Separability bounds on multiqubit moments due to positivity under partial transpose

TL;DR

This paper derives bounds on multiqubit moments imposed by positivity under partial transpose (PPT) and demonstrates their violation by entangled states, providing new criteria for detecting entanglement.

Contribution

It introduces novel PPT-based bounds on multiqubit moments and shows their effectiveness in identifying entanglement in various states.

Findings

PPT bounds on multiqubit moments can be violated by entangled states.

Pure three-qubit states with non-zero tangle violate PPT moment bounds.

PPT moment bounds precisely characterize separability in Werner states.

Abstract

Positivity of the density operator reflects itself in terms of sequences of inequalities on observable moments. Uncertainty relations for non-commuting 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 novel 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 non-zero tangle violate these PPT moment constraints. Further, we recover necessary and sufficient condition of separability in a multiqubit Werner state through PPT bounds on moments.