Resetting uncontrolled quantum systems

In Newtonian Physics, as well as in non-relativistic quantum theory, time is regarded as a real external parameter that is not subject to dynamics but describes the evolution of the whole universe in Newtonian absolute space. This leaves out the possibility to influence or manipulate it in any way.

This notion of time, however, does not correspond to the entity that we measure in the lab when we speak of, e.g., the time between a particle's production and its subsequent detection. Following this observation, in general relativity time is viewed as a relation between the states of different physical systems. This modern conception of time opens the door to warping the latter, i.e., to “moving” a physical system through time.

In this talk, I will present a non-relativistic scheme to warp the local time of a closed quantum system. More specifically, I will consider a scenario where we wish to bring a closed system of known Hilbert space dimension dS (the target), subject to an unknown Hamiltonian evolution, back to its quantum state at a past time t0. The target is out of our control: this means that we ignore both its free Hamiltonian and how the target interacts with other quantum systems we may use to influence it. Under these conditions, I will show that there exist quantum protocols which reset the target system to its exact quantum state at t0. Each "resetting protocol" is successful with non-zero probability for all possible free Hamiltonians and interaction unitaries, save a subset of zero measure. Moreover, in case a resetting protocol fails, it is possible to run a further protocol that, if successful, undoes both the natural evolution of the target and the effects of the failed protocol over the latter. By chaining in this fashion several such probabilistic protocols, one can substantially increase the overall probability of a successful resetting.

Event Type: 
Seminar
Scientific Area(s): 
Speaker(s): 
Event Date: 
Wednesday, October 10, 2018 - 16:00 to 17:30
Location: 
Bob Room
Room #: 
405