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Distillation of Entanglement between Distant Systems by Repeated Measurements on Entanglement Mediator

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 Added by Kazuya Yuasa
 Publication date 2004
  fields Physics
and research's language is English




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A recently proposed purification method, in which the Zeno-like measurements of a subsystem can bring about a distillation of another subsystem in interaction with the former, is utilized to yield entangled states between distant systems. It is shown that the measurements of a two-level system locally interacting with other two spatially separated not coupled subsystems, can distill entangled states from the latter irrespectively of the initial states of the two subsystems.



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We consider a non-interacting bipartite quantum system $mathcal H_S^Aotimesmathcal H_S^B$ undergoing repeated quantum interactions with an environment modeled by a chain of independant quantum systems interacting one after the other with the bipartite system. The interactions are made so that the pieces of environment interact first with $mathcal H_S^A$ and then with $mathcal H_S^B$. Even though the bipartite systems are not interacting, the interactions with the environment create an entanglement. We show that, in the limit of short interaction times, the environment creates an effective interaction Hamiltonian between the two systems. This interaction Hamiltonian is explicitly computed and we show that it keeps track of the order of the successive interactions with $mathcal H_S^A$ and $mathcal H_S^B$. Particular physical models are studied, where the evolution of the entanglement can be explicitly computed. We also show the property of return of equilibrium and thermalization for a family of examples.
Entanglement is a vital property of multipartite quantum systems, characterised by the inseparability of quantum states of objects regardless of their spatial separation. Generation of entanglement between increasingly macroscopic and disparate systems is an ongoing effort in quantum science which enables hybrid quantum networks, quantum-enhanced sensing, and probing the fundamental limits of quantum theory. The disparity of hybrid systems and the vulnerability of quantum correlations have thus far hampered the generation of macroscopic hybrid entanglement. Here we demonstrate, for the first time, generation of an entangled state between the motion of a macroscopic mechanical oscillator and a collective atomic spin oscillator, as witnessed by an Einstein-Podolsky-Rosen variance below the separability limit, $0.83 pm 0.02<1$. The mechanical oscillator is a millimeter-size dielectric membrane and the spin oscillator is an ensemble of $10^9$ atoms in a magnetic field. Light propagating through the two spatially separated systems generates entanglement due to the collective spin playing the role of an effective negative-mass reference frame and providing, under ideal circumstances, a backaction-free subspace; in the experiment, quantum backaction is suppressed by 4.6 dB. Our results pave the road towards measurement of motion beyond the standard quantum limits of sensitivity with applications in force, acceleration,and gravitational wave detection, as well as towards teleportation-based protocols in hybrid quantum networks.
Repeated measurements on a part of a bipartite system strongly affect the other part not measured, whose dynamics is regulated by an effective contracted evolution operator. When the spectrum of this operator is discrete, the latter system is driven into a pure state irrespective of the initial state, provided the spectrum satisfies certain conditions. We here show that even in the case of continuous spectrum an effective distillation can occur under rather general conditions. We confirm it by applying our formalism to a simple model.
In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system-environment dynamics that is trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an anicillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arisng from the procedure. In this paper we demonstrate the effectiveness of such a protocol by applying it to physically relevant multi-spin models, showing that the effective non-Hermitian Hamiltonian drives the system to a maximally entangled stationary state. In addition, we report a new recipe to construct a physical scenario where the quantum dynamics of a physical system represented by a given non-Hermitian Hamiltonian model may be simulated. The physical implications and the broad scope potential applications of such a scheme are highlighted.
The potential impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable real-world imperfections necessitate means to improve remote entanglement by local quantum operations. Here we realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit nodes. We demonstrate the heralded generation of two copies of a remote entangled state through single-photon-mediated entangling of the electrons and robust storage in the nuclear spins. After applying local two-qubit gates, single-shot measurements herald the distillation of an entangled state with increased fidelity that is available for further use. In addition, this distillation protocol significantly speeds up entanglement generation compared to previous two-photon-mediated schemes. The key combination of generating, storing and processing entangled states demonstrated here opens the door to exploring and utilizing multi-particle entanglement on an extended quantum network.
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