Computation from correlations - in classical, quantum and generalised theories

Abstract

Operational theories [1], defined in terms of the actions and observations of an experimenter, have been extremely successful as foils to quantum mechanics, providing a generic framework in which families of theories may be compared and classified. One area of particular interest has been in the non-classical correlations (often referred to non-locality) which can arise in quantum (and generalised) theories, when measurements are space-like separated. In the context of non-locality, one usually considers the correlations in separated measurements on isolated systems. A similar setting arises in In quantum computation theory, in measurement-based quantum computation, a model of computation of equivalent power to standard circuit model quantum computation. Measurements are made on isolated non-interacting quantum systems, and the non-classical correlations which arise embody (in some loose sense) the mechanism via which the computation is executed. These measurements are adaptive, meaning that bases are chosen dependent upon the outcome of prior measurements, but apart from this, the setting is essentially identical to a multi-party Bell non-locality experiment (e.g. [2]). In this talk I will review some recent work [3] in which Bell-type correlations are studied from the perspective of computation - in particular drawing parallels with measurement-based quantum computation. In particular, I shall give examples of results [3] which appear naturally in this setting, while being not so self-evident in more conventional approaches. Finally, I shall discuss approaches to and challenges in developing non-trivial models of correlation-based quantum computation in general operational theories. [1] See e.g. H. Barnum, J. Barrett, M. Leifer and A. Wilce, Phys. Rev. Lett., 99, 240501 (2007). [2] See e.g. R. F. Werner and M. M. Wolf, Phys. Rev. A 64, 032112 (2001), M. Zukowski, C. Brukner, Phys. Rev. Lett. 88 210401 (2002). [3] M.J. Hoban and D.E. Browne, http://arxiv.org/abs/1102.1438, M.J. Hoban et al, http://arxiv.org/abs/1009.5213, J. Anders and D.E. Browne http://arxiv.org/abs/0805.1002 .