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This chapter addresses quantum information transmission and processing. Quantum noise is dominant in long-haul transmission lines, even for strong signals. Amplifier noise is avoided by using a noise-free amplifier. Injecting a strongly squeezed state into an unused port of a coupler reduces branching noise. The next section explains the no-cloning theorem and the theory and experimental evidence for (imperfect) quantum cloning machines. The use of single photons for secure quantum key distribution in cryptography is then discussed. Entanglement as a quantum resource first appears in the explanation of quantum dense coding and the inverse process of quantum teleportation. The chapter ends with a brief discussion of quantum computing, including quantum parallelism, quantum logic gates, and quantum circuits. A survey of experiments in quantum computing is followed by a study of proposals for combining linear optics with local measurements to construct quantum computers.

This chapter introduces the notions of classical and quantum information and discusses simple protocols for their exchange. It defines the entropy as a quantitative measure of information, and investigates its mathematical properties and operational meaning. It discusses the extent to which classical information can be carried by a quantum system and derives a pertinent upper bound, the Holevo bound. One important application of quantum communication is the secure distribution of cryptographic keys; a pertinent protocol, the BB84 protocol, is discussed in detail. Moreover, the chapter explains two protocols where previously shared entanglement plays a key role, superdense coding and teleportation. These are employed to effectively double the classical information carrying capacity of a qubit, or to transmit a quantum state with classical bits, respectively. It is shown that both protocols are optimal.

This chapter discusses quantum information science (QIS), quantum key distribution (QKD), and quantum teleportation. The new field of QIS encompasses several overlapping subdisciplines: quantum computing, quantum key distribution (also known as quantum cryptography), and quantum metrology (the measurement of small parameters and weak forces with ultra-high precision). In QIS, bits of information are encoded in quantum states, which themselves can be in superposition states and/or entanglement states. Generically, the 0 and 1 quantum bits are represented as qubits (quantum bits). QKD, or quantum cryptography, is a completely secure method of secret communication, and will remain so even if a quantum computer becomes available. Quantum teleportation is one of the more exotic features to have emerged from the field of QIS. It refers to the ability to transfer an unknown quantum state from one location to another, possibly very distant, location by using quantum entanglement.

Cryptography is a method of secure communication between two or more parties. The crucial step is exchanging a key in a secure manner. There are, however, two problems with conventional cryptography. First the sender and the receiver should exchange the key through highly reliable and secure channels. The second problem is that a clever eavesdropper can, by a careful analysis of the sent information, reconstruct the key. In this chapter, schemes to overcome these problems are presented. First a scheme for exchanging a key over public channels, the so-called RSA algorithm, is discussed. Then the protocols for the quantum key distribution (QKD), the Bennett–Brassard-84 (BB-84) and Bennett-92(B-92) protocols, are then presented. The QKD protocols are exclusively derived using Bohr’s principle of complementarity. An application of these ideas to the design of secure quantum money is discussed.

EPR showed that quantum mechanics is not a local deterministic theory and on this account they argued that it is incomplete. Quantum mechanics predicts correlations over time-like separations. The suggested resolution in terms of local hidden variables is presented. Bell’s analysis leading to experimental tests is described. The experiment of Aspect, Grangier and Roger vindicating quantum mechanics is described. More refined experiments, avoiding conceivable biases, confirm this result. Then computing based on quantum principles is discussed. Bits with two states in a register would be replaced by qubits with values represented by points on the Bloch sphere. Basic gates are presented. Shor’s algorithm to decompose products of primes is described and a gate structure presented to implement it. Implementation would undermine current encryption methods. Quantum cryptography is described using the BB84 protocol. The no-cloning theorem protects this absolutely against attempts to intercept the encryption data.

Since Bell’s death, interest in his work and quantum foundations in general, and the amount of application of his work, have grown steadily. Work on Bell’s inequality has continued, each loophole has been closed independently, and in 2015 it seems that a loophole-free test will be achieved very soon. Also stimulated by Bell, discussion of fundamental aspects of quantum theory, a discussion which was scarcely tolerated in the days of the supremacy of the Copenhagen interpretation, is widespread and productive. Bell’s work has stimulated the conception and growth of quantum information theory, which encompasses quantum computation (or quantum computing), quantum cryptography (or quantum key distribution), and quantum teleportation, and there is now an enormous amount of work, both theoretical and practical.