Disentangling theorem and monogamy for entanglement negativity

Abstract

Entanglement negativity is a measure of mixed-state entanglement increasingly used to investigate and characterize emerging quantum many-body phenomena, including quantum criticality and topological order. We present two results for the entanglement negativity: a disentangling theorem, which allows the use of this entanglement measure as a means to detect whether a wave function of three subsystems $A,\phantom{\rule{0.28em}{0ex}}B$, and $C$ factorizes into a product state for parts $A{B}_{1}$ and ${B}_{2}C$; and a monogamy relation conjecture based on entanglement negativity, which states that if $A$ is very entangled with $B$, then $A$ cannot be simultaneously very entangled also with $C$.