Antiparallel spin does not always contain more information - art. no. 014301

We show that the Bloch vectors lying on any great circle comprise the large st set SL for which the parallel states \(n) over right arrow,(n) over righ t arrow > can always be exactly transformed into the antiparallel states \( n) over right arrow-(n) over right arrow >. Thus mon information about (n) over right arrow is not extractable from \(n) over right arrow,-(n) over ri ght arrow > than from \(n) over right arrow,(n) over right arrow > by any m easuring strategy, for (n) over right arrow is an element of S-L. Surprisin gly this most general transformation reduces to just a flip operation on th e second particle. We also show here that a probabilistic exact parallel to antiparallel transformation is not possible if the corresponding antiparal lel states span the whole Hilbert space of the two qubits. These considerat ions allow us to generalize a conjecture of Gisin and Popescu [Phys. Rev. L ett. 83, 432 (1993)].