From the early days of quantum mechanics until today, physicists have discussed the role played by probabilities and the nature of the collapse of the state of quantum systems subject to measurement. Erwin Schrödinger tried to dismiss these problems by declaring that quantum theory applies exclusively to large ensembles of particles, governed by mean values and absent of randomness. As late as 1952, Schrödinger thus claimed the very idea of experiments with single quantum particles to be “as absurd as the one of raising Ichtyosauria in the Zoo”.
A variety of single quantum systems are now routinely subject to experimental investigation in the laboratory. In the talk, I shall review methods used to control and describe the behavior of these Ichtyosauria in the quantum laboratory. I shall also demonstrate how exploration of these systems have inspired recent extensions to our understanding of what is a quantum state. Finally, I shall show examples of how the random jump behavior of quantum systems may truly benefit their applications in crucial technologies such as quantum information processing and quantum metrology.