Quantum information processing using spatial entanglement of cold gases.

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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.