Coherent versus measurement feedback: Linear systems theory for quantum information

TL;DR

This paper compares coherent and measurement feedback control in linear quantum systems, demonstrating that certain quantum control goals can only be achieved with coherent feedback through system theoretic analysis.

Contribution

It provides a systematic comparison of feedback schemes in quantum control, proving no-go theorems for measurement-based feedback and constructing coherent feedback controllers for key quantum information tasks.

Findings

Measurement-based feedback cannot achieve BAE, QND, or DFS.

Coherent feedback controllers can accomplish all three control goals.

System theoretic characterizations clarify the limitations and capabilities of feedback schemes.

Abstract

To control a quantum system via feedback, we generally have two options in choosing control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is the measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages/disadvantages, depending on the system and the control goal, hence their comparison in several situation is important. This paper considers a general open linear quantum system with the following specific control goals; back-action evasion (BAE), generation of a quantum non-demolished (QND) variable, and generation of a decoherence-free subsystem (DFS), all of which have important roles in quantum information science. Then some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand it is shown that, for each control goal, there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of BAE, QND, and DFS in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.