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The problem of optimally discriminating between two completely unknown qubitstates is generalized by allowing an error margin. It is visualized as adevice---the programmable discriminator---with one data and two program ports,each fed with a number of identically prepared qubits---the data and theprograms. The device aims at correctly identifying the data state with one ofthe two program states. This scheme has the unambiguous and the minimum-errorschemes as extremal cases, when the error margin is set to zero or it issufficiently large, respectively. Analytical results are given in the twosituations where the margin is imposed on the average error probability---weakcondition---or it is imposed separately on the two probabilities of assigningthe state of the data to the wrong program---strong condition. It is a generalfeature of our scheme that the success probability rises sharply as soon as asmall error margin is allowed, thus providing a significant gain over theunambiguous scheme while still having high confidence results.

Programmable discrimination with an error margin