We discover a simple factorization law describing how multipartite entanglement of a composite quantum system evolves when one of the subsystems undergoes an arbitrary physical process. This multipartite entanglement decay is determined uniquely by a single factor we call the entanglement resilience factor. Since the entanglement resilience factor is a function of the quantum channel alone, we find that multipartite entanglement evolves in exactly the same way as bipartite (two qudits) entanglement. For the two qubits case, our factorization law reduces to the main result of [T. Konrad, Nature Phys. 4, 99 (2008)10.1038/nphys885]. In addition, for a permutation P, we provide an operational definition of P asymmetry of entanglement, and find the conditions when a permuted version of a state can be achieved by local means.
We analyze a family of measures of general quantum correlations for composite systems, defined in terms of the bipartite entanglement necessarily created between systems and apparatuses during local measurements. For every entanglement monotone
E, this operational correspondence provides a different measure
QE of quantum correlations. Examples of such measures are the relative entropy of quantumness, the quantum deficit, and the negativity of quantumness. In general, we prove that any so-defined quantum correlation measure is always greater than (or equal to) the corresponding entanglement between the subsystems, ${Q}_{E}\ensuremath{\ge}E$, for arbitrary states of composite quantum systems. We analyze qualitatively and quantitatively the flow of correlations in iterated measurements, showing that general quantum correlations and entanglement can never decrease along von Neumann chains, and that genuine multipartite entanglement in the initial state of the observed system always gives rise to genuine multipartite entanglement among all subsystems and all measurement apparatuses at any level in the chain. Our results provide a comprehensive framework to understand and quantify general quantum correlations in multipartite states.
A characterization of multipartite quantum states having
N subsystems, based on negativities of matrices obtained by selective partial transposition of the state operator, is proposed. The
K-way partial transpose with respect to a subsystem is constructed by imposing constraints involving the states of
K subsystems of the multipartite composite system. The
K-way negativity, defined as the negativity of
K-way partial transpose, quantifies the
K-way coherences of the composite system. For an
N-partite system the fraction of
K-way negativity $(2\ensuremath{\le}K\ensuremath{\le}N)$, contributing to global negativity, is obtained. The entanglement measures for a given state $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}$ are identified as the partial
K-way negativities of the corresponding canonical state.