Some applications of entanglement

Entangled states constitute a powerful natural resource for QIP. In this section, two of the most interesting applications are illustrated superdense coding and the teleport. 

The superdense coding is a process, in which two bits of classical information are transmitted using only one quantum bit. Here the example of exchange of information between two parties Alice and Bob, is described. Suppose that initially Alice and Bob share qubits in an entangled cat state  

On the other hand, two classical bits have four possible sequences 00, 01, 10 or 11, each of them representing a possible message , which can be sent through a communication channel. Suppose that Alice wishes to send Bob the sequence 01. All she has to do is to apply the operator X on her qubit, of the entangled pair (say, the qubit a of the state ab)), transforming the state to  

After the operation, she sends her qubit to Bob, who applies the operations CNOTa (note that the control is in the first qubit) to the pair, and then Ha also on the first qubit  

After this, he performs a measurement in the computational basis, obtaining the sequence 01. In this way, Alice has sent two bits of classical information sending only one qubit. Any other sequence can be sent by just varying the first operation, i.e. the application of the X gate. 

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