# State protection by quantum control before and after noise

## TL;DR

This paper investigates the fundamental limits of protecting quantum states from noise using measurements and operations before and after noise, extending previous results to all finite dimensions and unital noise in qubits.

## Contribution

It proves that optimal protection protocols are either do nothing or discriminate and reprepare, generalizing earlier findings to broader noise models and dimensions.

## Key findings

- Optimal protocols are do nothing or discriminate and reprepare.
- The results apply to all finite-dimensional Hilbert spaces.
- Similar conclusions hold for any unital noise in qubits.

## Abstract

We discuss the possibility of protecting the state of a quantum system that goes through noise by measurements and operations before and after the noise process. We extend our previous result on nonexistence of "truly quantum" protocols that protect an unknown qubit state against the depolarizing noise better than "classical" ones [Phys. Rev. A, 95, 022321 (2017)] in two directions. First, we show that the statement is also true in any finite-dimensional Hilbert spaces, which was previously conjectured, the optimal protocol is either the do nothing protocol or the discriminate and reprepare protocol, depending on the strength of the noise. Second, in the case of a qubit, we show that essentially the same conclusion holds for any unital noise. These results describe the fundamental limitations in quantum mechanics from the viewpoint of control theory.