01474nas a2200169 4500008004100000245005300041210005100094300001100145490000700156520101500163100001301178700001601191700001301207700001501220700001601235856005301251 2015 eng d00aA geometric approach to quantum state separation0 ageometric approach to quantum state separation a1230150 v173 aProbabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure states in the general case where the known states have arbitrary a priori probabilities. The problem is formulated from a geometric perspective and shown to be equivalent to the problem of finding tangent curves within two families of conics that represent the unitarity constraints and the objective functions to be optimized, respectively. We present the corresponding analytical solutions in various forms. In the limit of perfect state separation, which is equivalent to unambiguous state discrimination, the solution exhibits a phenomenon analogous to a second order symmetry breaking phase transition. We also propose a linear optics implementation of separation which is based on the dual rail representation of qubits and single-photon multiport interferometry.1 aBagan, E1 aYerokhin, V1 aShehu, A1 aFeldman, E1 aBergou, J A uhttp://stacks.iop.org/1367-2630/17/i=12/a=123015