Entanglement purification in quantum information processing

The controlled manipulation of quantum information provides a number of promising applications, ranging from unconditionally secure communication over the simulation of arbitrary interacting quantum systems to the implementation of algorithms on quantum computers, which would allow one to solve certain problems (exponentially) faster than any classical computer could. All of these applications make use of unique features of quantum systems -such as entanglement- which do not have a counterpart in classical physics. Entanglement is at the heart of many such applications and can be viewed as a fundamental resource for quantum information processing. The creation of various kinds of pure entangled states is thus a central task in quantum information processing. Entanglement purification is a possible way to accomplish this task under realistic conditions, i.e. when imperfections in the distribution and the manipulation of quantum systems are taken into account. In entanglement purification, a few highly entangled states are created from a large number of slightly entangled states. It has recently become clear that entanglement purification is not only useful in the context of quantum communication, but seems to have a much broader scope with potential applications e.g. in fault tolerant quantum computation and quantum simulation. This research project deals with numerous aspects of entanglement purification. Existing protocols will be analyzed with respect to their implementation under realistic conditions. The achievable fidelity, thresholds for involved control operations for general noise models and a properly defined efficiency will be analyzed. The basic requirements for entanglement purification will be investigated, and based on the gained insight new protocols shall be designed which are capable of purifying other (multipartite) entangled states or states that are specially suitable for specific set-ups. The protocols will be optimized with respect to the achievable efficiency and/or fidelity. The concept of purification will be considered in a more general framework, ranging from purification of (non-local) subspaces over diminishing classical correlations between (non-local) pairs of mixed states to the purification of ground states of certain interaction Hamiltonians. Possible applications of entanglement purification in fault tolerant quantum computation, quantum error correction, quantum simulation, and secure multi-party communication and computation shall be investigated.

The controlled manipulation of quantum information provides a number of promising applications, ranging from unconditionally secure communication over the simulation of arbitrary interacting quantum systems to the implementation of algorithms on quantum computers, which would allow one to solve certain problems (exponentially) faster than any classical computer could. All of these applications make use of unique features of quantum systems -such as entanglement- which do not have a counterpart in classical physics. Entanglement is at the heart of many such applications and can be viewed as a fundamental resource for quantum information processing. The creation of various kinds of pure entangled states is thus a central task in quantum information processing. Entanglement purification is a possible way to accomplish this task under realistic conditions, i.e. when imperfections in the distribution and the manipulation of quantum systems are taken into account. In entanglement purification, a few highly entangled states are created from a large number of slightly entangled states. It has recently become clear that entanglement purification is not only useful in the context of quantum communication, but seems to have a much broader scope with potential applications e.g. in fault tolerant quantum computation and quantum simulation. This research project deals with numerous aspects of entanglement purification. Existing protocols will be analyzed with respect to their implementation under realistic conditions. The achievable fidelity, thresholds for involved control operations for general noise models and a properly defined efficiency will be analyzed. The basic requirements for entanglement purification will be investigated, and based on the gained insight new protocols shall be designed which are capable of purifying other (multipartite) entangled states or states that are specially suitable for specific set-ups. The protocols will be optimized with respect to the achievable efficiency and/or fidelity. The concept of purification will be considered in a more general framework, ranging from purification of (non-local) subspaces over diminishing classical correlations between (non-local) pairs of mixed states to the purification of ground states of certain interaction Hamiltonians. Possible applications of entanglement purification in fault tolerant quantum computation, quantum error correction, quantum simulation, and secure multi-party communication and computation shall be investigated.