Every positive-partial-transpose channel is claimed to become entanglement-breaking after finitely many iterations, but the paper's additional uniform bound of 3 for a large family is false as stated.
Composition of PPT Maps
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
M. Christandl conjectured that the composition of any trace preserving PPT map with itself is entanglement breaking. We prove that Christandl's conjecture holds asymptotically by showing that the distance between the iterates of any unital or trace preserving PPT map and the set of entanglement breaking maps tends to zero. Finally, for every graph we define a one-parameter family of maps on matrices and determine the least value of the parameter such that the map is variously, positive, completely positive, PPT and entanglement breaking in terms of properties of the graph. Our estimates are sharp enough to conclude that Christandl's conjecture holds for these families.
fields
quant-ph 1years
2026 1verdicts
REJECT 1representative citing papers
citing papers explorer
-
Every PPT channel has finite entanglement-breaking index
Every positive-partial-transpose channel is claimed to become entanglement-breaking after finitely many iterations, but the paper's additional uniform bound of 3 for a large family is false as stated.