Quantum advantages for transportation tasks - projectiles, rockets and quantum backflow

Abstract Consider a scenario where quantum particle is initially prepared in some bounded region of space and left to propagate freely. After time, we verify if the has reached distant target region. We find that there exist ‘ultrafast’ (‘ultraslow’) states, whose probability arrival greater (smaller) than any classical same with momentum distribution. For both projectiles rockets, prove advantage, quantified by difference between optimal probabilities, limited Bracken-Melloy constant c bm , originally introduced study phenomenon backflow. In this regard, substantiate 29-year-old conjecture ≈ 0.038 proving bounds 0.0315 ≤ 0.072. Finally, show that, modified projectile initial position distribution also fixed, advantage can reach 0.1262.