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arXiv:0707.4092 · Physical Review A

Continuous dynamical protection of two-qubit entanglement from uncorrelated dephasing, bit flipping, and dissipation

F. F. Fanchini, Reginaldo de Jesus Napolitano

Published Dec 13, 2007• 34 citations
arXivHTMLPDF

Abstract

We show that a simple arrangement of external fields, consisting of a static component and an orthogonal rotating component, can continuously decouple a two-qubit entangled state from uncorrelated dephasing, bit flipping, and dissipation at finite temperature. We consider a situation where an entangled state shared between two noninteracting qubits is initially prepared and left to evolve under environmental perturbations and the protection of external fields. To illustrate the protection of the entanglement, we solve numerically a master equation in the Born approximation, considering independent boson fields at the same temperature coupled to the different error agents of each qubit.

DOI
10.1103/physreva.76.062306

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We show that a simple arrangement of external fields, consisting of a static component and an orthogonal rotating component, can continuously decouple a two-qubit entangled state from uncorrelated dephasing, bit flipping, and dissipation at finite temperature. We consider a situation where an entangled state shared between two noninteracting qubits is initially prepared and left to evolve under environmental perturbations and the protection of external fields. To illustrate the protection of the entanglement, we solve numerically a master equation in the Born approximation, considering independent boson fields at the same temperature coupled to the different error agents of each qubit.
A field configuration utilizing local static fields and a few continuous-wave driving fields is constructed to achieve universal (but low-order) protection of two-qubit states. That is, two-qubit states can be protected against arbitrary system-environment coupling with control fields if their frequencies are sufficiently large as compared with the cutoff frequency of the environment. Equally important, we show that it is possible to construct driving fields to protect two-qubit entangling gates against decoherence, without assuming any particular form of system-environment coupling. Using a non-Markovian master equation, we further demonstrate the effectiveness of our continuous dynamical decoupling fields in protecting entanglement and the excellent performance of protected two-qubit gates in generating entanglement. The results are complementary to current studies of entanglement protection using universal dynamical decoupling pulse sequences.
We show, for the first time, that continuous dynamical decoupling can preserve the coherence of a two-qubit state as it evolves during a SWAP quantum operation. Hence, because the Heisenberg exchange interaction alone can be used for achieving universal quantum computation, its combination with continuous dynamical decoupling can also make the computation robust against general environmental perturbations. Furthermore, since the exchange-interaction Hamiltonian is invariant under rotations, the same control-field arrangement used to protect a stationary quantum-memory state can also preserve the coherence of the driven qubits. The simplicity of the required control fields greatly improves prospects for an experimental realization.
We investigate the control and protection of two-qubit entanglement through engineered interactions between two auxiliary harmonic oscillators. Each qubit is coupled to a local oscillator via a dephasing interaction, while the oscillators interact through independently tunable position-position and momentum-momentum couplings. Employing the characteristic-function representation, we obtain analytical solutions for the composite-system dynamics and examine how the stability properties of the coupled oscillators determine the evolution of two-qubit concurrence. Our analysis reveals distinct dynamical regimes exhibiting entanglement revivals, suppression, or decay, and identifies configurations in which oscillator interactions effectively reduce entanglement degradation. We further investigate the influence of thermal dissipation using local and global master-equation descriptions, demonstrating that suitable oscillator couplings can preserve substantial two-qubit entanglement under the dissipative conditions considered. These results establish a connection between the dynamical stability of auxiliary bosonic modes and the controllability of entanglement in discrete-variable quantum systems, providing a potential strategy for entanglement protection through engineered oscillator interactions.
This work investigates the use of dynamical decoupling to shield quantum discord from errors introduced by the environment. Specifically, a two-qubit system interacting with independent baths of bosons is considered. The initial conditions of the system were chosen as pure and mixed states, while the dynamical decouplingwas achieved by means of continuous fields. The effect of the temperature on the shielding of quantum discord is also studied. It is shown that although the quantum discord for particular initial states may be perfectly preserved over some finite time window in the absence of any protective field, the effectiveness of the dynamical decoupling with continuous fields depends essentially on the time scale required to preserve quantum discord. It is also shown that for these particular initial states the time for which the shielding of the quantum discord becomes effective decreases as the temperature increases.
Two noninteracting qubits, initially prepared in an entangled state, are coupled to their own independent environments and evolve under their influence. The reduced non-Markovian dynamics of two qubits is exact for arbitrary model parameters. Necessary and sufficient conditions for nonvanishing entanglement are formulated for both zero and nonzero temperatures and arbitrary time. It is shown that (i) entanglement dynamics can effectively be controlled by a finite quantum system coupled to one of the qubits and (ii) dynamical symmetry of the controlling quantum system can influence significantly entanglement of the qubits and results in its nonmonotonic decay.
Abstract Entanglement is an essential resource for quantum information processing; however, it is highly susceptible to decoherence induced by environmental interactions. In this work, we investigate the entanglement dynamics of a two-qubit system subjected to Markovian noise and explore the effectiveness of external control fields in preserving quantum correlations. Using the Lindblad master equation, we model the evolution of the system under two decoherence channels, namely, amplitude damping (spontaneous emission) and phase damping (dephasing). We introduce periodic driving and optimal control protocols to mitigate entanglement loss and analyze their impact using concurrence as a quantifier of two-qubit entanglement. Our numerical results reveal certain conditions under which sudden death of entanglement can be delayed or even prevented. Additionally, in the case of the initial state being a mixed state, we identify time regimes where entanglement revival occurs, providing insights into quantum error correction strategies. The results contribute to the broader understanding of quantum coherence preservation and have implications for quantum computing, secure quantum communication, and quantum memory design.