Translating Uncontrolled Systems in Time

Abstract

We show that there exist non-relativistic scattering experiments which, if successful, freeze out, speed up or even reverse the free dynamics of any ensemble of quantum systems present in the scattering region. This ``time translation'' effect is universal, i.e., it is independent of the particular interaction between the scattering particles and the target systems, or the (possibly non-Hermitian) Hamiltonian governing the evolution of the latter. The protocols require careful preparation of the probes which are scattered, and success is heralded by projective measurements of these probes at the conclusion of the experiment. We fully characterize the possible time translations which we can effect on multiple target systems through a scattering protocol of fixed duration. The core results are: a) when the target is a single system, we can translate it backwards in time for an amount proportional to the experimental runtime; b) when n targets are present in the scattering region, we can make a single system evolve n times faster (backwards or forwards), at the cost of keeping the remaining n−1 systems stationary in time. For high n our protocols therefore allow one to map, in short experimental time, a system to the state it would have reached with a very long unperturbed evolution in either positive or negative time.

Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality

“…[72], which provides a probabilistic heralded method to reset and invert unitary operations even in absence of control on the target system in a scheme which was extended and optimised in Ref. [73].…”

Demonstration of universal time-reversal for quantum processes

“…An alternative formulation using a scattering scenario is given in the Appendix. A full description, as well as the accompanying proofs, can be found in [6]. Given an unknown target system |Ψ , whose time evolution is described by U = e −i∆T H0 , where H 0 is an unknown Hamiltonian, our goal will be to rewind the system:…”

“…Recently there have been several works addressing this question, in which probabilistic protocols for 'rewinding' quantum systems were presented [7,8] and demonstrated in a lab setting [9,10]. These protocols work independently of both the free Hamiltonian guiding the time evolution of the system in question, and the system's interaction with the experimental apparatus.…”

“…These protocols work independently of both the free Hamiltonian guiding the time evolution of the system in question, and the system's interaction with the experimental apparatus. A major drawback of the protocols in [8] is that they suffer from low success probabilities, typically on the order of 10 −3 . The scheme in [7], on the other hand, allows for a form of Figure 1.…”

“…Instead of detecting the failure mode of the quantum SWITCH the photon is made to re-interfere with itself. Whenever it exits in the bottom right the commutator [U, V ] will have been applied (see [6]) The dashed path represents recursive applications of the diagram, through which the success probability can be made arbitrarily high, while the darker shaded area indicates the additional quantum SWITCHes needed.…”