## Wednesday, September 30, 2009

### Quantum Interferometer

Jonathan Dowling from Louisiana State University gave a presentation about the use of entangled photons for high precision interferometry [1] showing that they can lead to much better measurements than it is possible with classical light. These entangled photon states are of the form

Some problems remain such as the difficulty to produce NOON states with high power, but they are very promising anyway.

So far they devised how to make ingenious conditional measurements in order to generate NOON states.

Another important topic was the emulation of non-linear effects by conditional measurements within linear optics [2].

Refererences

1. J Dowling arXiv:0904.0163
2. G. G. Lapaire1, et al, Conditional linear-optical measurement schemes generate effective photon nonlinearities DOI: 10.1103/PhysRevA.68.042314
3. Jonathan Dowling ppt presentation

LaTeX was possible in this entry with MathTran

## Saturday, September 26, 2009

### Human chromosome 2

Humans have 23 chromosomes while all the other hominids have 24 chromosomes. The question is, how can this be possible if we are suppose to have a common ancestor. Now we know that human chromosome 2 is the result of the fusion of two chromosomes found in our relative hominids.

## Friday, September 25, 2009

### Quantum Feedback Control

Kurt Jacobs gave a presentation about Quantum Feedback Control. He showed how to introduce the action of weak continuous measurements into a master equation that. This equation resembles the Lindblad equation with an extra stochastic term, where the feedback can be introduced in the Hamiltonian. One application was to create a cat state of a harmonic oscillator.

The adiabatic quantum computer was proposed in arXiv:quant-ph/0001106v1 in order to solve certain type of problems.

For low dimensions it was shown that the adiabatic quantum computer is polynomial, for a certain problem with exponential complexity in a classical computer. Peter Young, who gave a presentation at Princeton yesterday, is using Quantum Montecarlo Simuations, as used in statistical mechanics for the partition function, in order to engage this problem for higher dimensions where direct simulations are not feasible.
The Complexity Of The Quantum Adiabatic Algorithm

## Wednesday, September 23, 2009

### Intelligence gene

The following article seems to indicate that there is a gene that is associated with higher intelligence, but those who have it are in disadvantage in high pressure exams
memory gene

## Tuesday, September 22, 2009

### Epigenetics

Epigenetics studies the effect of the environment on the expression of genes. A saw the following NOVA tv program
http://www.pbs.org/wgbh/nova/genes/issa.html
and I was very surprised.

### LaTeX in my blog

I want to write equations in my blog, so I found mimetex, but I could not run it from the cgi Princeton server. I do not know why. I may need to set up complicated permissions or there is a compatibility issue between mimetex and the cgi server.

Here I am testing the cgi provided by mimetex

$c=\sqrt{a^2+b^2}$

It works, but I can only use it as a test.

Another method, less elegant though, is using MathTran, which I used to make the following equation

## Monday, September 21, 2009

### Quantum mechanics in plants??

Profesor Gregory D. Scholes gave a presentation in Princeton about the possible role of quantum mechanical effects in the absorption of light and energy transfer in photosynthetic processes in plants.

www.nature.com/nature/journal/v431/n7006/full/431256a.html

This seems to be very controversial because they claim high coherence at room temperature. Personally I find it difficult to believe it but I'll wait and see more developments.

### PkPd

PKPD stands for Pharmacokinetic/Pharmacodynamic and it seems to be one of the most fruitful research areas in the boundaries between mathematics, statistics, chemistry and BIOLOGY.

http://en.wikipedia.org/wiki/Pharmacodynamics

Particularly, I am mostly interested in the modeling with differential equations and the use of control theory.

### Alpha

Alpha is what they call knowledge data base

http://www.wolframalpha.com/

The difference from regular search engines is is designed to deliver well formatted data.

For example, using "Dow Jones" it gives a very nice page with graphs, which can be downloaded along with the raw data from a Mathematica notebook.

The Dow Jones Industrial Average is one of the most important indexes in Wall street.

In the same way one can download the information for specific companies such as Toyota or Microsoft.

### International Mathematica User Conference 2009

I am going to give an oral presentation at the International Mathematica User Conference 2009 in Champaign Illinois. October 22-24.

List of presentations

My presentation is going to be about my package developed for performing Magnus expansions. This expansion can be used to find approximate solutions for systems of linear equations and linear operators in general

Magnus expansion in Wikipedia

## Sunday, September 20, 2009

### Entanglement measure

I developed a very nice method to measure the entanglement of pure states

Renan Cabrera, Herschel Rabitz, The landscape of quantum transitions driven by single-qubit unitary transformations with implications for entanglement, J. Phys. A: Math. Theor. 42 (2009) 275303.

doi: 10.1088/1751-8113/42/27/275303

This method is based in the measurement of the Bures distance between a given state and the closest separable state, which allows one to calculate the generalized Schmidt state. The entanglement can be measured from the coefficients of this Schmidt state.

### Bures measure

My paper about the calculation of the unitary part of the Bures measure was recently accepted for publication

Renan Cabrera, Herschel Rabitz, Calculation of the Unitary part of the Bures Measure for N-level Quantum Systems , Accepted at J. Phy A: Math. Theor.

This paper shows how the Bures measure can be expressed as the product of the measure of even euclidean balls. This means that we now have a simple and easy formula for sampling. The ultimate application will be in Bayesian quantum estimation.

My wikipedia article that explains the basics of the Bures metric is

http://en.wikipedia.org/wiki/Bures_metric

### Group theory for wireless communications

The technology of transmission of information between multiple antennas began to develop 10 years ago. The purpose is to increase the fidelity and transmission rate between multiple sources and multiple receptors.

The particular technology that I am interested mostly is in the Unitary Space-Time Codes (UST). In this technology, the information is encoded in blocks spanning space and time. In the simplest case, we could think of N antennas with a sequence of N pulses, so that the information block can be represented as an NxN complex matrix. It is mathematically convenient to use unitary matrices, so the name UST is justified in this case.

Inside the UST field I am paying attention to the Cayley encoding [1,2,3] because it seems to be elegant, simple and easy to understand.

References
1. Cayley Differential Unitary Space-Time Codes by B. Hochwald, B. Hassibi
2. Unitary space-time modulation via Cayley transform by Y Jing, B Hassibi
3. Yindi Jing Thesis
4. Representation Theory for High-Rate Multiple-Antenna Code Design by B. Hassibi, B. Hochwald, A. Shokrollahi, W. Sweldens
5. Differential Unitary Space-Time Modulation by B. Hochwald, W. Sweldens
6. Random Matrices for Wireless Communications
A. Tulino, S. Verdu (at Princeton)
7. Circuits for Wireless Communications: Selected Readingsby Banlue Srisuchinwong (Editor), Wanlop Surakampontorn (Editor), Sawasd Tantaratana (Editor)
8. Space-time coding for broadband wireless communications by By Georgios B. Giannakis, Zhiqiang Liu
9. Random Matrices For Wireless Communications I
10. Random Matrices For Wireless Communications II

http://mars.bell-labs.com/

More applications of group theory in engineering can be found at

http://www.usna.edu/Users/math/wdj/repn_thry_appl.htm

### Greetings

Hi, My name is Renan Cabrera L.

I am a physicist interested in quantum mechanics, group theory, and science in general.

My web page is

Renan Cabrera's Web Page