The Helstrom Bound

Quantum state discrimination between two wave functions on a ring is considered. The optimal minimum-error probability is known to be given by the Helstrom bound. A new strategy is introduced by inserting instantaneously two impenetrable barriers dividing the ring into two chambers. In the process, the candidate wave functions, as the insertion points become nodes, get entangled with the barriers and can, if judiciously chosen, be distinguished with smaller error probability. As a consequence, the Helstrom bound under idealised conditions can be violated.Comment: 4 page

Parafoveal-foveal overlap can facilitate ongoing word identification during reading: evidence from eye movements.

Readers continuously receive parafoveal information about the upcoming word in addition to the foveal information about the currently fixated word. Previous research (Inhoff, Radach, Starr, & Greenberg, 2000) showed that the presence of a parafoveal word that was similar to the foveal word facilitated processing of the foveal word. We used the gaze-contingent boundary paradigm (Rayner, 1975) to manipulate the parafoveal information that subjects received before or while fixating a target word (e.g., news) within a sentence. Specifically, a reader's parafovea could contain a repetition of the target (news), a correct preview of the posttarget word (once), an unrelated word (warm), random letters (cxmr), a nonword neighbor of the target (niws), a semantically related word (tale), or a nonword neighbor of that word (tule). Target fixation times were significantly lower in the parafoveal repetition condition than in all other conditions, suggesting that foveal processing can be facilitated by parafoveal repetition. We present a simple model framework that can account for these effects