### Abstract

In a recent work (Burgarth et al 2014, Nat. Commun. 5 5173), it was shown that a series of frequent measurements can project the dynamics of a quantum system onto a subspace in which the dynamics can be more complex. In this subspace, even full controllability can be achieved, although the controllability over the system before the projection is very poor since the control Hamiltonians commute with each other. We can also think of the opposite: any Hamiltonians of a quantum system, which are in general noncommutative with each other, can be made commutative by embedding them in an extended Hilbert space, thus the dynamics in the extended space becomes trivial and simple. This idea of making noncommutative Hamiltonians commutative is called 'Hamiltonian purification.' The original noncommutative Hamiltonians are recovered by projecting the system back onto the original Hilbert space through frequent measurements. Here, we generalise this idea to open-system dynamics by presenting a simple construction to make Lindbladians, as well as Hamiltonians, commutative on a larger space with an auxiliary system. We show that the original dynamics can be recovered through frequently measuring the auxiliary system in a non-selective way. Moreover, we provide a universal pair of Lindbladians that describe an 'accessible' open quantum system for generic system sizes. This allows us to conclude that through a series of frequent non-selective measurements a nonaccessible open quantum system generally becomes accessible. This sheds further light on the role of measurement backaction on the control of quantum systems.

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

Article number | 024001 |

Journal | Quantum Science and Technology |

Volume | 2 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2017 Jun 1 |

### Fingerprint

### Keywords

- measurement
- open quantum systems
- quantum control
- quantum Zeno effect

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Physics and Astronomy (miscellaneous)
- Electrical and Electronic Engineering
- Materials Science (miscellaneous)

### Cite this

*Quantum Science and Technology*,

*2*(2), [024001]. https://doi.org/10.1088/2058-9565/aa6759

**Lindbladian purification.** / Arenz, Christian; Burgarth, Daniel; Giovannetti, Vittorio; Nakazato, Hiromichi; Yuasa, Kazuya.

Research output: Contribution to journal › Article

*Quantum Science and Technology*, vol. 2, no. 2, 024001. https://doi.org/10.1088/2058-9565/aa6759

}

TY - JOUR

T1 - Lindbladian purification

AU - Arenz, Christian

AU - Burgarth, Daniel

AU - Giovannetti, Vittorio

AU - Nakazato, Hiromichi

AU - Yuasa, Kazuya

PY - 2017/6/1

Y1 - 2017/6/1

N2 - In a recent work (Burgarth et al 2014, Nat. Commun. 5 5173), it was shown that a series of frequent measurements can project the dynamics of a quantum system onto a subspace in which the dynamics can be more complex. In this subspace, even full controllability can be achieved, although the controllability over the system before the projection is very poor since the control Hamiltonians commute with each other. We can also think of the opposite: any Hamiltonians of a quantum system, which are in general noncommutative with each other, can be made commutative by embedding them in an extended Hilbert space, thus the dynamics in the extended space becomes trivial and simple. This idea of making noncommutative Hamiltonians commutative is called 'Hamiltonian purification.' The original noncommutative Hamiltonians are recovered by projecting the system back onto the original Hilbert space through frequent measurements. Here, we generalise this idea to open-system dynamics by presenting a simple construction to make Lindbladians, as well as Hamiltonians, commutative on a larger space with an auxiliary system. We show that the original dynamics can be recovered through frequently measuring the auxiliary system in a non-selective way. Moreover, we provide a universal pair of Lindbladians that describe an 'accessible' open quantum system for generic system sizes. This allows us to conclude that through a series of frequent non-selective measurements a nonaccessible open quantum system generally becomes accessible. This sheds further light on the role of measurement backaction on the control of quantum systems.

AB - In a recent work (Burgarth et al 2014, Nat. Commun. 5 5173), it was shown that a series of frequent measurements can project the dynamics of a quantum system onto a subspace in which the dynamics can be more complex. In this subspace, even full controllability can be achieved, although the controllability over the system before the projection is very poor since the control Hamiltonians commute with each other. We can also think of the opposite: any Hamiltonians of a quantum system, which are in general noncommutative with each other, can be made commutative by embedding them in an extended Hilbert space, thus the dynamics in the extended space becomes trivial and simple. This idea of making noncommutative Hamiltonians commutative is called 'Hamiltonian purification.' The original noncommutative Hamiltonians are recovered by projecting the system back onto the original Hilbert space through frequent measurements. Here, we generalise this idea to open-system dynamics by presenting a simple construction to make Lindbladians, as well as Hamiltonians, commutative on a larger space with an auxiliary system. We show that the original dynamics can be recovered through frequently measuring the auxiliary system in a non-selective way. Moreover, we provide a universal pair of Lindbladians that describe an 'accessible' open quantum system for generic system sizes. This allows us to conclude that through a series of frequent non-selective measurements a nonaccessible open quantum system generally becomes accessible. This sheds further light on the role of measurement backaction on the control of quantum systems.

KW - measurement

KW - open quantum systems

KW - quantum control

KW - quantum Zeno effect

UR - http://www.scopus.com/inward/record.url?scp=85047988935&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047988935&partnerID=8YFLogxK

U2 - 10.1088/2058-9565/aa6759

DO - 10.1088/2058-9565/aa6759

M3 - Article

AN - SCOPUS:85047988935

VL - 2

JO - Quantum Science and Technology

JF - Quantum Science and Technology

SN - 2058-9565

IS - 2

M1 - 024001

ER -