Peter W. Shor
Published 2003-05-07, updated 2003-07-03Version 4
We reduce the number of open additivity problems in quantum information theory by showing that four of them are equivalent. We show that the conjectures of additivity of the minimum output entropy of a quantum channel, additivity of the Holevo expression for the classical capacity of a quantum channel, additivity of the entanglement of formation, and strong superadditivity of the entanglement of formation, are either all true or all false.
Comments: now 20 pages, replaced to add a reference, remove a reference to a claimed result about locally minimal output entropy states (my proof of this was incorrect), correct minor typos, and add more explanation for the background of these conjectures
Equivalence of space and time-bins in DPS-QKD
Equivalence between quantum simultaneous games and quantum sequential games
Some equivalences between the auxiliary field method and the envelope theory
