Abstract

Quantum entanglement bears some resemblance to ordinary classical correlation, but there are important differences. In particular, whereas any number of classical variables can in principle be perfectly correlated with each other–the temperature fluctuations in ten different cities could conceivably be exactly parallel–any entanglement that exists between two quantum objects has the effect of limiting the entanglement that either of these objects can have with the rest of the world. In this talk I will discuss a number of examples of quantum systems in which this restriction on the sharing of entanglement can be expressed quantitatively. In the special case of three spin-1/2 particles A, B, and C, there is a convenient measure of entanglement called the concurrence in terms of which the trade-off between the AB entanglement and the AC entanglement takes a particularly simple form: the sum of the squares cannot exceed unity. For larger spins, preliminary results suggest that the limitation on entanglement sharing is less stringent. Finally, for a collection of many spin-1/2 particles arranged in a line, the problem of sharing entanglement points to an interesting feature of antiferromagnetic chains, namely, that they favor states with high nearest-neighbor entanglement.

© 2001 Optical Society of America