Quantum information processing using spatial entanglement of cold gases.

当某些气体，例如玻色气体被冷却时，它们可以在宏观尺度上显示量子效应。一种这样的效应就是纠缠。纠缠是两个模之间的非局域关联，这意味着当我们知道一个模在做什么时，即使两个模相隔很远，我们也可以确定地预测另一个模的行为。通常情况下，人们会认为纠缠模是粒子，或者它们的内部自由度，但最近的研究表明，空间区域之间可以存在纠缠。这种类型的纠缠称为空间纠缠，其形式为空间模间的非局域粒子数关联。我们可以在多大程度上利用这种类型的纠缠来处理量子信息，这是这个提议的关注点。量子信息科学始于十多年前，当时人们意识到，在执行某些算法时，量子系统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中更密集地编码。除了通常的量子计算电路模型外，另一种方法是基于测量的或集群状态计算。在这里，最初准备了一个巨大的量子比特纠缠结构，称为团簇状态，并以特定的顺序对单个量子比特进行测量，破坏了纠缠，但推动了计算。可以使用光学晶格中的中性原子来创建团簇态，在光学晶格中，整个量子比特阵列在三个扫掠运动中纠缠在一起，但这里很难处理单个量子比特。另一方面，光学方案已经产生了四个模团簇态，其中单个量子比特很容易测量，但团簇的产生是很有可能的。这里提出的研究的动机是这样一个事实，即冷气体中已经存在空间纠缠，这样就不需要在计算之前创建团簇状态。此外，我们可以随心所欲地定义空间模式，从而确保单个量子比特的可寻址能力。因此，发现自然界中的团簇状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，我们想要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，并在信息论的背景下描述冷气体的基本物理。我们将比较相互作用气体和非相互作用气体的纠缠结构，从而比较计算能力，我们预计相互作用气体将是普遍量子计算所必需的。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，并接连开启相互作用。如果环境与气体随机相互作用，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。然而，如果环境是可控的，那么一种有用的计算自然就会发生。最后，在前面工作的基础上，我们想要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。我们将关注如何对空间模式进行测量和旋转。例如，为了进行单量子比特测量，人们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，将是这里的焦点。

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.