Quantum Entanglement
Quantum entanglement is a subtle nonlocal correlation among the parts of a quantum system that has no classical analog. Thus entanglement is best characterized and quantified as a feature of the system that cannot be created through local operations that act on the different parts separately, or by means of classical communication among the parts.
In the case of a pure quantum state of a system divided into two parts, the entanglement can be completely characterized because it can be reversibly converted to a standard currency. If many identical copies of a given state are available, then it is possible with local operations and classical communication to "distill" the entanglement into a standard form — many copies of a two-qubit Bell pair. And the Bell pairs, with local operations and classical communication, can be transformed back into many copies of the original state, with negligible losses. Thus the number of distillable Bell pairs provides a universal measure of bipartite pure state entanglement.
The situation is far more subtle and interesting for the case of entangled bipartite mixed states, or for pure-state entanglement with more than two parts. For example, some bipartite mixed states exhibit bound entanglement -- though entanglement is necessary to create these states, none of this entanglement can be distilled into Bell pairs. Another significant surprise is that even bipartite states with no entanglement can exhibit a peculiar kind of quantum nonlocality. One can construct a quantum book with two pages, such that it is impossible to read the book one page at a time, even though the two pages are not entangled with one another.
Since entanglement cannot be created locally, an entangled state shared by two widely separated parties can be a valuable resource (Fig. 3). One application of shared entanglement is a novel quantum communication protocol called quantum teleportation. If one party (Alice) possesses a qubit in an unknown state, she cannot observe the state without disturbing it. But if she shares a Bell pair with another party (Bob), then Alice can convey a perfect replica of her state to Bob by sending him just two bits of classical information. In the process, the shared Bell pair is consumed, and Alice’s original is destroyed. An odd feature of quantum teleportation is that the unknown state can take values in a continuum; nevertheless, thanks to the pre-existing shared entanglement, Bob needs to receive only two classical bits to recover the perfect replica. This protocol has been convincingly demonstrated in the laboratory.
http://www.nsf.gov/pubs/2000/nsf00101/images/figure3.gif
Figure 3: Two related tasks that require quantum entanglement as a resource. In quantum teleportation, Alice receives a qubit in an unknown state, and destroys it by performing a Bell measurement on that qubit and a member of an entangled pair of qubits that she shares with Bob. She sends a two-bit classical message (her measurement outcome) to Bob, who then performs a unitary transformation on his member of the pair to reconstruct a perfect replica of the unknown state. In superdense coding, Alice receives a two-bit classical message, transmits the message by performing a unitary transformation on a member of an entangled pair that she shares with Bob, and then sends that qubit to Bob. Thus one qubit suffices to carry two classical bits of information.
