Effective Subspace for Pure State Transfer Induced by Measurements

TL;DR

This paper demonstrates that in measurement-induced quantum control of an N-level system with pure initial and target states, the control space can be simplified to a subspace spanned by these states, streamlining control strategies.

Contribution

It proves that the control space reduces to a subspace spanned by initial and target states in pure state transfer, simplifying quantum control design.

Findings

Control space reduces to span of initial and target states.

Simplifies measurement-induced control strategies.

Applicable to general N-level quantum systems.

Abstract

One main goal of quantum control is to steer a quantum system toward an expected state or dynamics. For measurement-induced quantum control, measurements serve as the only control, which is like the cases in quantum Zeno and anti-zeno effects. In this paper, this scenario will be investigated in a general $N$-level quantum system. It is proved that, when the intial and expected states are both pure, the control space could be reduced to an effective subspace spanned by these two states only. This result will greatly simplify the measurement-induced control strategy of an $N$-level quantum system.