Abstract
We consider a scenario where we wish to bring a closed system of known Hilbert space dimension $d_S$ (the target), subject to an unknown Hamiltonian evolution, back to its quantum state at a past time $t_0$. The target is out of our control: this means that we ignore both its free Hamiltonian and how the system interacts with other quantum systems we may use to influence it. Under these conditions, we prove that there exist protocols within the framework of non-relativistic quantum physics which reset the target system to its exact quantum state at $t_0$. Each "resetting protocol" is successful with non-zero probability for all possible free Hamiltonians and interaction unitaries, save a subset of zero measure. When the target is a qubit and the interaction is sampled from the Haar measure, the simplest resetting circuits have a significant average probability of success and their implementation is within reach of current quantum technologies. Finally, we find that, in case the 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 protocols, one can substantially increase the overall probability of a successful resetting.
Highlights
In Newtonian physics, as well as in nonrelativistic 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
If U is taken uniformly according to the Haar mR easure, we find that the average probability of success dUpðx 1⁄4 0jU; W4Þ is approximately 0.2170
We have proven that there exist probabilistic nonrelativistic quantum protocols that allow one to bring an uncontrolled quantum system to a past state
Summary
In Newtonian physics, as well as in nonrelativistic 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. Special relativity teaches us that we can decrease the flow of time within a physical system just by accelerating and decelerating it with respect to us This would allow us to carry a time-warp experience with 0 < τ0 < τ. [5], where the authors show how to use linear superpositions of space-time metrics to accelerate, slow, or reverse the unitary time evolution of a closed quantum system At this point, it is worth remarking that there is nothing mysterious about time warp in itself. The simplest protocols just require control over three qubits and, can be implemented with current quantum technologies
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