Resource Bounded Unprovability of Computational Lower Bounds

This paper introduces new notions of asymptotic proofs, PT(polynomial-time)-extensions, PTM(polynomial-time Turing machine)-omega-consistency, etc. on formal theories of arithmetic including PA (Peano Arithmetic). This paper shows that P not= NP (more generally, any super-polynomial-time lower bound in PSPACE) is unprovable in a PTM-omega-consistent theory T, where T is a consistent PT-extension of PA. This result gives a unified view to the existing two major negative results on proving P not= NP, Natural Proofs and relativizable proofs, through the two manners of characterization of PTM-omega-consistency. We also show that the PTM-omega-consistency of T cannot be proven in any PTM-omega-consistent theory S, where S is a consistent PT-extension of T.Comment: 78 page

Serial-parallel conversion for single photons with heralding signals

We present serial-parallel conversion for a heralded single photon source (heralded SPS). We theoretically show that with the heralding signal, the serial-parallel converter can route a stream of n photons to n different spatial modes more efficiently than is the case without using a heralding signal. We also experimentally demonstrate serial-parallel conversion for two photons generated from a heralded SPS. We achieve a conversion efficiency of 0.533 \pm 0.003, which exceeds the maximum achievable efficiency of 0.5 for serial-parallel conversion using unheralded photons, and is double the efficiency (0.25) for that using beamsplitters. When the losses in the optical converter are corrected for, the efficiency of the current setup can be increased up to 0.996 \pm 0.006.Comment: 8 pages, 5 figure

Demonstration of an optical quantum controlled-NOT gate without path interference

We report the first experimental demonstration of an optical quantum controlled-NOT gate without any path interference, where the two interacting path interferometers of the original proposals (Phys. Rev. A {\bf 66}, 024308 (2001), Phys. Rev. A {\bf 65}, 012314 (2002)) have been replaced by three partially polarizing beam splitters with suitable polarization dependent transmittances and reflectances. The performance of the device is evaluated using a recently proposed method (Phys. Rev. Lett. {\bf 94}, 160504 (2005)), by which the quantum process fidelity and the entanglement capability can be estimated from the 32 measurement results of two classical truth tables, significantly less than the 256 measurement results required for full quantum tomography.Comment: 4 pages, 3 figure

Localized knowledge spillovers and patent citations: A distance-based approach

We develop a new approach to localized knowledge spillovers by incorporating the concept of control patents (Jaffe, Trajtenberg and Henderson 1993) into the distance-based test of localization (Duranton and Overman, 2005). Using microgeographic data, we identify localization distance while allowing for cross-boundary spillovers, unlike the existing literature where the extent of localized knowledge spillovers is detected at the state or metropolitan statistical area level. We revisit the recent debate by Thompson and Fox-Kean (2005) and Henderson, Jaffe and Trajtenberg (2005) on the existence of localized knowledge spillovers, and find solid evidence supporting localization, even when finer controls are used.

Dispersion cancellation in high resolution two-photon interference

The dispersion cancellation observed in Hong-Ou-Mandel (HOM) interference between frequency-entangled photon pairs has been the basis of quantum optical coherence tomography and quantum clock synchronization. Here we explore the effect of phase dispersion on ultranarrow HOM dips. We show that the higher-order dispersion, the line width of the pump laser, and the spectral shape of the parametric fluorescence have a strong effect on the dispersion cancellation in the high-resolution regime with several experimental verifications. Perfect dispersion cancellation with a linewidth of 3\mu m is also demonstrated through 25 mm of water.Comment: 6 pages, 6 figure