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arXiv:2005.06930 · Physics Letters A

Almost perfect transmission of multipartite entanglement through disordered and noisy spin chains

Rafael Vieira, Gustavo Rigolin

Published May 8, 2020• 12 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2020.126536

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Abstract We study spin chains submitted to disturbed kick trains described by classical dynamical processes. The spin chains are coupled by Heisenberg and Ising-Z models. We consider chaotic processes by using the kick irregularity in the multipartite system (the spin chain). We show that both couplings transmit the chaos disorder differently along the spin chain but conserve the horizon of coherence (when the disorder into the kick bath is transmitted to the spin chain). An example of information transmission between the spins of the chain coupled by a Heisenberg interaction shows the interest of the horizon of coherence. The use of some chosen stationary kicks disturbed by a chaotic environment makes it possible to modify the information transmission between the spins and to perform a free control during the horizon of coherence.
We present a protocol in which two or more parties can share multipartite entanglement over noisy quantum channels. The protocol is based on the entanglement purification presented by Shor and Preskill [Phys. Rev. Lett. 85, 441 (2000)] and the quantum teleportation via an isotropic state. We show that a nearly perfect purification implies a nearly perfect sharing of multipartite entanglement between two parties so that the protocol can assure a faithful sharing of multipartite entanglement with Shor and Preskill's proof on the entanglement purification.
The issue of quantum states' transfer -- in particular, for so-called Perfect State Transfer (PST) -- in the networks represented by the spin chains seems to be one of the major concerns in quantum computing. Especially, in the context of future communication methods that can be used in broadly defined computer science. The chapter presents a definition of Hamiltonian describing the dynamics of quantum data transfer in one-dimensional spin chain, which is able to transfer the state of unknown qudits. The main part of the chapter is the discussion about possibility of entangled states' perfect transfer, in particular, for the generalized Bell states for qudits. One of the sections also contains the results of numerical experiments for the transmission of quantum entangled state in a noisy quantum channel.