Information and communication in polygon theories

Generalized probabilistic theories (GPT) provide a framework in which one can formulate physical theories that includes classical and quantum theories, but also many other alternative theories. In order to compare different GPTs, we advocate an approach in which one views a state in a GPT as a resource, and quantifies the cost of interconverting between different such resources. We illustrate this approach on polygon theories (Janotta et al. New J. Phys 13, 063024, 2011) that interpolate (as the number n of edges of the polygon increases) between a classical trit (when n=3) and a real quantum bit (when n=infinity). Our main results are that simulating the transmission of a single n-gon state requires more than one qubit, or more than log(log(n)) bits, and that n-gon states with n odd cannot be simulated by n'-gon states with n' even (for all n,n'). These results are obtained by showing that the classical capacity of a single n-gon state with n even is 1 bit, whereas it is larger than 1 bit when n is odd; by showing that transmitting a single n-gon state with n even violates information causality; and by showing studying the communication complexity cost of the nondeterministic not equal function using n-gon states.Comment: 18 page

Simultaneous spin-based Boolean logic operations with re-programmable functionality

Construction of parallel logic gates at nano-scale level undoubtedly improves the efficiency of computable operations. In this work we put forward a new idea of designing two distinct logical operations {\em simultaneously} in the two output leads of a three-terminal bridge setup which on one hand is highly stable as all the results are valid for a wide range of parameter values and on the other hand easy to engineer. Our system can be reprogrammed to have all the two-input logic gates with two operations at a time by selectively choosing the physical parameters describing the system, viz, Rashba spin-orbit (SO) interaction, magnetic flux, and Fermi energy. Finally, we explore the possible storage mechanism as well using our model.Comment: 6 pages, 5 figures (Accepted for Publication in Europhysics Letters

Anomalous magnetic response of a quasi-periodic mesoscopic ring in presence of Rashba and Dresselhaus spin-orbit interactions

We investigate the properties of persistent charge current driven by magnetic flux in a quasi-periodic mesoscopic Fibonacci ring with Rashba and Dresselhaus spin-orbit interactions. Within a tight-binding framework we work out individual state currents together with net current based on second-quantized approach. A significant enhancement of current is observed in presence of spin-orbit coupling and sometimes it becomes orders of magnitude higher compared to the spin-orbit interaction free Fibonacci ring. We also establish a scaling relation of persistent current with ring size, associated with the Fibonacci generation, from which one can directly estimate current for any arbitrary flux, even in presence of spin-orbit interaction, without doing numerical simulation. The present analysis indeed gives a unique opportunity of determining persistent current and has not been discussed so far.Comment: 10 pages, 16 figures (Accepted for Publication in: The European Physical Journal B-Condensed Matter and Complex Systems