Asymmetric Quantum Codes: New Codes from Old

In this paper we extend to asymmetric quantum error-correcting codes (AQECC) the construction methods, namely: puncturing, extending, expanding, direct sum and the (u|u + v) construction. By applying these methods, several families of asymmetric quantum codes can be constructed. Consequently, as an example of application of quantum code expansion developed here, new families of asymmetric quantum codes derived from generalized Reed-Muller (GRM) codes, quadratic residue (QR), Bose-Chaudhuri-Hocquenghem (BCH), character codes and affine-invariant codes are constructed.Comment: Accepted for publication Quantum Information Processin

A dual 2D model for the Quantum Hall Fluid

We present a dual two dimensional model for the Quantum Hall Fluid depending on two parameters and show that this model has topologically non-trivial vacua which are infrared stable fixed points of the Renormalization Group. The model has a discrete (modular) symmetry which reproduces the fenomenological law of corresponding states and allows for an unified description of the critical points corresponding to Hall plateaus in terms of a 2 dimensional Conformal Field Theory.Comment: 10 pages, Revtex, no figure

Optimal purification of a generic n-qudit state

We propose a quantum algorithm for the purification of a generic mixed state $\rho$ of a $n$-qudit system by using an ancillary $n$-qudit system. The algorithm is optimal in that (i) the number of ancillary qudits cannot be reduced, (ii) the number of parameters which determine the purification state $|\Psi>$ exactly equals the number of degrees of freedom of $\rho$, and (iii) $|\Psi>$ is easily determined from the density matrix $\rho$. Moreover, we introduce a quantum circuit in which the quantum gates are unitary transformations acting on a $2n$-qudit system. These transformations are determined by parameters that can be tuned to generate, once the ancillary qudits are disregarded, any given mixed $n$-qudit state.Comment: 8 pages, 9 figures, remarks adde

Credit Creation: Reconciling Legal and Regulatory Incentives

As international organizations adopt new legal standards to promote access to credit through the modernization of national secured transactions law, the lack of coordination with regulatory standards for banking institutions thwarts the effectiveness of these efforts. In recognizing the relevance of the problem, UNCITRAL - for the first time since its establishment - is currently considering how to coordinate secured transactions law reforms with the implementation of the Basel Accord. In a similar vein, the problem is currently approached by other international organisations. Although efforts at the national level to coordinate legal and regulatory standards are commendable, coordination between secured transactions law and capital requirements should be addressed at the highest level of the lawmaking process, i.e. when international soft-laws are defined. To advance this argument, the key functions of secured transactions law and capital requirements are isolated and a holistic understanding of the legal and regulatory rules governing the creation of credit is presented. The Article steers away from the idea that banks are mere intermediaries and offers a fresh understanding of the role of regulatory capital in controlling credit creation, through the management of risk. Within this context, the incentives created by secured transactions law and capital requirements are examined by comparing the capital charges for different credit protections, including credit derivatives and commercial loans to small business. First, it emerges that the implementation of new secured transactions law and the limited ability of security interests in personal property to reduce regulatory capital under the Basel Accords stimulate the creation of credit outside the banking system. Second, to control this phenomenon, the Article shows that it is essential to reconcile the incentive structures created by international legal and regulatory standards