Fragile entanglement statistics

Dorje C. Brody, Lane P. Hughston, David M. Meier

Published 2015-05-07Version 1

If X and Y are independent, Y and Z are independent, and so are X and Z, one might be tempted to conclude that X, Y, and Z are independent. But it has long been known in classical probability theory that such a conclusion, intuitive as it may seem, is not true in general. In quantum mechanics one would expect that analogous statistics ought to emerge for configurations of particles in suitably chosen entangled states. The explicit construction of such a special state, however, along with the identification of the associated observables whose measurement outcomes admit this property, is not immediately apparent. It is shown here that the required configuration takes the form of a GHZ state, and a family of observables is identified with the property that for a given N-particle GHZ state, the measurement-outcome statistics of any choice of 2, 3, ..., N-1 particles are independent, even though the measurement-outcome statistics for all N particles are not independent.