Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.

Vertical handover supporting pervasive computing in future wireless networks

A variety of current and future wired and wireless networking technologies can be transformed into a seamless communication environments through application of context-based vertical handovers. Such seamless communication environments are needed for future pervasive/ubiquitous systems. Pervasive systems are context aware and need to adapt to context changes, including network disconnections and changes in network Quality of Service (QoS). Vertical handover is one of many possible adaptation methods. It allows users to roam freely between heterogeneous networks while maintaining the continuity of their applications. This paper proposes a vertical handover mechanism suitable for multimedia applications in pervasive systems. The paper focuses on the handover decision making process which uses context information regarding user devices, user location, network environment and requested QoS. (C) 2004 Elsevier B.V. All rights reserved.

On the distributed compression of quantum information

The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian-Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction.

Verifying abstract information flow properties in fault tolerant security devices

The verification of information flow properties of security devices is difficult because it involves the analysis of schematic diagrams, artwork, embedded software, etc. In addition, a typical security device has many modes, partial information flow, and needs to be fault tolerant. We propose a new approach to the verification of such devices based upon checking abstract information flow properties expressed as graphs. This approach has been implemented in software, and successfully used to find possible paths of information flow through security devices.

Active node supporting context-aware vertical handover in pervasive computing environment with redundant positioning

A major requirement for pervasive systems is to integrate context-awareness to support heterogeneous networks and device technologies and at the same time support application adaptations to suit user activities. However, current infrastructures for pervasive systems are based on centralized architectures which are focused on context support for service adaptations in response to changes in the computing environment or user mobility. In this paper, we propose a hierarchical architecture based on active nodes, which maximizes the computational capabilities of various nodes within the pervasive computing environment, while efficiently gathering and evaluating context information from the user's working environment. The migratable active node architecture employs various decision making processes for evaluating a rich set of context information in order to dynamically allocate active nodes in the working environment, perform application adaptations and predict user mobility. The active node also utilizes the Redundant Positioning System to accurately manage user's mobility. This paper demonstrates the active node capabilities through context-aware vertical handover applications.

A geometric approach to quantum circuit lower bounds

What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation, U, without the use of ancilla qubits? We show that a lower bound on the minimal size is provided by the length of the minimal geodesic between U and the identity, I, where length is defined by a suitable Finsler metric on the manifold SU(2(n)). The geodesic curves on these manifolds have the striking property that once an initial position and velocity are set, the remainder of the geodesic is completely determined by a second order differential equation known as the geodesic equation. This is in contrast with the usual case in circuit design, either classical or quantum, where being given part of an optimal circuit does not obviously assist in the design of the rest of the circuit. Geodesic analysis thus offers a potentially powerful approach to the problem of proving quantum circuit lower bounds. In this paper we construct several Finsler metrics whose minimal length geodesics provide lower bounds on quantum circuit size. For each Finsler metric we give a procedure to compute the corresponding geodesic equation. We also construct a large class of solutions to the geodesic equation, which we call Pauli geodesics, since they arise from isometries generated by the Pauli group. For any unitary U diagonal in the computational basis, we show that: (a) provided the minimal length geodesic is unique, it must be a Pauli geodesic; (b) finding the length of the minimal Pauli geodesic passing from I to U is equivalent to solving an exponential size instance of the closest vector in a lattice problem (CVP); and (c) all but a doubly exponentially small fraction of such unitaries have minimal Pauli geodesics of exponential length.