Dissipative remote-state preparation in an interacting medium

TL;DR

This paper introduces a method for remote quantum state preparation using local dissipation in an interacting medium, enabling state control without direct medium manipulation.

Contribution

It develops a framework for stabilizing target states remotely via local dissipation and provides explicit construction methods applicable to various lattice geometries.

Findings

Constructed a local dissipation scheme for remote state stabilization.

Proved uniqueness of steady states in chain geometries.

Showed convergence time is faster than inverse spectral gap.

Abstract

Standard quantum state preparation methods work by preparing a required state locally and then distributing it to a distant location by a free-space propagation. We instead study procedures of preparing a target state at a remote location in the presence of an interacting background medium on which no control is required, manipulating only local dissipation. In mathematical terms, we characterize a set of reduced steady states stabilizable by local dissipation. An explicit local method is proposed by which one can construct a wanted one-site reduced steady state at an arbitrary remote site in a lattice of any size and geometry. In the chain geometry we also prove uniqueness of such a steady state. We demonstrate that the convergence time to fixed precision is smaller than the inverse gap, and we study robustness of the scheme in different medium interactions.