Irreducible multi-particle correlations in states without maximal rank
Abstract
In a system of n quantum particles, the correlations are classified into a series of irreducible k-particle correlations (2 k n), where the irreducible k-particle correlation is the correlation appearing in the states of k particles but not existing in the states of k-1 particles. A measure of the degree of irreducible k-particle correlation is defined based on the maximal entropy construction. By adopting a continuity approach, we overcome the difficulties in calculating the degrees of irreducible multi-particle correlations for the multi-particle states without maximal rank. In particular, we obtain the degrees of irreducible multi-particle correlations in the n-qubit stabilizer states and the n-qubit generalized GHZ states, which reveals the distribution of multi-particle correlations in these states.