Randomness is valid at large numbers

Randomness is a central concept to statistics and physics. Here, a statistical analysis shows experimental evidence that tossing coins and finding last digits of prime numbers are identical regarding statistics for equally likely outcomes. This analysis explains why randomness in equally likely outcomes can be valid only at large numbers.Comment: 4 pages, 3 figure

Entanglement of thermal scalar fields in a compact space space

Using the thermal Green's function approach we propose a general method to investigate entanglement of the vacuum state or thermal ground states in an arbitrary dimensional space-time. As an application we show quantum separability of the massive thermal scalar field vacuum in the 1+1 dimensional cylindrical space-time. Separability is demonstrated using the positive partial transpose criterion for effective two-mode Gaussian states of collective operators. In this case, for all mass and temperature values entanglement is absent between the collective operators.Comment: title change

Deciding whether a quantum state has secret correlations is an NP-complete problem

From the NP-hardness of the quantum separability problem and the relation between bipartite entanglement and the secret key correlations, it is shown that the problem deciding whether a given quantum state has secret correlations in it or not is in NP-complete.Comment: 3 pages, revtex, no fig, typos correcte

Physical aging in article page views

Statistics of article page views is useful for measuring the impact of individual articles. Analyzing the temporal evolution of article page views, we find that article page views usually decay over time after reaching a peak, especially exhibiting relaxation with nonexponentiality. This finding suggests that relaxation in article page views resembles physical aging as frequently found in complex systems.Comment: 3 pages with 1 figur

The M-sigma Relation of Super Massive Black Holes from the Scalar Field Dark Matter

We explain the M-sigma relation between the mass of super massive black holes in galaxies and the velocity dispersions of their bulges in the scalar field or the Bose-Einstein condensate dark matter model. The gravity of the central black holes changes boundary conditions of the scalar field at the galactic centers. Owing to the wave nature of the dark matter this significantly changes the galactic halo profiles even though the black holes are much lighter than the bulges. As a result the heavier the black holes are, the more compact the bulges are, and hence the larger the velocity dispersions are. This tendency is verified by a numerical study. The M-sigma relation is well reproduced with the dark matter particle mass $m\simeq 5\times 10^{-22} eV$

Dark energy from vacuum entanglement

We suggest that vacuum entanglement energy associated with the entanglement entropy of the universe is the origin of dark energy. The observed properties of dark energy can be explained by using the nature of entanglement energy without modification of gravity or exotic matter. From the number of degrees of freedom in the standard model, we obtain the equation of state parameter $\omega^0_\Lambda\simeq -0.93$ and $d\simeq 0.95$ for the holographic dark energy, which are consistent with current observational data at the 95% confidence level.Comment: to be published in JCA

Holographic Dark Energy and Quantum Entanglement

In this paper, we briefly review the holographic dark energy model and introduce the idea that dark energy is a kind of thermal energy related to the quantum entanglement of the vacuum across a cosmic future event horizon. The holographic dark energy model comes from a theoretical attempt to apply the holographic principle to the dark energy problem and follows the idea that the short distance cut-off or ultraviolet (UV) cut-off is related to the long distance cut-off or infrared (IR) cut-off. The IR cut-off relevant to dark energy is the size of the future event horizon. This model gives a holographic dark energy comparable to the observational data. Though this model is in good agreement with observational data, some problems (non-locality, circular logic, causality problem, $\it etc.$) exist due to the use of the future event horizon as a present IR cut-off. These problems of the holographic dark energy model are considerably resolved using action principle and equations of motion. Finally, we discuss the relation between quantum entanglement and dark energy which is connected to the more fundamental relation between entanglement and gravity.Comment: to be published in JKP

Radial Acceleration Relation from Ultra-light Scalar Dark matter

We show that ultra-light scalar dark matter (fuzzy dark matter) in galaxies has a quantum mechanical typical acceleration scale about 10^{-10}\,\mbox{ms}^{-2}, which leads to the baryonic Tully-Fisher relation. Baryonic matter at central parts of galaxies acts as a boundary condition for dark matter wave equation and influences stellar rotation velocities in halos. Without any modification of gravity or mechanics this model also explains the radial acceleration relation and MOND-like behavior of gravitational acceleration found in galaxies having flat rotation curves. This analysis can be extended to the Faber-Jackson relation

Qubit geometry and conformal mapping

Identifying the Bolch sphere with the Riemann sphere(the extended complex plane), we obtain relations between single qubit unitary operations and M\"{o}bius transformations on the extended complex plane.Comment: 3 pages, 1 figure, revtex, title changed, minor modification

Quantum Shift Register

We consider a quantum circuit in which shift and rotation operations on qubits are performed by swap gates and controlled swap gates. These operations can be useful for quantum computers performing elementary arithmetic operations such as multiplication and a bit-wise comparison of qubits.Comment: 3 pages, 4 figures, revte