# Undergraduate Research Weekend In Quantum Game Theory

Are you interested in

- learning what it's like to do research?
- learning some interesting new mathematics?
- gaining experience that could be useful when applying for REUs (Research Experiences for Undergraduates)?

The Department of Mathematics will be running an undergraduate research weekend on November 13-14, 2015. We will provide the background knowledge, the research problems, and the food. You will provide your time, enthusiasm, willingness to learn and to work with others.

**What do you have to do?**

Apply by using the application form below. If you do not see the form, log into your SUNY Geneseo gmail account and reload the page.

Or you can email cooney@geneseo.edu by **Friday, October 30, 2015 **with the following information:

Your name, email address, major, year (Freshman, Sophomore, Junior, or Senior), and, optionally, a sentence or two on why you are interested in participating.

If there are a lot of applicants, then sophomores, juniors, and math majors may receive preference.

**What should you know?**

You should have taken Math 233 (Linear Algebra) and Math 239 (Introduction to Proofs). No knowledge of Physics will be needed for this weekend. It would be helpful to be somewhat familiar with the basics of probability (What does it mean for something to have a probability of 0.2? What does it mean for two events to be independent?).

**When will the research weekend be held?**

4:00-6:00 p.m., Friday, November 13

9:00-5:00 p.m., Saturday, November 14

(Exact times may change slightly.)

**Where?**

South Hall.

**Format?**

There will be a colloquium talk on Friday afternoon that will introduce the topic of Quantum Game Theory. On Saturday, you will work in groups on research problems. Later, each group will provide mini-presentations to the other participants, explaining what they have discovered.

**The topic?**

**Quantum Game Theory****:** Here's an example. A referee asks Alice and Bob questions *x* and *y* chosen from the set *{0,1}* with each choice being equally likely*.* Without talking to each other or knowing what question the other person received, Alice and Bob respond with answers *a* and *b* chosen from the set *{0,1}*. Whether they win or lose is decided according to the following table:

So, if they both receive question *0*, they would win if Alice and Bob both provide the answer *0* or if Alice and Bob both provide the answer *1*. It would be easy to always win this game if they could communicate, but they are not allowed to do so. What strategy can they agree on in advance that will give them the best chance of winning?

How do things change if they are allowed to share quantum resources? Counterintuitively, the real world, the one in which we live, runs by rules which allow Alice and Bob to do noticeably better than common sense would indicate. In quantum game theory, it might be possible for Alice and Bob to receive questions or to provide answers which are both *0* and *1* at the same time. They can also use a resource called entanglement to increase their chance of winning.

Quantum Game Theory will allow us to explore the power of these quantum resources, the same resources that allow for new ways of sending information like Quantum Teleportation, new ways of keeping that information secret like Quantum Cryptography, or could allow for building powerful Quantum Computers.

Come learn some new ideas, ideas so new that it was in the New York Times this week when an experiment was done to show that Alice and Bob can indeed do spookily well when they play this game. (They phrase things differently, but the experiment was basically the same as the game above.)

Tentative Schedule:

**Friday, November 13, 2015 **

4:00 - 5:00 p.m. Colloquium Talk

5:00 - 6:00 p.m. Pizza and social time. This time will give us a chance to talk and to get to know one another.

**Saturday, November 14, 2015**

9:00 - 10:30 a.m.: Introductory talk and problems

10:30 - 11:00 p.m.: Coffee Break

11:00 - 12:00 p.m.: Problem-solving

12:00 - 1:00 p.m.: Lunch Break

1:00 - 3:00 p.m.: Back to work

3:00 - 5:00 p.m.: Mini-presentations