D-outcome measurement for a nonlocality test

For the purpose of the nonlocality test, we propose a general correlation observable of two parties by utilizing local $d$-outcome measurements with SU($d$) transformations and classical communications. Generic symmetries of the SU($d$) transformations and correlation observables are found for the test of nonlocality. It is shown that these symmetries dramatically reduce the number of numerical variables, which is important for numerical analysis of nonlocality. A linear combination of the correlation observables, which is reduced to the Clauser-Horne-Shimony-Holt (CHSH) Bell's inequality for two outcome measurements, is led to the Collins-Gisin-Linden-Massar-Popescu (CGLMP) nonlocality test for $d$-outcome measurement. As a system to be tested for its nonlocality, we investigate a continuous-variable (CV) entangled state with $d$ measurement outcomes. It allows the comparison of nonlocality based on different numbers of measurement outcomes on one physical system. In our example of the CV state, we find that a pure entangled state of any degree violates Bell's inequality for $d(\ge 2)$ measurement outcomes when the observables are of SU($d$) transformations.Comment: 16 pages, 2 figure

Comprehensive wealth measurement and spatial hedonic analysis : social capital and social amenities

The last decade has seen a growing interest in the concept of comprehensive wealth, which is defined as including intangible and non-market as well as tangible and market assets. This dissertation responds to this rising interest by developing explicit concepts, indicators, and sources of data necessary to measure comprehensive wealth at various spatial scales. It achieves this by generalizing the general spatial equilibrium model proposed by Roback (1982). The key contributions of this research are the extension and application of the comprehensive wealth concept to measure the value of social amenities generated as a result of public and private investments in social and other types of capital. This dissertation extends the Roback model by identifying appropriate data on local income, land values, and place-based amenities at the county level in the contiguous 48 states of the United States. This dissertation reports substantial findings based on the empirical analysis. While the results are largely consistent with those of Roback and other, more recent papers and with theoretical expectations, this study found significantly different effects of amenities on wages and land values between metro and non-metro counties due to different marginal effects on wages and land values. The analysis also found significant spatial interaction effects, which influence the magnitude of the full implicit price for social amenity variables, again with significant differences between metro and non-metro counties. Finally, the extended model is able to determine whether the social amenities are at optimal levels. There are important implications of this research. Policies to enhance social amenities from immobile social capital and local public services can reduce both real costs of production and the societal opportunity costs of development in the long term. Well-designed policy and investment in immobile and non-marketed amenities of a location will make a place more attractive and sustainable, conferring benefits to residents and local businesses. The proposed typology can be useful for designing policy and investment plans for sustainable regional economic development. The model can also be used to conduct simulations to predict the effects of policy on comprehensive wealth given locally unique and dynamic combinations of regional assets. Keywords: Comprehensive Wealth; Spatial Equilibrium Model; Non-market Valuation; Social Amenities; Social CapitalIncludes biblographical reference

Entanglement transfer from continuous variables to qubits

We show that two qubits can be entangled by local interactions with an entangled two-mode continuous variable state. This is illustrated by the evolution of two two-level atoms interacting with a two-mode squeezed state. Two modes of the squeezed field are injected respectively into two spatially separate cavities and the atoms are then sent into the cavities to resonantly interact with the cavity field. We find that the atoms may be entangled even by a two-mode squeezed state which has been decohered while penetrating into the cavity.Comment: 5 pages, 4 figure

Critical behavior in ultra-strong-coupled oscillators

We investigate the strong coupling regime of a linear $x$-$x$ coupled harmonic oscillator system, by performing a direct diagonalization of the hamiltonian. It is shown that the $x$-$x$ coupled hamiltonian can be equivalently described by a Mach-Zehnder-type interferometer with a quadratic unitary operation in each of its arms. We show a sharp transition of the unitary operation from an elliptical phase rotator to an elliptical squeezer as the coupling gets stronger, which leads to the continuous generation of entanglement, even for a significantly thermal state, in the ultra-strong coupled regime. It is also shown that this critical regime cannot be achieved by a classical Hookian coupling. Finally, the effect of a finite-temperature environment is analyzed, showing that entanglement can still be generated from a thermal state in the ultra-strong coupled regime, but is destroyed rapidly

Any multipartite entangled state violating Mermin-Klyshko inequality can be distilled for almost all bipartite splits

We study the explicit relation between violation of Bell inequalities and bipartite distillability of multi-qubit states. It has been shown that even though for $N\ge 8$ there exist $N$-qubit bound entangled states which violates a Bell inequality [Phys. Rev. Lett. {\bf 87}, 230402 (2001)], for all the states violating the inequality there exists at least one splitting of the parties into two groups such that pure-state entanglement can be distilled [Phys. Rev. Lett. {\bf 88}, 027901 (2002)]. We here prove that for all $N$-qubit states violating the inequality the number of distillable bipartite splits increases exponentially with $N$, and hence the probability that a randomly chosen bipartite split is distillable approaches one exponentially with $N$, as $N$ tends to infinity. We also show that there exists at least one $N$-qubit bound entangled state violating the inequality if and only if $N\ge 6$.Comment: 4 pages, 2 figure

Completely-Positive Non-Markovian Decoherence

We propose an effective Hamiltonian approach to investigate decoherence of a quantum system in a non-Markovian reservoir, naturally imposing the complete positivity on the reduced dynamics of the system. The formalism is based on the notion of an effective reservoir, i.e., certain collective degrees of freedom in the reservoir that are responsible for the decoherence. As examples for completely positive decoherence, we present three typical decoherence processes for a qubit such as dephasing, depolarizing, and amplitude-damping. The effects of the non-Markovian decoherence are compared to the Markovian decoherence.Comment: 8 pages, 1 figur