Abstract This chapter discusses some of the ways in which quantum entanglement can be used for quantum communication. Suppose Alice and Bob share an entangled state: they can use it for dense coding, in which Alice sends Bob just one qubit of an entangled pair, which delivers two bits of classical information. Alice and Bob can also use an entangled state for teleportation, in which a qubit in a unknown quantum state is teleported from Alice to Bob when Alice sends Bob two classical bits. Entanglement swapping is an example of a tripartite communication protocol. If Alice and Bob share entanglement, and Bob and Charlie share entanglement, entanglement swapping can be used to entangle Alice and Charlie. Even if Alice and Bob are entangled, Alice cannot communicate with Bob without sending him classical bits or qubits, which prevents Alice and Bob from breaking the laws of relativity. This chapter also discusses Pauli matrices and the extension of Hilbert spaces.
Abstract This chapter discusses some of the ways in which quantum entanglement can be used for quantum communication. Suppose Alice and Bob share an entangled state: they can use it for dense coding, in which Alice sends Bob just one qubit of an entangled pair, which delivers two bits of classical information. Alice and Bob can also use an entangled state for teleportation, in which a qubit in a unknown quantum state is teleported from Alice to Bob when Alice sends Bob two classical bits. Entanglement swapping is an example of a tripartite communication protocol. If Alice and Bob share entanglement, and Bob and Charlie share entanglement, entanglement swapping can be used to entangle Alice and Charlie. Even if Alice and Bob are entangled, Alice cannot communicate with Bob without sending him classical bits or qubits, which prevents Alice and Bob from breaking the laws of relativity. This chapter also discusses Pauli matrices and the extension of Hilbert spaces.
We are now ready to look at our first protocols for quantum information. In this section, we examine two communication protocols which can be implemented using the tools we have developed in the preceding sections. These protocols are known as superdense coding and quantum teleportation. Both are inherently quantum: there are no classical protocols which behave in the same way. Both involve two parties who wish to perform some communication task between them. In descriptions of such communication protocols (especially in cryptography), it is very common to name the two parties ‘Alice’ and ‘Bob’, for convenience. We will follow this tradition. We will repeatedly refer to communication channels. A quantum communication channel refers to a communication line (e.g. a fiberoptic cable), which can carry qubits between two remote locations. A classical communication channel is one which can carry classical bits (but not qubits).1 The protocols (like many in quantum communication) require that Alice and Bob initially share an entangled pair of qubits in the Bell state The above Bell state is sometimes referred to as an EPR pair. Such a state would have to be created ahead of time, when the qubits are in a lab together and can be made to interact in a way which will give rise to the entanglement between them. After the state is created, Alice and Bob each take one of the two qubits away with them. Alternatively, a third party could create the EPR pair and give one particle to Alice and the other to Bob. If they are careful not to let them interact with the environment, or any other quantum system, Alice and Bob’s joint state will remain entangled. This entanglement becomes a resource which Alice and Bob can use to achieve protocols such as the following. Suppose Alice wishes to send Bob two classical bits of information. Superdense coding is a way of achieving this task over a quantum channel, requiring only that Alice send one qubit to Bob. Alice and Bob must initially share the Bell state Suppose Alice is in possession of the first qubit and Bob the second qubit.
This chapter begins our first exciting application of the postulates of the quantum theory to quantum communication. We study the fundamental, unit quantum communication protocols. These protocols involve a single sender Alice and a single receiver Bob. The protocols are ideal and noiseless because we assume that Alice and Bob can exploit perfect classical communication, perfect quantum communication, and perfect entanglement. At the end of this chapter, we suggest how to incorporate imperfections into these protocols for later study. Alice and Bob may wish to perform one of several quantum informationprocessing tasks, such as the transmission of classical information, quantum information, or entanglement. Several fundamental protocols make use of these resources: 1. We will see that noiseless entanglement is an important resource in quantum Shannon theory because it enables Alice and Bob to perform other protocols that are not possible with classical resources only. We will present a simple, idealized protocol for generating entanglement, named entanglement distribution . 2. Alice may wish to communicate classical information to Bob. A trivial method, named elementary coding , is a simple way of doing so and we discuss it briefly. 3. A more interesting technique for transmitting classical information is superdense coding . It exploits a noiseless qubit channel and shared entanglement to transmit more classical information than would be possible with a noiseless qubit channel alone. 4. Finally, Alice may wish to transmit quantum information to Bob. A trivial method for her to do so is to exploit a noiseless qubit channel. However, it is useful to have other ways for transmitting quantum information because such a resource is difficult to engineer in practice. An alternative, surprising method for transmitting quantum information is quantum teleportation . The teleportation protocol exploits classical communication and shared entanglement to transmit quantum information. Each of these protocols is a fundamental unit protocol and provides a foundation for asking further questions in quantum Shannon theory. In fact, the discovery of these latter two protocols was the stimulus for much of the original research in quantum Shannon theory. One could take each of these protocols and ask about its performance if one or more of the resources involved is noisy rather than noiseless. Later chapters of this book explore many of these possibilities.
Abstract Chapter 14 discusses the quantum communication protocol called quantum teleportation, which uses the quantum correlations in an entangled particle pair shared between two observers to transmit the information stored in the (unknown) quantum state of a target system from one of the observers to the other. After reviewing the theoretical basics we showcase some of the important experimental demonstrations of teleportation. We then turn to more general protocols related to teleportation such as entanglement swapping, and the general formalism of isometries, before inspecting the option of delayed-choice entanglement swapping. In the light of these findings we compare teleportation to classical information transfer and inspect the related dense-coding protocol. Finally, we give an overview of basic quantum key distribution protocols is given, including the Bennett-Brassard-84 protocol based on conjugate coding and the entanglement-based Ekert-91 protocol
This chapter begins our first exciting application of the postulates of the quantum theory to quantum communication. We study the fundamental, unit quantum communication protocols. These protocols involve a single sender, whom we name Alice, and a single receiver, whom we name Bob. The protocols are ideal and noiseless because we assume that Alice and Bob can exploit perfect classical communication, perfect quantum communication, and perfect entanglement. At the end of this chapter, we suggest how to incorporate imperfections into these protocols for later study. Alice and Bob may wish to perform one of several quantum information-processing tasks, such as the transmission of classical information, quantum information, or entanglement. Several fundamental protocols make use of these resources: 1. We will see that noiseless entanglement is an important resource in quantum Shannon theory because it enables Alice and Bob to perform other protocols that are not possible with classical resources only. We will present a simple, idealized protocol for generating entanglement, named entanglement distribution . 2. Alice may wish to communicate classical information to Bob. A trivial method, named elementary coding , is a simple way for doing so and we discuss it briefly. 3. A more interesting technique for transmitting classical information is superdense coding . It exploits a noiseless qubit channel and shared entanglement to transmit more classical information than would be possible with a noiseless qubit channel alone. […]
The beauty of the quantum circuit lies in the fact that it can perform certain tasks which are impossible in the classical world. For example, consider teleportation and superdense coding. Teleportation is a quantum task in which an unknown quantum state is transmitted from a sender (Alice) to a spatially separated receiver (Bob) via an entangled quantum channel and with the help of some classical communications. Dense coding is another communication scheme in which if Alice and Bob share a prior entanglement then one of them can send n bits of classical information to the other by communicating m-qubits (m < n). Before we go into the technical details of these two schemes let us try to lucidly visualize the uniqueness of teleportation. Suppose Alice and Bob are spatially separated and Alice wants to send an unknown quantum state |ψ〉 = α|0〉 + β|1〉 to Bob. For some reason she is not allowed to send the state directly through a quantum channel. She cannot measure it and send the information to Bob because the moment she will try to measure the state, it will collapse either to |0〉 or to |1〉. But the state can be sent by using a simple quantum circuit (pre-shared entanglement) and some classical communications. In the process the unknown quantum state gets destroyed at Alice’s end and reappears at Bob’s end. The state never exists in the communication channel. This process is called quantum teleportation. The uniqueness of quantum teleportation will be clearer if we note that the Fax is not an example of teleportation because the original copy remains with the sender. Again a letter posted in a letter box is not an example of teleportation because the letter exists (travels) in its original form in the communication channel. In brief, there is no classical analogue of quantum teleportation. The same is true for dense coding. In this chapter we will describe these two unique quantum communication schemes and discuss their significance and applications.
Quantum communication, as a vital area of quantum information science, aims to leverage quantum phenomena—particularly entanglement—to achieve tasks that are impossible or inefficient in classical systems. It plays a key role in the development of secure communication protocols and advanced information processing. This paper focuses on one such protocol, dense coding, which enables the transmission of two classical bits using only one entangled quantum particle.”We introduce the mathematical and physical foundations of quantum communication, such as the entangled state and Kronecker product. Then we propose the quantum communication protocol, namely dense coding using Bell states. It offer unique advantages that are beyond the classical parts. For this purpose, we in detail analyze the quantum measurements using Pauli gates and identity matrix, as well as the transmission of particle from Alice to Bob. They are necessary steps for dense coding. Then we analyze how Bob finishes the protocol using measurement over two qubits.