Correspondence between continuous-variable and discrete quantum systems of arbitrary dimensions

We establish a mapping between a continuous-variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite-dimensional Hilbert space and thus can be considered as a universal resource of entanglement. An explicit example of the map and a proposal for its experimental realization are discussed.

On the Condition Number Distribution of Complex Wishart Matrices

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

Dimension theory and nonstable K1 of quadratic modules

Employing Bak’s dimension theory, we investigate the nonstable quadratic K-group K1,2n(A, ) = G2n(A, )/E2n(A, ), n 3, where G2n(A, ) denotes the general quadratic group of rank n over a form ring (A, ) and E2n(A, ) its elementary subgroup. Considering form rings as a category with dimension in the sense of Bak, we obtain a dimension filtration G2n(A, ) G2n0(A, ) G2n1(A, ) E2n(A, ) of the general quadratic group G2n(A, ) such that G2n(A, )/G2n0(A, ) is Abelian, G2n0(A, ) G2n1(A, ) is a descending central series, and G2nd(A)(A, ) = E2n(A, ) whenever d(A) = (Bass–Serre dimension of A) is finite. In particular K1,2n(A, ) is solvable when d(A) <.

Greenberger-Horne-Zeilinger nonlocality in arbitrary even dimensions

We generalize Greenberger-Horne-Zeilinger (GHZ) nonlocality to every even-dimensional and odd-partite system. For the purpose we employ concurrent observables that are incompatible and nevertheless have a common eigenstate. It is remarkable that a tripartite system can exhibit the genuinely high-dimensional GHZ nonlocality.

Preparing students for interprofessional practice: exploring the intra-personal dimension

This paper appears in the Canadian-based, leading interprofessional education journal. Pre-qualification healthcare education can be viewed as having three inter-related components, intra-professional, interprofessional and intra-personal learning; the third of these underpinning the other two. Understanding more about personal learning needs can contribute to preparation for interprofessional interaction. A Studying and Learning Preferences Inventory (SALPI) was developed and validated for use with a range of healthcare professionals to assist in this process.