Experimental Measurement of Mixed State Geometric Phase by Quantum Interferometry using NMR

Geometric phase has been proposed as one of the promising methodologies to perform fault tolerant quantum computations. However, since decoherence plays a crucial role in such studies, understanding of mixed state geometric phase has become important. While mixed state geometric phase was first introduced mathematically by Uhlmann, recently Sjoqvist et al. [Phys. Rev. Lett. 85(14), 2845 (2000)] have described the mixed state geometric phase in the context of quantum interference and shown theoretically that the visibility as well as the shift of the interference pattern are functions of geometric phase and the purity of the mixed state. Here we report the first experimental study of the dependence of interference visibility and shift of the interference pattern on the mixed state geometric phase by Nuclear Magnetic Resonance.Comment: 7 Figures. Physics Letters A (In Press

Relaxation of Pseudo pure states : The Role of Cross-Correlations

In Quantum Information Processing by NMR one of the major challenges is relaxation or decoherence. Often it is found that the equilibrium mixed state of a spin system is not suitable as an initial state for computation and a definite initial state is required to be prepared prior to the computation. As these preferred initial states are non-equilibrium states, they are not stationary and are destroyed with time as the spin system relaxes toward its equilibrium, introducing error in computation. Since it is not possible to cut off the relaxation processes completely, attempts are going on to develop alternate strategies like Quantum Error Correction Codes or Noiseless Subsystems. Here we study the relaxation behavior of various Pseudo Pure States and analyze the role of Cross terms between different relaxation processes, known as Cross-correlation. It is found that while cross-correlations accelerate the relaxation of certain pseudo pure states, they retard that of others.Comment: 23 pages, 9 figure

Quantum information processing by NMR using a 5-qubit system formed by dipolar coupled spins in an oriented molecule

Quantum Information processing by NMR with small number of qubits is well established. Scaling to higher number of qubits is hindered by two major requirements (i) mutual coupling among qubits and (ii) qubit addressability. It has been demonstrated that mutual coupling can be increased by using residual dipolar couplings among spins by orienting the spin system in a liquid crystalline matrix. In such a case, the heteronuclear spins are weakly coupled but the homonuclear spins become strongly coupled. In such circumstances, the strongly coupled spins can no longer be treated as qubits. However, it has been demonstrated elsewhere, that the $2^N$ energy levels of a strongly coupled N spin-1/2 system can be treated as an N-qubit system. For this purpose the various transitions have to be identified to well defined energy levels. This paper consists of two parts. In the first part, the energy level diagram of a heteronuclear 5-spin system is obtained by using a newly developed heteronuclear z-cosy (HET-Z-COSY) experiment. In the second part, implementation of logic gates, preparation of pseudopure states, creation of entanglement and entanglement transfer is demonstrated, validating the use of such systems for quantum information processing.Comment: 23 pages, 8 figure

Predicating from an early age: edusemiotics and the potential of children’s preconceptions

This paper aims to explain how semiotics and constructivism can collaborate in an educational epistemology by developing a joint approach to prescientific conceptions. Empirical data and findings of constructivist research are interpreted in the light of Peirce’s semiotics. Peirce’s semiotics is an anti-psychologistic logic (CP 2.252; CP 4.551; W 8:15; Pietarinen in Signs of logic, Springer, Dordrecht, 2006; Stjernfelt in Diagrammatology. An investigation on the borderlines of phenomenology, ontology and semiotics, Springer, Dordrecht, 2007) and relational logic. Constructivism was traditionally developed within psychology and sociology and, therefore, some incompatibilities can be expected between these two schools. While acknowledging the differences, we explain that constructivism and semiotics share the assumption of realism that knowledge can only be developed upon knowledge and, therefore, an epistemological collaboration is possible. The semiotic analysis performed confirms the constructivist results and provides a further insight into the teacher-student relation. Like the constructivist approach, Peirce’s doctrine of agapism infers that the personal dimension of teaching must not be ignored. Thus, we argue for the importance of genuine sympathy in teaching attitudes. More broadly, the article also contributes to the development of postmodern humanities. At the end of the modern age, the humanities are passing through a critical period of transformation. There is a growing interest in semiotics and semiotic philosophy in many areas of the humanities. Such a case, on which we draw, is the development of a theoretical semiotic approach to education, namely edusemiotics (Stables and Semetsky, Pedagogy and edusemiotics: theoretical challenge/practical opportunities, Sense Publishers, Rotterdam, 2015)