Research Interests:
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the desire to construct dagger-compact categories of such... more
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the desire to construct dagger-compact categories of such models. We show that no such composite has the exceptional Jordan algebra as a direct summand, nor does any such composite exist if one factor has an exceptional summand, unless the other factor is a direct sum of one-dimensional Jordan algebras (representing essentially a classical system). Moreover, we show that any composite of simple, non-exceptional EJAs is a direct summand of their universal tensor product, sharply limiting the possibilities.These results warrant our focussing on concrete Jordan algebras of hermitian matrices, i.e., euclidean Jordan algebras with a preferred embedding in a complex matrix algebra. We show that these can be organized in a natural way as a symmetric monoidal category, albeit one that is not compact closed. We then co...
Research Interests:
We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this... more
We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying four natural physical principles possess a well-defined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle model to be well-defined. The four principles are: causality (roughly, no signalling from the future), purification (each mixed state arises as the marginal of a pure state of a larger system), strong symmetry (existence of a rich set of nontrivial reversible transformations), and informationally consistent composition (roughly: the information capacity of a composite system is the sum of the capacities of its constituent subsystems). Sorkin has defined a hierarchy of conceivable interference behaviours, where the order in the hierar...
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
State Spaces We model a physical system by an ordered vector space A with a (closed, pointed, generating) positive cone A+, which we regard as consisting of un-normalized “states”. We also posit a distinguished order unit, that is, a... more
State Spaces We model a physical system by an ordered vector space A with a (closed, pointed, generating) positive cone A+, which we regard as consisting of un-normalized “states”. We also posit a distinguished order unit, that is, a linear functional uA that is strictly positive on non-zero positive elements of A; this defines a compact convex set ΩA = u −1 A (1) of normalized states. We shall call an ordered linear space, equipped with such a functional—more formally: a pair (A, uA)—an abstract state space. If (A, uA) and (B, uB) are abstract state spaces, we write A ≤ B to indicate that (i) A is a subspace of B; (ii) A+ ⊆ B+; and (iii) uA is the restriction of uB to A+. Similarly, A ≃ B, read “A is isomorphic to B”, means that there exists an invertible, positive linear mapping A→ B, with a positive inverse, and taking the order unit of A to that of B. Equivalently, such a mapping takes A’s normalized state space ΩA bijectively
Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the... more
Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
We review some of our recent results (with collaborators) on information processing in an ordered linear spaces framework for probabilistic theories. These include demonstrations that many "inherently quantum" phenomena are in... more
We review some of our recent results (with collaborators) on information processing in an ordered linear spaces framework for probabilistic theories. These include demonstrations that many "inherently quantum" phenomena are in reality quite general characteristics of non-classical theories, quantum or otherwise. As an example, a set of states in such a theory is broadcastable if, and only if, it is