Unavoidable decoherence in the quantum control of an unknown state

TL;DR

The paper demonstrates that controlling an unknown quantum state into a multi-dimensional decoherence-free subspace inevitably involves decoherence, making pure states become mixed, thus limiting the effectiveness of coherent control for this task.

Contribution

It proves that achieving control into a multi-dimensional decoherence-free subspace necessarily involves decoherence, regardless of the control mechanism used.

Findings

Control into multi-dimensional decoherence-free subspaces induces decoherence.

Coherent control offers no fundamental advantage over measurement-based feedback in this context.

Almost any pure state is transformed into a mixed state during such control processes.

Abstract

A common objective for quantum control is to force a quantum system, initially in an unknown state, into a particular target subspace. We show that if the subspace is required to be a decoherence-free subspace of dimension greater than 1, then such control must be decoherent. That is, it will take almost any pure state to a mixed state. We make no assumptions about the control mechanism, but our result implies that for this purpose coherent control offers no advantage, in principle, over the obvious measurement-based feedback protocol.