REVIEW 3 cited by
A Closed Form for Moment-Based Entanglement Tests Associated to the PPT Criterion
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
Neven et al. have explored an unexpected alliance between the mathematical insights of Sir Isaac Newton and Ren\'e Descartes which culminates in the reduction of the Positive Partial Transpose (PPT) criterion to an equivalent hierarchy of entanglement tests based on the moments of the partial transpose. By repurposing these classical results in the context of modern quantum theory, they illuminate new pathways for entanglement verification. Here, we expand on this work by providing a closed form for the inequalities defining these entanglement tests and producing an equivalent set of graph theoretic conditions on the weighted graph induced by the partial transpose.
Forward citations
Cited by 3 Pith papers
-
Detecting entanglement from few partial transpose moments and their decay via weight enumerators
Any three PT moments of orders k<l<m certify NPT entanglement if p_l > p_k^x p_m^{1-x}, and Stieltjes-m equals PPT when ρ^Γ has at most (m+1)/2 distinct eigenvalues.
-
Simultaneous Estimation of Partial-Transpose Moments with Active Memory Independent of the Moment Order
A qubit-reuse protocol estimates partial-transpose moments p_2 to p_K simultaneously to additive error ε using O(K log K / ε²) copies and at most 2n+1 active qubits independent of K, with matching Ω(K/ε²) lower bounds.
-
Detecting entanglement from few partial transpose moments and their decay via weight enumerators
Entanglement is certified if any three PT moments satisfy p_l > p_k^x p_m^{1-x} with x=(m-l)/(m-k), and quantum weight enumerators describe moment decay under local noise.
Discussion (0). Sign in to comment.