Distinguishability of hyperentangled Bell state by linear evolution and local projective measurement

Measuring an entangled state of two particles is crucial to many quantum communication protocols. Yet Bell state distinguishability using a finite apparatus obeying linear evolution and local measurement is theoretically limited. We extend known bounds for Bell-state distinguishability in one and two variables to the general case of entanglement in $n$ two-state variables. We show that at most $2^{n+1}-1$ classes out of $4^n$ hyper-Bell states can be distinguished with one copy of the input state. With two copies, complete distinguishability is possible. We present optimal schemes in each case.Comment: 5 pages, 2 figure

Utilizing the chicken as an animal model for human craniofacial ciliopathies

The chicken has been a particularly useful model for the study of craniofacial development and disease for over a century due to their relatively large size, accessibility, and amenability for classical bead implantation and transplant experiments. Several naturally occurring mutant lines with craniofacial anomalies also exist and have been heavily utilized by developmental biologist for several decades. Two of the most well known lines, talpid(2) (ta(2)) and talpid(3) (ta(3)), represent the first spontaneous mutants to have the causative genes identified. Despite having distinct genetic causes, both mutants have recently been identified as ciliopathic. Excitingly, both of these mutants have been classified as models for human craniofacial ciliopathies: Oral-facial-digital syndrome (ta(2)) and Joubert syndrome (ta(3)). Herein, we review and compare these two models of craniofacial disease and highlight what they have revealed about the molecular and cellular etiology of ciliopathies. Furthermore, we outline how applying classical avian experiments and new technological advances (transgenics and genome editing) with naturally occurring avian mutants can add a tremendous amount to what we currently know about craniofacial ciliopathies