A key feature of quantum information science is the understanding that groups of two or more quantum objects can have states that are entangled, such that the members of an entangled collection of objects do not have their own Line individual quantum states, only the group as a whole. Although one can use the (5) mathematics of quantum theory to reason about entanglement, there is a great danger that the classical basis of our analogies will mislead us. Despite its strangeness, for a long time entanglement was regarded as a curiosity and was mostly ignored by physicists and this changed when Bell predicted and confirmed that entangled quantum systems exhibit behavior. that is impossible in (10) a classical world-impossible even if one could change the laws of physics to try to emulate the quantum predictions within a classical framework of any sort. The idea that entanglement falls wholly outside the scope of classical physics prompted researchers to ask whether entanglement might be useful as a resource for solving information-processing problems in new ways. (15) Entanglement measures improve how researchers can analyze tasks such as quantum teleportation and algorithms on quantum-mechanical computers. Classical computation and communications have a well-developed assortment of error-correcting codes to protect information against the depredations of noise, an example being the repetition code. This scheme represents the bit 0 as a (20) string of three bits, 000, and the bit 1 as a string of three bits, 111. If the noise is relatively weak, it may sometimes flip one of the bits in a triplet, changing, for instance, 000 to 010, but it will flip two bits in a triplet far less often. Whenever we encounter 010 (or 100 or 001), we can be almost certain the correct value is 000, or 0. (25) Initially it appeared to be impossible to develop codes for quantum error correction because quantum mechanics forbids us from learning with certainty the unknown state of a quantum object-the obstacle, again, of trying to extract more than one bit from a quantum bit. One cannot examine each copy of a quantum bit and see that one copy must be discarded without altering each and (30) every copy in the process, and making the copies in the first place is nontrivial: quantum mechanics forbids taking an unknown quantum bit and reliably making a duplicate, a result known as the no-cloning theorem. Clever ideas developed independently by Shor showed quantum error correction can be performed without ever learning the states of the quantum bits or needing to clone them. (35) As with the triplet code, each value is represented by a set of quantum bits and it is as if one ran the triplet 010 through a circuit that could spot that the middle bit was different and flip it 'sight unseen'. The author suggests that, prior to Bell, the suggestion that entangled quantum systems exhibit behavior. impossible in the world of classical physics would probably have been viewed with