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arXiv:1001.1785 · Physical Review A

Channel capacities of an exactly solvable spin-star system

Nigum Arshed, A. H. Toor, Daniel A. Lidar

Published Jun 30, 2010• 30 citations
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Abstract

We calculate the entanglement-assisted and -unassisted channel capacities of an exactly solvable spin star system, which models the quantum dephasing channel. The capacities for this non-Markovian model exhibit a strong dependence on the coupling strengths of the bath spins with the system, the bath temperature, and the number of bath spins. For equal couplings and bath frequencies, the channel becomes periodically noiseless.

DOI
10.1103/physreva.81.062353

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We calculate the entanglement-assisted and -unassisted channel capacities of an exactly solvable spin star system, which models the quantum dephasing channel. The capacities for this non-Markovian model exhibit a strong dependence on the coupling strengths of the bath spins with the system, the bath temperature, and the number of bath spins. For equal couplings and bath frequencies, the channel becomes periodically noiseless.
We study non Markovian quantum systems for communication of quantum information. The quantum capacities of an exactly solvable spin-star system are analytically determined.Our results show that they strongly depend on the bath frequencies and system-bath coupling.The Ising spin-bath becomes noisy as the bath temperature is increased decreasing its capacity to transmit information.For random couplings and bath frequencies, recurrences of coherence are small in amplitude and rapidly die out. However, full periodic recurrences occur for equal coupling and frequencies. For small number of bath spins, the capacities are higher at low temperature.We also study two time-correlated non-unital channels for the transmission of classical and quantum information, provided limited or unlimited entanglement is shared prior to the communication.The noise over two successive uses of the channel is assumed to be time-correlated Markov noise.For amplitude-damping channel, the capacities exhibit strong dependence on channel memory.They decrease as the channel noise increases and reduce to zero when noise is maximum. However, our results show that the capacities are always non-zero, in the presence of channel memory.This is similar to the superactivation phenomenon. For perfect memory channel, the capacities acquire maximum value.Finally, we determine the entanglement-assisted classical capacity of generalized amplitude-damping channel. Our results show that depending on the channel noise and system-reservoir coupling, there exists a memory threshold.Below this threshold, the capacity decreases as channel memory increases.However, the capacity increases with memory beyond this threshold and is maximum for perfect memory channels.
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The reduced dynamics of a central spin coupled to a bath of NNN spin-12\frac{1}{2}21​ particles arranged in a spin star configuration is investigated. The exact time evolution of the reduced density operator is derived, and an analytical solution is obtained in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ of an infinite number of bath spins, where the model shows complete relaxation and partial decoherence. It is demonstrated that the dynamics of the central spin cannot be treated within the Born-Markov approximation. The Nakajima-Zwanzig and the time-convolutionless projection operator technique are applied to the spin star system. The performance of the corresponding perturbation expansions of the non-Markovian equations of motion is examined through a comparison with the exact solution.
The spin-boson model, describing a two-level system coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong coupling regime. Here, we additionally consider dephasing as a source of Markovian dissipation on top of the non-Markovian dynamics due to an Ohmic bath, and investigate the dynamics of the spin. We show that the characteristic frequency of the spin dynamics, while strongly renormalized by the bosonic bath, changes in a simple fashion (or does not change at all) with dephasing. To obtain these results, we develop an exact nonperturbative method known as the stochastic Schr\"odinger equation, mimicking the Ohmic bath via a stochastic magnetic field combined with the Lindblad quantum master equation due to dephasing, which allows us to numerically compute the dynamics. Furthermore, we derive weak-coupling analytic results utilizing the well-known noninteracting blip approximation. Our findings are relevant to quantum simulation of the spin-boson model in the regime of strong coupling in trapped ions and circuit QED architectures among others.
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We consider the buildup and decay of two-spin entanglement through phase interactions in a finite environment of surrounding spins, as realized in quantum computing platforms based on arrays of atoms, molecules, or nitrogen vacancy centers. The non-Markovian dephasing caused by the spin environment through Ising-type phase interactions can be solved exactly and compared to an effective Markovian treatment based on collision models. In a first case study on a dynamic lattice of randomly hopping spins, we find that non-Markovianity boosts the dephasing rate caused by nearest-neighbor interactions with the surroundings, degrading the maximum achievable entanglement. However, we also demonstrate that additional three-body interactions can mitigate this degradation, and that randomly timed reset operations performed on the two-spin system can help sustain a finite average amount of steady-state entanglement. In a second case study based on a model nuclear magnetic resonance system, we elucidate the role of bath correlations at finite temperature on non-Markovian dephasing. They speed up the dephasing at low temperatures while slowing it down at high temperatures, compared to an uncorrelated bath, which is related to the number of thermally accessible spin configurations with and without interactions.