Positivity of the density operator reflects itself in terms of sequences of inequalities on observable moments. Uncertainty relations for noncommuting observables form a subset of these inequalities. In addition, criterion of positivity under partial transposition (PPT) imposes distinct bounds on moments, violations of which signal entanglement. We present bounds on some sets of composite moments, consequent to positive partial transposition of the density operator and report their violation by entangled multiqubit states. In particular, we derive separability bounds on a multiqubit moment matrix (based on PPT constraints on bipartite divisions of the density matrix) and show that three-qubit pure states with nonzero tangle violate these PPT moment constraints. Further, we recover a necessary and sufficient condition of separability in a multiqubit Werner state through PPT bounds on moments.

• Received 19 August 2008

DOI:https://doi.org/10.1103/PhysRevA.78.062334