Superdense coding: Difference between revisions

Revision as of 11:07, 28 October 2005

Revision as of 12:38, 6 February 2006

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'''Superdense coding''' is a technique used in [[quantum information theory]]. It uses [[quantum entanglement]] to send data. The process can be explained as follows:

If Alice wished to send information to Bob by sending qubits, it might seem at first that she can only send one bit per qubit. For example, if she wished to send the bit 0 she could send a qubit in the state <math>|0\rangle</math> and if she wished to send 1 she could send a qubit in the state <math>|1\rangle</math>. It turns out, however, that entanglement can be used to transfer information more efficiently than this. The process by which this is possible is known as superdense coding. The basic principle of the process is simple, Alice has two bits of information that she wishes to send to Bob and wants to do this by sending only one qubit. This can be done if Alice and Bob each have one half of an entangled pair of qubits. By using local operations on her qubit, Alice can cause the pair to be in any of the four [[Bell statesstate]]s <math>|\Phi^+\rangle</math>, <math>|\Phi^-\rangle</math>, <math>|\Psi^+\rangle</math> and <math>|\Psi^-\rangle</math> of her choosing. If Alice then sends her qubit to Bob then he can use a [[Bell state measurement]] to determine the state of the pair. If Alice and Bob had previously agreed that Alice would cause the pair to be in state <math>|\Phi^+\rangle</math> if she wanted to send the bit stream 00, <math>|\Phi^-\rangle</math> for 01, <math>|\Psi^+\rangle</math> for 10 and <math>|\Psi^-\rangle</math> for 11 then with the results of the Bell state measurement Bob would have received two bits of information from Alice, even though she only sent one qubit to him.