2014/01/31 by Ting Gao, Fengli Yan, S. J. van Enk · 2 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physrevlett.112.180501
published as PRL 112, 180501 (2014)
arxiv created 2014/05/18 · arxiv updated 2014/05/20
We consider the concept of "the permutationally invariant (PI) part of a density matrix," which has proven very useful for both efficient quantum state estimation and entanglement characterization of N-qubit systems. We show here that the concept is, in fact, basis-dependent, but that this basis dependence makes it an even more powerful concept than has been appreciated so far. By considering the PI part ρ\rm PI of a general (mixed) N-qubit state ρ, we obtain: (i) strong bounds on quantitative nonseparability measures, (ii) a whole hierarchy of multi-partite separability criteria (one of which entails a sufficient criterion for genuine N-partite entanglement) that can be experimentally determined by just 2N+1 measurement settings, (iii) a definition of an efficiently measurable degree of separability, which can be used for quantifying a novel aspect of decoherence of N qubits, and (iv) an explicit example that shows there are, for increasing N, genuinely N-partite entangled states lying closer and closer to the maximally mixed state. Moreover, we show that if the PI part of a state is k-nonseparable, then so is the actual state. We further argue to add as requirement on any multi-partite entanglement measure E that it satisfy E(ρ)≥ E(ρ\rm PI), even though the operation that maps ρ→ρ\rm PI is not local.