Distributed entanglement - art. no. 052306

Consider three qubits A, B, and C which may be entangled with each other. W e show that there is a trade-off between A's entanglement with B and its en tanglement with C. This relation is expressed in terms of a measure of enta nglement called the concurrence, which is related to the entanglement of fo rmation. Specifically, we show that the squared concurrence between A and B , plus the squared concurrence between A and C, cannot be greater than the squared concurrence between A and the pair BC. This inequality is as strong as it could be, in the sense that for any values of the concurrences satis fying the corresponding equality, one can find a quantum state consistent w ith those values. Further exploration of this result leads to a definition of an essential three-way entanglement of the system, which is invariant un der permutations of the qubits.