Danny and me just had our paper on quantum goblins published in PRA. This is the first publication from my Phd, and my first PRA.

After comments from the editor we changed the name from (the arXive version's) "Quantum discord and local demons" to "Quantum discord, local operations, and Maxwell’s demons"

In the paper we discuss three different types of quantum discord, the first is the original introduced by Zurek, the second was introduced by Zurek in relation to Maxwell's demons. We introduced the third in relation to a slightly different formulation of the same Maxwell's demon idea. During our conversations with various people we discovered that many people don't realize that  Zurek's second version of discord is different from the first one, so we used the opportunity to point out the difference. We also showed that all three versions of discord agree on which states have zero discord.

This work really started happening when I was too lazy to calculate discord in some 3x3 system, Danny and me then found that there is a very easy way to verify if a system has zero discord (it's in the paper). We then decided that maybe this method could give us a different version of discord, this different version of discord turned out to be very cool because it was related to thermodynamics.  We basically showed that this third version of discord is the difference in the amount of work that can be done by Maxwell's demons with access to the whole system (non local demons) and demons with access to just part of the system (local demons) since the local demons are not as "strong" as the non local ones , we called them goblins (It started the other way around, but Alex Terno told us that goblins are weaker then demons).

We have a few other results in the paper relating different types of discord to various other things,  generally trying to make the whole idea of different types of discord less confusing and showing the physics related to each one. Finally we also  showed that by looking at the discord of a density matrix (made up of probabilities of having different pure states)  we can't know if the  states which make up the density matrix are locally distinguishable.

Before we published I gave some talks on this work, one talk can be found here.

Yesterday at lunch Stojan and me were talking about the history of spin. Here is a very cool story about it

http://www.lorentz.leidenuniv.nl/history/spin/goudsmit.html

No  one solved the riddle from two weeks ago (hats), i'm still wating for the answer.

Light bulbs

You are standing in front of a wall with 100 light bulbs and 100 switches numbered 1 to 100.
the light bulbs  are all off, and the switches have the following effect:
flipping a switch will change the state of all the bulbs that are multiples of that switch (so flipping 10 will change the state of 10,20,30,40..100)
you decide to flip the switches one by one, how many light bulbs will be lit at the end?

flipping the first switch(1) will turn all the bulbs on, flipping the second (2) will then turn off all the even numbers etc... finally turning the 100th switch (100) will change the state of the 100th bulb.


enjoy.

No one solved last week's riddle yet so here's a small hint.
The answer is 1, but what's the algorithm?
For all those who asked, the prisoners cannot use any special methods
like timing their answers etc... the only information each prisoner can send is a single bit (i.e either black or white) but
that has to also be his guess for the hat.

In the mean while, here's a simple one

what are the next numbers in this series

18, 46, 94, 63, 52, ...

In a really harsh prison the sadistic warden decided to give 100 prisoners the following task:
They must stand in a line, and he will put a hat on each of their heads. The hats can be either black or white. Then each prisoner will be allowed to say one word, either "black" or "white", trying to guess what hat he has. At the end of the game, all prisoners who got their color right will be released, all the rest will be killed. If any prisoner brakes any rule (looks backwards, says any other word, jumps , pokes, etc..) everyone will be killed.

What is their best strategy to get the minimum amount of prisoners killed ? How many prisoners are risking their lives using such a strategy?
The can decide on the stratagy ahead of time.

Again the rules. They all follow the algorithm. They can all hear what the fellow prisoners say. Each prisoner can see all the guys ahead of him , but non of those behind. They can all say either "black" or "white" once but the order of talking is
whatever they want. The number of black and white hats is unknown (but there are  100 hats in total). 

 

 

A few people solved last week's murder mystery. It's quite obvious that Bill killed his brother hoping the girl would come to the funeral.
While the logical connection is simple, it takes a twisted mind to see the solution. The story is that this riddle was used to test psychopaths.
This makes this weeks hike very interesting since Lauri , Ingo and me all solved the riddle. (and it's on Halloween).
As for 2000!mod2003 Gavin is the only one who solved it. I guess i owe you a beer.

Today's riddle requires some thought although it seems easy at first sight.

What is the longest day on the equator, how long is it?
what is the shortest day, how long is that?

Think about your answer.

Last weeks riddle has not been solved by anyone yet. I'm giving you all a chance to try it again for another week.

In the meanwhile i have a small hint: The answer is 1001 - but how do you calculate it? The beer offer still stands.

And another easy but interesting riddle. This one took me 10 seconds to solve, but more about that next week....

The riddle:

During his mother's funeral Bill saw the most beautiful girl he has ever seen. It was love at first sight

for him, but being distracted for one second he lost sight of her and did not see her again....

Two weeks later Bill's brother was murdered

Who killed him and why?

Please don't post the answer to this one here, send me an email, tell me the answer or just keep it to yourself

I will give the answer next week.

And don't forget 2000!mod2003.

Well done to Johann, Ingo and all others who solved last week's riddle. I was surprised to find that my solution was not as good as theirs.
As i promised , this week i'll give a hard one. It took me a month to solve and i'll buy a uni bar guiness to the first person to solve it this week. Since it involves a calculation I don't want only the answer but also the general method for solving it without a computer. A mathematician friend of mine solved it in about 5 mins and said any decent mathematician should be able to solve it in less then 10.
The riddle: 2000!mod2003
where ! is factorial and mod is the modulo defined as the operation that finds the remainder of division of one number by another eg 7mod5=2 or 39mod3=0.

Hint:2003 is a prime number

If you know the easy (mathematician's solution) you don't get a beer.

Have fun.

Hi all,
The only person to send me an answer to last week's riddle was Johann. So this week I'm going for an easy one with the promise of a really hard one next week.

After building a 100 story tower, the engineers were faced with a new problem. What's the highest level from which you safely throw an egg without it braking. As usual with the budgeting of such large projects, getting money for the little things is hard and the engineers were given only two eggs to find the maximum height. This could be an easy problem , but being computer engineers rather then civil engineers they decided they must find the fastest "worst case" method of getting the answer i.e the minimum number of eggs throws in the worst case scenario.

here is an example of a bad method. start on the first floor and throw the egg, if it doesn't break go to the second etc.. until the egg breaks. In the worst case this will require 99 tests.

Remember you have 2 eggs, and by the end of the test , both can (and should) be broken.

What is the minimum number of throws in the worst case? (what algorithm do you use).

You can send the answer by email.

Hint: the number is between 2 and 34.

This week's riddle is the one Ingo wanted to give everyone last week.

One day the king's advisor told him that one of his banks was stealing his gold by making false coins, the advisor did not know which bank . So the king collected 12 coins, one from each bank and told his advisor to find the false one using 3 measurements on scales. After thinking about it for
a moment the advisor told the king that this was a very easy task and made the measurements. What was his strategy ?

The rules:

There are 12 coins
The false coin is either heavier or lighter then a real coin (this is unknown)
There is one false coin.
for each measurement an equal number of coins should be placed on each hand of the scale, if both weigh the same (there is no false coin on either hand) the scales will be balanced , otherwise the lighter one will go up and the heavier one will go down.
There are only 3 measurements and there is no way to cheat (make half a measurement, measure half a coin, add coins while measuring etc..)!