Quantum information processing using spatial entanglement of cold gases.

当某些气体（例如玻色气体）冷却时，它们可以在宏观尺度上表现出量子效应。其中一种效应就是纠缠。纠缠是两种模式之间的非局域关联，这意味着当我们知道另一种模式在做什么的时候，我们可以确定地预测其中一种模式的行为，即使这两种模式相隔很远。通常人们会认为纠缠模式是粒子，或它们的内部自由度，但最近表明纠缠可以存在于空间区域之间。这种类型的纠缠被称为空间纠缠，它以空间模式之间的非局域粒子数相关的形式存在。我们在多大程度上可以使用这种类型的纠缠进行量子信息处理是本提案所关注的。量子信息科学开始于十多年前，当时人们意识到量子系统在执行某些算法时比经典计算机提供了更快的速度。加速的一个可能原因是量子纠缠，它允许信息比经典系统更密集地编码。除了量子计算常用的电路模型外，另一种方法是基于测量或簇态计算。在这里，一个被称为簇态的量子比特的大纠缠结构最初被准备好，并以特定的顺序对单个量子比特进行测量，破坏纠缠，但推动计算向前发展。簇态可以使用光学晶格中的中性原子来创建，其中整个量子比特阵列在三次横扫运动中纠缠在一起，但在这里单个量子比特很难处理。另一方面，光学方案产生了四模簇态，其中单个量子比特很容易测量，但簇的产生是极有可能的。这里提出的研究的动机是，在冷气体中已经存在空间纠缠，因此在消除计算之前需要创建群集状态。此外，我们可以随意定义空间模式，这样我们就可以确保单个量子比特的可寻址性。因此，在自然界中找到簇态将是一个非常重要的结果。这项提议有三个主要目的。首先，我们希望了解利用冷气体的空间纠缠结构可以执行的量子信息处理任务，并在信息理论背景下描述冷气体的底层物理。我们将比较相互作用和非相互作用气体的纠缠结构和计算能力，我们期望相互作用气体对于通用量子计算是必要的。其次，我们想了解与环境的相互作用如何支持和阻碍量子信息处理任务。在这里，有必要将空间的纠缠区域耦合到特定的环境中，并依次打开相互作用。如果环境与气体随机交互，我们预计不会发生有用的计算，但我们将了解在存在错误的情况下计算的效率如何。然而，如果环境是可控的，那么一个有用的计算可能自然发生。最后，根据前期工作的结果，我们想探索利用冷气体的空间纠缠进行量子信息处理的实验可行性。我们将关注如何在空间模式上进行测量和旋转。例如，为了进行单量子位测量，需要测量特定空间模式下的原子数量。目前这个问题还没有解决，这将是这里的重点。

When certain gases, for instance Bose gases, are cooled they can display quantum effects on a macroscopic scale. One such effect is entanglement. Entanglement is a non-local correlation between two modes, which means we can predict with certainty the behaviour of one mode when we know what the other is doing, even if the two are separated by great distances. Normally one would consider the entangled modes to be particles, or their internal degrees of freedom, but recently it was shown that entanglement can exist between regions of space. This type of entanglement is called spatial entanglement and takes the form of non-local particle number correlations between spatial modes. The extent to which we can use this type of entanglement for quantum information processing is the concern of this proposal.Quantum information science began just over ten years ago when it was realised that quantum systems provide a speed up over classical computers when performing certain algorithms. One possible reason for the speed up is quantum entanglement, which allows information to be encoded more densely than in classical systems. Besides the usual circuit model of quantum computation, one other method is measurement-based or cluster state computation. Here a large entangled structure of qubits, called a cluster state, is initially prepared and measurements are made on single qubits in a particular order, destroying the entanglement, but driving the computation forward. Cluster states can be created using neutral atoms in optical lattices where entire arrays of qubits are entangled in three sweeping movements, but here single qubits are difficult to address. On the other hand optical schemes have generated four mode cluster states, where the individual qubits are easy to measure, but the creation of the cluster is highly probable. The proposed research here is motivated by the fact that spatial entanglement is already present in cold gases, so that the need to create a cluster state before computation is eliminated. Moreover we are free to define the spatial modes as we please so we can ensure the addressability of individual qubits. Finding a cluster state in nature would therefore be a very important result. There are three main aims of this proposal. Firstly, we would like to understand the quantum information processing tasks that can be performed using the spatial entanglement structure of cold gases and to describe the underlying physics of cold gases in an information-theoretic context. We will compare the entanglement structure, and hence computational capabilities, of interacting and non-interacting gases and we expect that interacting gases will be necessary for universal quantum computation. Secondly, we would like to understand how interactions with the environment support and hinder quantum information processing tasks. Here it will be necessary to couple the entangled regions of space to certain environments and switch the interactions on in succession. If the environments interact randomly with the gas we expect that no useful computation takes place, but we will learn how efficiently a computation can take place in the presence of errors. If, however, the environment is controlled then a useful computation might naturally take place.Finally, drawing on the results from the earlier work, we would like to explore the experimental feasibility of quantum information processing using spatial entanglement of cold gases. We will be concerned with how to make measurements and rotations on the spatial modes. For instance, in order to make single qubit measurements, one will need to measure the number of atoms in a particular spatial mode. At the moment this problem has not been solved and will be of focus here.