# Targeting pure quantum states by strong noncommutative dissipation

## TL;DR

This paper presents a criterion for engineering pure quantum states as steady states of open quantum systems using strong dissipation, with explicit formulas and practical examples like Bell and spin-helix states.

## Contribution

It introduces a necessary and sufficient condition for pure state stabilization via strong noncommutative dissipation in Lindblad systems, including explicit dissipative strength formulas.

## Key findings

- Derived a criterion for pure state stabilization in the Zeno limit.
- Provided explicit formulas for the required dissipative strength.
- Demonstrated the approach with Bell, N-qubit, and spin-helix states.

## Abstract

We propose a solution to the problem of realizing a predefined and arbitrary pure quantum state, based on the simultaneous presence of coherent and dissipative dynamics, noncommuting on the target state and in the limit of strong dissipation. More precisely, we obtain a necessary and sufficient criterion whereby the nonequilibrium steady state (NESS) of an open quantum system described by a Lindblad master equation approaches a target pure state in the Zeno regime, i.e., for infinitely large dissipative coupling. We also provide an explicit formula for the characteristic dissipative strength beyond which the purity of the NESS becomes effective, thus paving the way to an experimental implementation of our criterion. For an illustration, we deal with targeting a Bell state, an arbitrary pure state of $N$ qubits, and a spin-helix state of $N$ qubits.