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arXiv:1306.4451 · Physical Review A

Purifying entanglement of noisy two-qubit states via entanglement swapping

Wei Song, Ming Yang, Zhuo‐Liang Cao

Published Jan 21, 2014• 17 citations
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Abstract

Two qubits in pure entangled states going through separate paths and interacting with their own individual environments will gradually lose their entanglement. Here we show that the entanglement change of a two-qubit state due to amplitude damping noises can be recovered by entanglement swapping. Some initial states can be asymptotically purified into maximally entangled states by iteratively using our protocol.

DOI
10.1103/physreva.89.014303

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Two qubits in pure entangled states going through separate paths and interacting with their own individual environments will gradually lose their entanglement. Here we show that the entanglement change of a two-qubit state due to amplitude damping noises can be recovered by entanglement swapping. Some initial states can be asymptotically purified into maximally entangled states by iteratively using our protocol.
We study the time evolution of two two-state systems (two qubits) initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherence.
Abstract We investigate the entanglement swapping under phase damping global noise and amplitude damping global noise. The two qubits the intermediate user holds during the entanglement swapping process first suffer from a global noise before the Bell measurement is carried out. Based on this assumption, the influence of global phase damping noise and global amplitude damping noise on the output entanglement of entanglement swapping is investigated, respectively. Our findings imply that the output entanglement is completely independent of the phase damping global noise and determined by the input entanglement when entanglement swapping is performed in a global phase damping noise environment. In addition, when entanglement swapping is executed in an amplitude damping environment, the output entanglement oscillates periodically with time, and the output entanglement may disappear at some points and reappear at others. In this case, we need not only to improve the input entanglement but also to control the evolution time of the amplitude damping global noise to ensure the optimal output entanglement. Our findings may help experimentalists to avoid and utilize environmental noise in entanglement swapping.
Entanglement of a system changes due to interactions with the environment. A typical type of interaction is amplitude damping. If we add a detector to monitor the environment and only select the no-damping outcome, this amplitude damping is modified into a weak measurement. Here we show that the entanglement change of a two-qubit state due to amplitude damping or weak measurement can be probabilistically reversed. For the amplitude-damping case, the entanglement partially recovers under most conditions. For the weak-measurement case, the recovery of the initial entangled state is exact. The reversal procedure involves another weak measurement, preceded and followed by bit flips applied to both qubits. We propose a linear optics scheme for the experimental demonstration of these procedures.
Abstract Based on the quantum technique of environment-assisted measurement and quantum measurement reversal, we systematically investigate the restoration of quantum entanglement for distributing a two-qubit pure state via three typical kinds of noisy quantum channels-amplitude damping, phase damping and depolarizing quantum channels. Special attention is paid to the unsymmetrical two-qubit arbitrarily entangled states transmission. The analytical or numerical simulations results show that for arbitrarily one-qubit entangled state or two-qubit states transmission, the output distant entanglement could be drastically restored to the initial value in all these three cases.
This paper investigates the degradation mechanism of the photon-number-encoded entanglement swapping protocol under the amplitude damping noise channel. By establishing a beam splitter physical model to simulate the energy dissipation process, the evolution density matrix of the input states [Formula: see text] and [Formula: see text] under independent noise channels is analytically derived, and the density matrix, fidelity, and concurrence of the target particle pair after entanglement swapping are presented. Furthermore, for the case where the initial states are maximally entangled states, this paper numerically simulates the variation curves of the fidelity and concurrence of the system after entanglement swapping with the noise parameter. The results show that as the noise intensity increases, both the fidelity and concurrence of the target system exhibit a decreasing trend. Simultaneously, due to the presence of noise, even if the input states are maximally entangled, the entanglement of the target system after swapping may be destroyed. Based on this, the study further deduces the constraint conditions required to maintain system entanglement in this scenario. Given the restrictive effect of these constraints on entanglement maintenance, this paper also specifically examines the fidelity and concurrence of the target state output from entanglement swapping in the case of 50 : 50 beam splitters when the input states are both maximally entangled. The research finds that in this case, since the constraints are not satisfied, even if the input states are maximally entangled, the entanglement of the output state completely disappears.