Quantum phase estimation using path-symmetric entangled states

We study the sensitivity of phase estimation using a generic class of path-symmetric entangled states $|\varphi\rangle|0\rangle+|0\rangle|\varphi\rangle$, where an arbitrary state $|\varphi\rangle$ occupies one of two modes in quantum superposition. This class of states includes the previously considered states, i.e. $NOON$ states and entangled coherent states, as special cases. With its generalization, we identify the practical limit of phase estimation under energy constraint that is characterized by the photon statistics of the component state $|\varphi\rangle$. We first show that quantum Cramer-Rao bound (QCRB) can be lowered with super-Poissonianity of the state $|\varphi\rangle$. By introducing a component state of the form $|\varphi\rangle=\sqrt{q}|1\rangle+\sqrt{1-q}|N\rangle$, we particularly show that an arbitrarily small QCRB can be achieved even with a finite energy in an ideal situation. For practical measurement schemes, we consider a parity measurement and a full photon-counting method to obtain phase-sensitivity. Without photon loss, the latter scheme employing any path-symmetric states $|\varphi\rangle|0\rangle+|0\rangle|\varphi\rangle$ achieves the QCRB over the entire range $[0,2\pi]$ of unknown phase shift $\phi$ whereas the former does so in a certain confined range of $\phi$. We find that the case of $|\varphi\rangle=\sqrt{q}|1\rangle+\sqrt{1-q}|N\rangle$ provides the most robust resource against loss among the considered entangled states over the whole range of input energy. Finally we also propose experimental schemes to generate these path-symmetric entangled states.Comment: 10 pages, 5 figures, published versio

Increasing and decreasing entanglement characteristics for continuous variables by a local photon subtraction

We investigate how the entanglement characteristics of a non-Gaussian entangled state are increased or decreased by a local photon subtraction operation. The non-Gaussian entangled state is generated by injecting a single-mode non-Gaussian state and a vacuum state into a 50:50 beam splitter. We consider a photon-added coherent state and an odd coherent state as a single-mode non-Gaussian state. In the regime of small amplitude, we show that the performance of quantum teleportation and the second-order Einstein-Podolsky- Rosen-type correlation can both be enhanced, whereas the degree of entanglement decreases, for the output state when a local photon subtraction operation is applied to the non-Gaussian entangled state. The counterintuitive effect is more prominent in the limit of nearly zero amplitude.Comment: Published version, 7 pages, 3 figure

City farming and sustainable urban development :a case study of Seoul, South Korea

PhD ThesisThe aims of the thesis are to find out the causal mechanism of city farming and to examine the hypothesis that city farming conforms to the conditions of sustainable urban development. As far as methodology is concerned, the thesis employs a realist approach. In the realist methodology, to understand what is as significant as to know why. Therefore, the thesis pays much attention to the conceptualisation of city farming and sustainable urban development. Vacant land in Seoul, the precondition of city farming, occurred basically through the natural process of urban expansion, but most importantly due to the growth-oriented land development policies. City farming is at the moment an opportunistic and illegal use of vacant land under the negligence of planning control. Led by a leading agent, the city farmers on each case site have colonised vacant land through the reality and practice learning. However, city farmers' egoistic action has an unintended consequence of making vacant land an unofficial open space. The thesis also identifies that city farming on the case sites conforms to the elements of sustainable urban development. The elements developed in the thesis are future, nature, participation, equity, and selfreliance. The thesis suggests three criteria for each element with which the hypothesis is examined. The thesis concludes that the modern planning system in South Korea has failed to take into consideration the socio-economic and environmental aspects of city farming. It, therefore, suggests that future planning system promote activities or projects which comply with the principles of sustainable urban development. Although the modern planning system in Seoul has failed to cope with the rapid land use change shown in the case studies, the thesis proposes that the planner's role has become more important than ever before in this age of environmental concerns

The Octonions

The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon their applications in quantum logic, special relativity and supersymmetry.Comment: 56 pages LaTeX, 11 Postscript Figures, some small correction