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arXiv:1104.0718 · Physical Review A

Initializing an unmodulated spin chain to operate as a high-quality quantum data bus

Abolfazl Bayat, Leonardo Banchi, Sougato Bose, Paola Verrucchi

Published Jun 23, 2011• 37 citations
arXivHTMLPDF

Abstract

We study the quality of state and entanglement transmission through quantum channels described by spin chains varying both the system parameters and the initial state of the channel. We consider a vast class of one-dimensional many-body models which contains some of the most relevant experimental realizations of quantum data buses. In particular, we consider spin-$1/2$ $\mathit{XY}$ and $\mathit{XXZ}$ models with open boundary conditions. Our results show a significant difference between free-fermionic (noninteracting) systems ($\mathit{XY}$) and interacting ones ($\mathit{XXZ}$), where in the former case initialization can be exploited for improving the entanglement distribution, while in the latter case it also determines the quality of state transmission. In fact, we find that in noninteracting systems the exchange with fermions in the initial state of the chain always has a destructive effect, and we prove that it can be completely removed in the isotropic $\mathit{XX}$ model by initializing the chain in a ferromagnetic state. On the other hand, in interacting systems constructive effects can arise by scattering between hopping fermions and a proper initialization procedure. Our results are an example in which state and entanglement transmission show maxima at different points as the interactions and initializations of spin chain channels are varied.

DOI
10.1103/physreva.83.062328

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We study the quality of state and entanglement transmission through quantum channels described by spin chains varying both the system parameters and the initial state of the channel. We consider a vast class of one-dimensional many-body models which contains some of the most relevant experimental realizations of quantum data buses. In particular, we consider spin-1/21/21/2 XY\mathit{XY}XY and XXZ\mathit{XXZ}XXZ models with open boundary conditions. Our results show a significant difference between free-fermionic (noninteracting) systems (XY\mathit{XY}XY) and interacting ones (XXZ\mathit{XXZ}XXZ), where in the former case initialization can be exploited for improving the entanglement distribution, while in the latter case it also determines the quality of state transmission. In fact, we find that in noninteracting systems the exchange with fermions in the initial state of the chain always has a destructive effect, and we prove that it can be completely removed in the isotropic XX\mathit{XX}XX model by initializing the chain in a ferromagnetic state. On the other hand, in interacting systems constructive effects can arise by scattering between hopping fermions and a proper initialization procedure. Our results are an example in which state and entanglement transmission show maxima at different points as the interactions and initializations of spin chain channels are varied.
High-quality quantum-state and entanglement transfer can be achieved in an unmodulated spin bus operating in the ballistic regime, which occurs when the endpoint qubits A and B are nonperturbatively coupled to the chain by a suitable exchange interaction j 0 . Indeed, the transition amplitude characterizing the transfer quality exhibits a maximum for a finite optimal value j opt 0 ( N ), where N is the channel length. We show that j opt 0 ( N ) scales as N −1/6 for large N and that it ensures a high-quality entanglement transfer even in the limit of arbitrarily long channels, almost independently of the channel initialization. For instance, for any chain length the average quantum-state transmission fidelity exceeds 90% and decreases very little in a broad neighbourhood of j opt 0 ( N ). We emphasize that, taking the reverse point of view, should j 0 be experimentally constrained, high-quality transfer can still be obtained by adjusting the channel length to its optimal value.
We revisited the effectiveness of state and entanglement transmission through a spin-chain-based quantum channel while altering the system parameters and the channel's initial state. Our research is focused on the spin-1/2 XX chain with Dzyaloshinskii-Moriya (DM) interaction and the aim is to measure entanglement dynamics between different part of the chain. The speed of entanglement propagation is utilized to probe the evolution of the system via three scenarios: (i) pure Heisenberg interaction, (ii) pure DM interaction, and (iii) collaboration of both types of couplings. To accomplish this, we employ the fermionization approach to obtain an exact solution to the problem. Aside from investigating the influence of magnetic interaction type on entanglement transfer, the effect of selecting the initial state has also been studied. As a result, we discovered that the phase factor regulating the system's initial state induces sharp drops in the propagation speed of entanglement. We also showed how to predict the location of these dramatic drops using the language of wave interference. In addition, the fastest transmission occurs at a special value of the phase factor in which the highest amount of entanglement reaches the system's different pairs. On the other hand, we observe a continuous and flat range of this factor in which the least amount of entanglement is transmitted and for them we have a sharp drop in the speed profile.
We investigate the multiple use of a ferromagnetic spin chain for quantum and classical communications without resetting. We find that the memory of the state transmitted during the first use makes the spin chain a qualitatively different quantum channel during the second transmission, for which we find the relevant Kraus operators. We propose a parameter to quantify the amount of memory in the channel and find that it influences the quality of the channel, as reflected through fidelity and entanglement transmissible during the second use. For certain evolution times, the memory allows the channel to exceed the memoryless classical capacity (achieved by separable inputs) and in some cases it can also enhance the quantum capacity.
The transfer of quantum states between distant nodes is one of the most fundamental tasks in quantum-information processing. Recent studies show that the antiferromagnetic spin chain initially prepared in a multi-excitation state can provide suitable pathways for quantum state transfer. In this paper, we investigate the quality of state transfer through a uniformly coupled antiferromagnetic spin chain where the initial state of the channel varies with the number of spin excitations. Firstly, by analyzing the dynamics of observables for the output qubit using the information-flux approach, the explicit relation about how the average fidelity of state transfer depends on the initial state of the spin channel is obtained. The results show that the average fidelity of state transfer through a multi-excitation spin channel only relates to the parity of the number of spin excitations in the channel. Then we compare the maximum average fidelity of state transfer through the odd-excitation with those through the even-excitation spin channels, and provide a simple criterion to optimize the quality of state transfer by choosing appropriate channels from the odd-excitation and the even-excitation channels. Compared with the previous studies which initialize the chains into the ground state of the ferromagnetic medium or the Nel state, the maximum average fidelity of state transfer is evidently enhanced by using the optimized channel. Moreover, we analyze the entanglement distribution through the channel having different number of spin excitations via the information-flux approach. It is found that the quality of entanglement distribution not only relates to the number of initial spin excitations present in the channel, but also depends on the initial ordering of these excited spins. The numerical results suggest that the amount of distributed entanglement and duration of distribution in the channel where all spins are down or up are larger than those in other excited channels. Based on these results, we can choose appropriate quantum channels for state transfer and entanglement distribution in practice.
A strongly coupled spin chain can mediate long-distance effective couplings or entanglement between remote qubits and can be used as a quantum data bus. We study how the fidelity of a spin-1/2 Heisenberg chain as a spin bus is affected by static random exchange couplings and magnetic fields. We find that, while nonuniform exchange couplings preserve the isotropy of the qubit effective couplings, they cause the energy levels, the eigenstates, and the magnitude of the couplings to vary locally. On the other hand, random local magnetic fields lead to an avoided level crossing for the bus ground-state manifold and cause the effective qubit couplings to be anisotropic. Interestingly, the total magnetic moment of the ground state of an odd-size bus may not be parallel to the average magnetic field. Its alignment depends on both the direction of the average field and the field distribution, in contrast with the ground state of a single spin which always aligns with the applied magnetic field to minimize the Zeeman energy. Lastly, we calculate sensitivities of the spin bus to such local variations, which are potentially useful for evaluating decoherence when dynamical fluctuations in the exchange coupling or magnetic field are considered.
The capability of faithfully transmit quantum states and entanglement through quantum channels is one of the key requirements for the development of quantum devices. Different solutions have been proposed to accomplish such a challenging task, which, however, require either an ad hoc engineering of the internal interactions of the physical system acting as the channel or specific initialization procedures. Here we show that optimal dynamics for efficient quantum-state and entanglement transfer can be attained in generic quantum systems with homogeneous interactions by tuning the coupling between the system and the two attached qubits. We devise a general procedure to determine the optimal coupling, and we explicitly implement it in the case of a channel consisting of a spin-12\frac{1}{2}21​XY\mathit{XY}XY chain. The quality of quantum-state and entanglement transfer is found to be very good and, remarkably, almost independent of the channel length.