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arXiv:quant-ph/0504090 · Physics Letters A

Generation of Werner states and preservation of entanglement in a noisy environment

Lech Jakóbczyk, Anna Jamróz

Published Aug 23, 2005• 7 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2005.08.033

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Quantum entanglement, a key resource in quantum information processing, is reduced by interaction between the quantum system concerned and its unavoidable noisy environment. Therefore it is of particular importance to study the dynamical properties of entanglement in open quantum systems. In this work, we mainly focus on two qubits coupled to an adjustable environment, namely a semi-infinite transmission line. The two qubits’ relaxations, through individual channels or collective channel or both, can be adjusted by the qubits’ transition frequencies. We examine entanglement dynamics in this model system with initial Werner state, and show that the phenomena of entanglement sudden death and revival can be observed. Due to the hardness of preparing the Werner state experimentally, we introduce a new type of entangled state called pseudo-Werner state, which preserves as much entangling property as the Werner state, and more importantly, it is experiment friendly. Furthermore, we provide detailed procedures for generating pseudo-Werner state and studying entanglement dynamics with it, which can be straightforwardly implemented in a superconducting waveguide quantum electrodynamics system.
Partial teleportation of entanglement is to teleport one particle of an entangled pair through a quantum channel. This is conceptually equivalent to quantum swapping. We consider the partial teleportation of entanglement in the noisy environment, employing the Werner-state representation of the noisy channel for the simplicity of calculation. To have the insight of the many-body teleportation, we introduce the measure of correlation information and study the transfer of the correlation information and entanglement. We find that the fidelity becomes smaller as the initial state is entangled more for a given entanglement of the quantum channel. The entangled channel transfers at least some of the entanglement to the final state.
In this work we analyse how a protocol of joint, periodically repeated measurements influences the preservation of state coherence and thereby maintains entanglement in two-qubit systems prepared in a Werner state. By modeling the linear interactions of each qubit with independent dissipative environments (with coefficients , ) together with the dispersive interactions (with coefficients ), we introduce the algorithmic “efficiency” parameter , which quantitatively characterises how strongly these measurements slow down the loss of coherence and support the underlying quantum correlations.. For the maximally entangled input state (Werner state parameter ), the efficiency shows a hyperbolic dependence on the dispersive‐coupling parameter in the strong linear-coupling regime, when , In the opposite regime, when , efficiency asymptotically approaches unity, indicating a loss of capability to suppress decoherence in environments dominated by dispersive interactions. A comprehensive numerical study has been performed on the entanglement-preservation efficiency across all three relevant parameters—namely, the linear and dispersive couplings of each qubit to the environment and the Werner-state parameter that quantifies the initial entanglement. The algorithm’s performance is analyzed in various limiting cases, including the minimal and maximal values of the Werner parameter examined in this work, as well as scenarios in which the linear-interaction strength approaches the dispersive one. The results obtained indicate that carefully tailored measurement schemes, combined with a high level of quantum-system entanglement, can effectively neutralize the deleterious influence of the environment. This paves the way for formulating detailed, quantitatively substantiated recommendations for tuning dynamic coherence-protection procedures that enhance the reliability of entanglement preservation across a variety of quantum algorithms, including entanglement-based quantum-cryptography protocols (BB84, E91/BBM92, DI-QKD, as well as multi-correlation quantum secret-sharing schemes such as HBB99) and variational algorithms for materials simulation (VQE, ADAPT-VQE, QITE, VQSD and related UCC-based approaches).