Quantum Dense Coding and Quantum Teleportation

Abstract

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 fiber-optic 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 |β 00 = 1 √ 2 |00 + |11 . (5.0.1) 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. 1 Often the term 'channel' is used to refer to the mathematical transformation that occurs on bits or qubits when undergoing a general quantum operation. We will use this term in this sense in Chapter 10.