Quantum correlations from local amplitudes and the resolution of the Einstein-Podolsky-Rosen nonlocality puzzle

The Einstein-Podolsky-Rosen nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is resolved if the quantum correlations are calculated directly from local quantities which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes, and calculate an amplitude correlation function.Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that the measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently `nonlocal' effects like quantum teleportation and entanglement swapping are different from what is usually assumed. Bell type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples we discuss the quantum correlations of two-particle maximally entangled states and the three-particle GHZ entangled state.Comment: Std. Latex, 11 pages, 1 table. Prepared for presentation at the International Conference on Quantum Optics, ICQO'2000, Minsk, Belaru

Quantum complexities of ordered searching, sorting, and element distinctness

We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list, we prove a lower bound of \frac{1}{\pi}(\ln(N)-1) accesses to the list elements for ordered searching, a lower bound of \Omega(N\log{N}) binary comparisons for sorting, and a lower bound of \Omega(\sqrt{N}\log{N}) binary comparisons for element distinctness. The previously best known lower bounds are {1/12}\log_2(N) - O(1) due to Ambainis, \Omega(N), and \Omega(\sqrt{N}), respectively. Our proofs are based on a weighted all-pairs inner product argument. In addition to our lower bound results, we give a quantum algorithm for ordered searching using roughly 0.631 \log_2(N) oracle accesses. Our algorithm uses a quantum routine for traversing through a binary search tree faster than classically, and it is of a nature very different from a faster algorithm due to Farhi, Goldstone, Gutmann, and Sipser.Comment: This new version contains new results. To appear at ICALP '01. Some of the results have previously been presented at QIP '01. This paper subsumes the papers quant-ph/0009091 and quant-ph/000903

Scaling Property of the global string in the radiation dominated universe

We investigate the evolution of the global string network in the radiation dominated universe by use of numerical simulations in 3+1 dimensions. We find that the global string network settles down to the scaling regime where the energy density of global strings, $\rho_{s}$, is given by $\rho_{s} = \xi \mu / t^2$ with $\mu$ the string tension per unit length and the scaling parameter, $\xi \sim (0.9-1.3)$, irrespective of the cosmic time. We also find that the loop distribution function can be fitted with that predicted by the so-called one scale model. Concretely, the number density, $n_{l}(t)$, of the loop with the length, $l$, is given by $n_{l}(t) = \nu/[t^{3/2} (l + \kappa t)^{5/2}]$ where $\nu \sim 0.0865$ and $\kappa$ is related with the Nambu-Goldstone(NG) boson radiation power from global strings, $P$, as $P = \kappa \mu$ with $\kappa \sim 0.535$. Therefore, the loop production function also scales and the typical scale of produced loops is nearly the horizon distance. Thus, the evolution of the global string network in the radiation dominated universe can be well described by the one scale model in contrast with that of the local string network.Comment: 18 pages, 9 figures, to appear in Phys. Rev.

Evolution of a global string network in a matter dominated universe

We evolve the network of global strings in the matter-dominated universe by means of numerical simulations. The existence of the scaling solution is confirmed as in the radiation-dominated universe but the scaling parameter $\xi$ takes a slightly smaller value, $\xi \simeq 0.6 \pm 0.1$, which is defined as $\xi = \rho_{s} t^{2} / \mu$ with $\rho_{s}$ the energy density of global strings and $\mu$ the string tension per unit length. The change of $\xi$ from the radiation to the matter-dominated universe is consistent with that obtained by Albrecht and Turok by use of the one-scale model. We also study the loop distribution function and find that it can be well fitted with that predicted by the one-scale model, where the number density $n_{l}(t)$ of the loop with the length $l$ is given by $n_{l}(t) = \nu/[t^2 (l + \kappa t)^2]$ with $\nu \sim 0.040$ and $\kappa \sim 0.48$. Thus, the evolution of the global string network in the matter-dominated universe can be well described by the one-scale model as in the radiation-dominated universe.Comment: 10 pages, 5 figure

A Systematic Review of Magnesium Sulfate for Perinatal Neuroprotection: What Have We Learnt From the Past Decade?

There is an important unmet need to improve long term outcomes of encephalopathy for preterm and term infants. Meta-analyses of large controlled trials suggest that maternal treatment with magnesium sulfate (MgSO4) is associated with a reduced risk of cerebral palsy and gross motor dysfunction after premature birth. However, to date, follow up to school age has found an apparent lack of long-term clinical benefit. Because of this inconsistency, it remains controversial whether MgSO4 offers sustained neuroprotection. We systematically reviewed preclinical and clinical studies reported from January 1 2010, to January 31 2020 to evaluate the most recent advances and knowledge gaps relating to the efficacy of MgSO4 for the treatment of perinatal brain injury. The outcomes of MgSO4 in preterm and term-equivalent animal models of perinatal encephalopathy were highly inconsistent between studies. None of the perinatal rodent studies that suggested benefit directly controlled body or brain temperature. The majority of the studies did not control for sex, study long term histological and functional outcomes or use pragmatic treatment regimens and many did not report controlling for potential study bias. Finally, most of the recent preterm or term human studies that tested the potential of MgSO4 for perinatal neuroprotection were relatively underpowered, but nevertheless, suggest that any improvements in neurodevelopment were at best modest or absent. On balance, these data suggest that further rigorous testing in translational preclinical models of perinatal encephalopathy is essential to ensure safety and best regimens for optimal preterm neuroprotection, and before further clinical trials of MgSO4 for perinatal encephalopathy at term are undertaken

Spatial Distribution of Nucleosynthesis Products in Cassiopeia A: Comparison Between Observations and 3D Explosion Models

We examine observed heavy element abundances in the Cassiopeia A supernova remnant as a constraint on the nature of the Cas A supernova. We compare bulk abundances from 1D and 3D explosion models and spatial distribution of elements in 3D models with those derived from X-ray observations. We also examine the cospatial production of 26Al with other species. We find that the most reliable indicator of the presence of 26Al in unmixed ejecta is a very low S/Si ratio (~0.05). Production of N in O/S/Si-rich regions is also indicative. The biologically important element P is produced at its highest abundance in the same regions. Proxies should be detectable in supernova ejecta with high spatial resolution multiwavelength observations.Comment: To appear in the Conference Proceedings for the "10th Symposium on Nuclei in the Cosmos (NIC X)", July 27 - August 1 2008, Mackinack Island, Michigan, US

Observing Long Cosmic Strings Through Gravitational Lensing

We consider the gravitational lensing produced by long cosmic strings formed in a GUT scale phase transition. We derive a formula for the deflection of photons which pass near the strings that reduces to an integral over the light cone projection of the string configuration plus constant terms which are not important for lensing. Our strings are produced by performing numerical simulations of cosmic string networks in flat, Minkowski space ignoring the effects of cosmological expansion. These strings have more small scale structure than those from an expanding universe simulation - fractal dimension 1.3 for Minkowski versus 1.1 for expanding - but share the same qualitative features. Lensing simulations show that for both point-like and extended objects, strings produce patterns unlike more traditional lenses, and, in particluar, the kinks in strings tend to generate demagnified images which reside close to the string. Thus lensing acts as a probe of the small scale structure of a string. Estimates of lensing probablity suggest that for string energy densities consistant with string seeded structure formation, on the order of tens of string lenses should be observed in the Sloan Digital Sky Survey quasar catalog. We propose a search strategy in which string lenses would be identified in the SDSS quasar survey, and the string nature of the lens can be confirmed by the observation of nearby high redshift galaxies which are also be lensed by the string.Comment: 24 pages revtex with 12 postscript firgure

Contribution of Long Wavelength Gravitational Waves to the CMB Anisotropy

We present an in depth discussion of the production of gravitational waves from an inflationary phase that could have occurred in the early universe, giving derivations for the resulting spectrum and energy density. We also consider the large-scale anisotropy in the cosmic microwave background radiation coming from these waves. Assuming that the observed quadrupole anisotropy comes mostly from gravitational waves (consistent with the predictions of a flat spectrum of scalar density perturbations and the measured dipole anisotropy) we describe in detail how to derive a value for the scale of inflation of $(1.5-5)\times 10^{16}$GeV, which is at a particularly interesting scale for particle physics. This upper limit corresponds to a 95\% confidence level upper limit on the scale of inflation assuming only that the quadrupole anisotropy from gravitational waves is not cancelled by another source. Direct detection of gravitational waves produced by inflation near this scale will have to wait for the next generation of detectors.Comment: (LaTeX 16 pages), 2 figures not included, YCTP-P16-9

Third quantization of f(R)f(R)-type gravity

We examine the third quantization of $f(R)$-type gravity, based on its effective Lagrangian in the case of a flat Friedmann-Lemaitre-Robertson-Walker metric. Starting from the effective Lagrangian, we execute a suitable change of variable and the second quantization, and we obtain the Wheeler-DeWitt equation. The third quantization of this theory is considered. And the uncertainty relation of the universe is investigated in the example of $f(R)$-type gravity, where $f(R)=R^2$. It is shown, when the time is late namely the scale factor of the universe is large, the spacetime does not contradict to become classical, and, when the time is early namely the scale factor of the universe is small, the quantum effects are dominating.Comment: 9 pages, Arbitrary constants in (4.19) are changed to arbitrary functions of $\varphi$. Conclusions are not changed. References are added. Typos are correcte

Quantum Cryptography Based on the Time--Energy Uncertainty Relation

A new cryptosystem based on the fundamental time--energy uncertainty relation is proposed. Such a cryptosystem can be implemented with both correlated photon pairs and single photon states.Comment: 5 pages, LaTex, no figure