Lindbladian purification

Christian Arenz, Daniel Burgarth, Vittorio Giovannetti, Hiromichi Nakazato, Kazuya Yuasa

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    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 languageEnglish
    Article number024001
    JournalQuantum Science and Technology
    Volume2
    Issue number2
    DOIs
    Publication statusPublished - 2017 Jun 1

    Fingerprint

    Hamiltonians
    purification
    Purification
    controllability
    Hilbert space
    Hilbert spaces
    Controllability
    embedding
    Open systems
    projection

    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

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

    In: Quantum Science and Technology, Vol. 2, No. 2, 024001, 01.06.2017.

    Research output: Contribution to journalArticle

    Arenz, Christian ; Burgarth, Daniel ; Giovannetti, Vittorio ; Nakazato, Hiromichi ; Yuasa, Kazuya. / Lindbladian purification. In: Quantum Science and Technology. 2017 ; Vol. 2, No. 2.
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