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In a recent work [D. K. Burgarth et al., Nat. Commun. 5, 5173 (2014)] 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, and 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 generalize 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 which describes 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.
We introduce a quantity called the coherence of purification which can be a measure of total quantumness for a single system. We prove that coherence of purification is always more than the coherence of the system. For a pure state, the coherence of
We discuss a protocol based on quenching a purified quantum system that allows to capture bulk spectral features. It uses an infinite temperature initial state and an interferometric strategy to access the Loschmidt amplitude, from which the spectral
Single-photon entanglement is a simple form of entanglement that exists between two spatial modes sharing a single photon. Despite its elementary form, it provides a resource as useful as polarization-entangled photons and it can be used for quantum
We report the experimental realization of the purification protocol for single qubits sent through a depolarization channel. The qubits are associated with polarization encoded photon particles and the protocol is achieved by means of passive linear
We present a number of rapid-purification feedback protocols for optical homodyne detection of a single optical qubit. We derive first a protocol that speeds up the rate of increase of the average purity of the system, and find that like the equivale