat forgotten over time, or has become a bit rusty, or even worse, completely obliterated by one's academic or professional specialization!

This is why this book includes a couple of chapters on probability basics. Should such basics be crystal clear in the reader's mind, however, then these two chapters could be skipped at once. They can always be revisited later for backup, should some of the associated concepts and tools present any hurdles in the following chapters. This being stated, some expert readers may yet dare testing their knowledge by considering some of this chapter's (easy) problems, for starters. Finally, any parent or teacher might find the first chapter useful to introduce children and teens to probability.

I have sought to make this review of probabilities basics as simple, informal, and practical as it could be. Just like the rest of this book, it is definitely not intended to be a math course, according to the canonic theorem–proof–lemma–example suite. There exist scores of rigorous books on probability theory at all levels, as well as many Internet sites providing elementary tutorials on the subject.

This relatively short but mathematically intense chapter brings us to the core of Shannon's information theory, with the definition of channel capacity and the subsequent, most famous channel coding theorem (CCT), the second most important theorem from Shannon (next to the source coding theorem, described in Chapter 8). The formal proof of the channel coding theorem is a bit tedious, and, therefore, does not lend itself to much oversimplification. I have sought, however, to guide the reader in as many steps as is necessary to reach the proof without hurdles. After defining channel capacity, we will consider the notion of typical sequences and typical sets (of such sequences) in codebooks, which will make it possible to tackle the said CCT. We will first proceed through a formal proof, as inspired from the original Shannon paper (but consistently with our notation, and with more explanation, where warranted); then with different, more intuitive or less formal approaches.

Channel capacity

In Chapter 12, I have shown that in a noisy channel, the mutual information, H(X;Y) = H(Y) − H(Y|X), represents the measure of the true information contents in the output or recipient source Y, given the equivocation H(Y|X), which measures the informationless channel noise. We have also shown that mutual information depends on the input probability distribution, p(x).

This chapter represents our first step into quantum information theory (QIT). The key to operating such a transition is to become familiar with the concept of the quantum bit, or qubit, which is a probabilistic superposition of the classical 0 and 1 bits. In the quantum world, the classical 0 and 1 bits become the pure states |0〉 and |1〉, respectively. It is as if a coin can be classically in either heads or tails states, but is now allowed to exist in a superposition of both! Then I show that qubits can be physically transformed by the action of unitary matrices, which are also called operators. I show that such qubit transformations, resulting from any qubit manipulation, can be described by rotations on a 2D surface, which is referred to as the Bloch sphere. The Pauli matrices are shown to generate all such unitary transformations. These transformations are reversible, because they are characterized by unitary matrices; this property always makes it possible to trace the input information carried by qubits. I will then describe different types of elementary quantum computations performed by elementary quantum gates, forming a veritable “zoo” of unitary operators, called I, X, Y, Z, H, CNOT, CCNOT, CROSSOVER or SWAP, controlled-U, and controlled-controlled-U. These gates can be used to form quantum circuits, involving any number of qubits, and of which several examples and tools for analysis are provided. Finally, the concept of tensor product, as progressively introduced through the above description, is eventually formalized.