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# Annotated Bibliography: Thomas-Peter’s Real-World Quantum Sensors: Evaluating Resources for Precision Measurement

Thomas-Peter, N., Smith, B. J., Datta, A., Zhang, L., Dorner, U., & Walmsley, I. A. (2011). Real-world quantum sensors: evaluating resources for precision measurement. Physical review letters, 107(11), 113603.

Type: Journal Article

Summary: The paper proposed a way of testing whether a measurement scheme breaks the standard quantum limit, because the normal limit is calculated using Fisher information and quantum Fisher information when the channel and the detection are ideal. The calculation in this paper included experimental imperfections.

# Atomic Clocks: a really quick review

## What is atomic clock?

An atomic clock is a time keeping device that uses the frequency of an atomic transition $f_0$ as the standard of time. This frequency is measured by measuring the probability of state transition after the atoms interact with an electromagnetic field of frequency $f_p$. The probability peaks when $f_p=f_0$. This frequency is set as the standard of 9,192,631,770 Hz for Cs-133 clock.

The measurement of the probability is done periodically determined by the time of flight of the atoms in the setup (going across the chamber in the beam clock, the time for the atom to travel up and down the path in the atomic fountain). $f_p$ is set to different frequency each time.

## What is the precision?

The precision of this method is equivalent to a shift of 1 second in 300 million years for cesium atomic fountain ($10^{-16}$ Hz) [2].

## Properties of transition and sources of noise

For a transition to be suitable for being a frequency standards, there are some properties [1] such as

1. The linewidth of the transition has to be small. (Linewidth introduces noise in the frequency standard.)
2. The interaction time between the atoms and light has to be long. (The signal is average over a long time.)
3. The laser has small linewidth. (Again, linewidth introduces noise.)
4. The signal-to-noise ratio for the transition is high.
5. The transition should not be affected by electromagnetic field.
6. Velocity of atoms has to be low. (Minimize the frequency error due to Doppler effect.)

## Why do we need this precision?

The importance of atomic clocks is not in daily time keeping, but in applications like GPS where precise time keeping translate into a measure distance. With large conversion factor (the speed of light), the precision of the atomic clock is crucial in getting the position on the surface of the earth correctly.

Source:

1. Bauch, Andreas. “Caesium atomic clocks: function, performance and applications.” Measurement Science and Technology 14.8 (2003): 1159.
2. Laura Ost “NIST Launches a New U.S. Time Standard: NIST-F2 Atomic Clock.” (2014) Retrieved from http://www.nist.gov/pml/div688/nist-f2-atomic-clock-040314.cfm

# Annotated Bibliography: Leoński’s Quantum Scissors — finite dimensional states engineering

W. Leoński, A. Kowalewska-Kudłaszyk, Chapter 3 – Quantum Scissors – Finite-Dimensional States Engineering, In: Emil Wolf, Editor(s), Progress in Optics, Elsevier, 2011, Volume 56, Pages 131-185. http://dx.doi.org/10.1016/B978-0-444-53886-4.00003-4. http://arxiv.org/abs/1312.0118 (Mickiewicz University, Poland)

Type: Book Chapter

Summary: They discuss methods of generating finite dimensional Fock-basis state from infinite-dimensional space and truncation. They describe coherent states (finite and infinite), squeezed state, and entangled state on Fock basis, as they use these states to generate a general state later. They go on to describe the method of generating truncated states using quantum scissors.

Linear quantum scissors (LQS) methods use the beam splitters as their main component in creating a general state of N photon. The state is controlled in part by the input state. One of the method uses Mach-Zehnder interferometer as the setup. The state is mostly post-selected with the exception of the BS-array scheme.

Nonlinear quantum scissors (NQS) methods involve Kerr medium inside high-Q cavity or Mach-Zehnder interferometer, fed by coherent and vacuum state. The state is post-selected. In this case, the photons are generated by the nonlinear medium and therefore cannot reach high number Fock state. The most shown in the paper is $\left|2\right\rangle$.

This work also include discussions on limitation and imperfection of the schemes of LQS and its connection to quantum teleportation.

Comments: This chapter is a review of the existing proposed techniques. Some of these techniques must have been implemented, but it is not clear which nor that seems to be the focus of the work.

From the perspective of quantum-enhanced metrology, NQS is not a very useful technique because the probability of getting high Fock states get progressively smaller because of the weak nonlinear interaction. LQS is more the way to go. although the input state requires might still be unrealistic (high number Fock state, for example).

# Resources: Writing

## Technical Writings:

1. Michael Alley. The craft of scientific writing. Springer Science & Business Media, 1996.

#### Candidacy Proposal

1. Holly Rushmeier. Preparing Your Thesis Proposal and Becoming a Ph.D. Candidate, Yale University, 2012. http://preview.tinyurl.com/mt26t5p

# Resources: Quantum Information

## Quantum Channel

1. Griffiths, Robert B. “Quantum Channels, Kraus Operators, POVMs.” Quantum Computation and Quantum Information Theory Course Notes, Carnegie Mellon University (Spring 2010)(2010). http://quantum.phys.cmu.edu/QCQI/qitd411.pdf Annotated Bibliography
2. Leifer, Matt. “The Choi-Jamiolkowski Isomorphism: You’re Doing It Wrong!” (2011) http://mattleifer.info/2011/08/01/the-choi-jamiolkowski-isomorphism-youre-doing-it-wrong/

## State Generation

1. W. Leoński, A. Kowalewska-Kudłaszyk, Chapter 3 – Quantum Scissors – Finite-Dimensional States Engineering, In: Emil Wolf, Editor(s), Progress in Optics, Elsevier, 2011, Volume 56, Pages 131-185. http://dx.doi.org/10.1016/B978-0-444-53886-4.00003-4. http://arxiv.org/abs/1312.0118 (Mickiewicz University, Poland) Annotated Bibliography

# Annotated Bibliography: Griffiths’s Quantum Channels, Kraus Operators, POVMs

Griffiths, Robert B. “Quantum Channels, Kraus Operators, POVMs.” Quantum Computation and Quantum Information Theory Course Notes, Carnegie Mellon University (Spring 2010) (2010).
http://quantum.phys.cmu.edu/QCQI/qitd411.pdf

Type: Lecture note

Summary: The source describes key concepts relating to quantum channel and POVM. The examples are related to quantum communication channels and examples are that of a single-qubit channel. It also presents multiple representations of a quantum channel, but does not explicitly show the connection between them. The author briefly discuss POVM as extension of the channel formalism.

Comments: The source is intended as a summary of sort. It is not in itself complete and often refers to the course’s references. The mathematics is minimal for this type of subject and not rigorous. The source does not employ the standard terminologies of the field which can often cause confusion especially in the part of the representations.

Just for bookmarking…for now. I really should get reading sometime soon.

This started out as a list of top Computer Science blogs, but it more closely resembles a set: the order is irrelevant and there are no duplicate elements; membership of this set of blogs satisfies all of the following conditions:

1. they are written by computer scientists and focus on computer science research;
2. they are of consistently high quality;
3. I regularly read them.

N.B. I have deliberately excluded blogs primarily focusing on computer science education (for another time).

• The Endeavour by John D. Cook (@JohnDCook)

John’s blog cuts across using computing, programming and mathematics to solve real-world problems, pulling in his wide expertise as a mathematics professor, programmer, consultant, manager and statistician. Some great posts across the technical and socio-technical spectrum. Also runs a number of useful Twitter tip accounts, including @CompSciFact, @UnixToolTip, @RegexTip and @TeXtip.

• Serious Engineering by Anthony Finkelstein (@profserious)

Anthony is Dean of the Faculty of…

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