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arXiv:1607.00095 · Physical Review A

High-fidelity entangled Bell states via shortcuts to adiabaticity

Koushik Paul, Amarendra K. Sarma

Published Nov 2, 2016• 31 citations
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Abstract

We present a couple of protocols based on shortcut to adiabaticity techniques for rapid generation of robust entangled Bell states in a pair of two-state systems. Our protocol relies on the so-called transitionless quantum driving (TQD) algorithm and Lewis-Riesenfeld invariant (LRI) method. Both TQD and LRI methods result in high fidelity in population transfer. Our study shows that it is possible to prepare an entangled state in extremely short time without losing robustness and efficiency.

DOI
10.1103/physreva.94.052303

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We present a couple of protocols based on shortcut to adiabaticity techniques for rapid generation of robust entangled Bell states in a pair of two-state systems. Our protocol relies on the so-called transitionless quantum driving (TQD) algorithm and Lewis-Riesenfeld invariant (LRI) method. Both TQD and LRI methods result in high fidelity in population transfer. Our study shows that it is possible to prepare an entangled state in extremely short time without losing robustness and efficiency.
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We consider a pair of coupled spins with Ising interaction in z-direction and study the problem of generating efficiently the triplet Bell state. We initially analyze the transitionless quantum driving shortcut to adiabaticity method and point out its limitations when the available duration approaches zero. In this short time limit we explicitly calculate the fidelity of the method and find it to be much lower than unity, no matter how large the available control fields become. We find that there is a lower bound on the necessary time to complete this transfer, set by the finite value of the interaction between the spins. We then use numerical optimal control to find bang-bang pulse sequences, as well as, smooth controls, which can generate high levels of the target Bell state in the minimum possible time. Finally, we explain how this method can be adapted for the efficient generation of general quantum entanglement in the system. The results of the present work are not restricted only to spin systems, but is expected to find also applications in other physical systems which can be modeled as interacting spins, such as, for example, coupled quantum dots.
Recently, a novel three-dimensional entangled state called tree-type entanglement, which is likely to have applications for improving quantum communication security, was prepared via adiabatic passage by Song et al. Here we propose two schemes for fast generating tree-type three-dimensional entanglement among three spatially separated atoms via shortcuts to adiabatic passage. With the help of quantum Zeno dynamics, two kinds of different but equivalent methods, Lewis-Riesenfeld invariants and transitionless quantum driving, are applied to construct shortcuts to adiabatic passage. The comparisons between the two methods are discussed. The strict numerical simulations show that the tree-type three-dimensional entangled states can be fast prepared with quite high fidelities and the two schemes are both robust against the variations in the parameters, atomic spontaneous emissions and the cavity-fiber photon leakages.
We consider a pair of coupled spins with Ising interaction in the zzz direction and study the problem of generating efficiently the triplet Bell state. We initially analyze the transitionless quantum driving shortcut to adiabaticity method and point out its limitations when the available duration approaches zero. In this short time limit we explicitly calculate the fidelity of the method and find it to be much lower than unity, no matter how large the available control fields become. We find that there is a lower bound on the necessary time to complete this transfer, set by the finite value of the interaction between the spins. We then use numerical optimal control to find bang-bang pulse sequences, as well as, smooth controls, which can generate high levels of the target Bell state in the minimum possible time. The results of the present work are not restricted only to spin systems, but are expected also to find applications in other physical systems which can be modeled as interacting spins, for example, coupled quantum dots.
Shortcut to adiabaticity (STA) techniques have the potential to drive a system beyond the adiabatic limits. Here, we present a robust and efficient method for wireless power transfer (WPT) between two coils based on the so-called transitionless quantum driving (TQD) algorithm. We show that it is possible to transfer power between the coils significantly fast compared to its adiabatic counterpart. The scheme is fairly robust against the variations in the coupling strength and the coupling distance between the coils. Also, the scheme is found to be reasonably immune to intrinsic losses in the coils.