### Abstract

To control a quantum system via feedback, we generally have two options in choosing a 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 measurementbased feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. 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 the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.

Original language | English |
---|---|

Article number | 041029 |

Journal | Physical Review X |

Volume | 4 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Optics
- Quantum information
- Quantum physics

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Coherent versus measurement feedback : Linear systems theory for quantum information.** / Yamamoto, Naoki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Coherent versus measurement feedback

T2 - Linear systems theory for quantum information

AU - Yamamoto, Naoki

PY - 2014

Y1 - 2014

N2 - To control a quantum system via feedback, we generally have two options in choosing a 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 measurementbased feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. 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 the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.

AB - To control a quantum system via feedback, we generally have two options in choosing a 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 measurementbased feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. 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 the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.

KW - Optics

KW - Quantum information

KW - Quantum physics

UR - http://www.scopus.com/inward/record.url?scp=84921530582&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921530582&partnerID=8YFLogxK

U2 - 10.1103/PhysRevX.4.041029

DO - 10.1103/PhysRevX.4.041029

M3 - Article

AN - SCOPUS:84921530582

VL - 4

JO - Physical Review X

JF - Physical Review X

SN - 2160-3308

IS - 4

M1 - 041029

ER -