Can you tell apart identical twins easily? Identical twins are quite close to each other so it is hard to figure out who it is at a glimpse. Each twin, however, lives his/her own life, like classical particles having its own trajectory. We can consider the twin paradox in special relativity as an example, assuming that we cannot distinguish identical twins before sending one of them to space. After sending one of twins to space in a high-speed rocket, we can distinguish one twin on the earth from the other twin coming back to the earth, due to gravitational time dilation. In the same sense, we can also distinguish classical particles because they are also in macroscopic dimensions controlled by deterministic mechanics. Now the question is whether we can distinguish quantum particles too? The answer is in one of our papers, http://arxiv.org/abs/1212.5338v3 .

# All posts by Su-Yong Lee

# Collective behavior in life and quantum physics

Individuals usually lead fairly solitary lives; except on the occasions when they congregate for social activities, like, baseball or football. On these occasions they demonstrate a type of collective behavior which is motivated by their interests.

Do you know that we can find the same phenomenon in quantum physics? Distinguishable noninteracting particles work separately. However after interacting with another distinguishable particle, they often work together and demonstrate collective behavior. We call these phenomena composite particles. Do you know any of the well-known composite particles in physics? Ubiquitous examples include anyons, and cobosons. But there are a plethora of other examples which inspire a rapidly developing field of research.

# Can we derive a non-contextual inequality from a simple game?

Have you ever thought about whether we can derive an inequality, like the ones used in quantum information science, from any classic game? These inequalities help us identify the boundaries between classical and quantum behaviors.

Everybody knows the classic game, Rock-Paper-Scissors. It can be extended such as Rock-Paper-Scissors-Lizard-Spock, which was shown in “The Big Bang Theory”, one of the US TV network comedies. From this classic game, we can derive one of the non-contextual inequalities, i.e., KCBS inequality [PRL 101, 020403 (2008)].

Here is the rules:

1. Rock crushes lizard.

2. Lizard poisons Spock.

3. Spock smashes scissors.

4. Scissors cut paper.

5. Paper covers rock.

6. Rock breaks scissors.

7. Scissors decapitate lizard.

8. Lizard eats paper.

9. Paper disproves Spock.

10 Spock vaporizes rock.

The rules are referred to Wikipedia Rock-Paper-Scissors-Lizard-Spock. For two persons playing the game, we find that any fair player will win 2/5 of the time on average. If a player has only five different selection cards, then on average one person can defeat the other twice, i.e. 2/5 are multiplied by 5 selections. The scenario of winning the classical game gives us the same classical bound on a pentagram inequality in KCBS inequality. Coincidentally, the Rock-Paper-Scissors-Lizard-Spock game has a pentagram shape due to the relations (1-10) above.

What do you think? It might be some controversial; but it is interesting that we can try to derive another inequality from a game in our daily life :). To find out more about these contextual inequalities check out our latest review. Come out, come out, wherever it is!