This leads to what is popularly known as ``spooky action at a distance”, and maximal entanglement leads to perfect correlation.Īnother famous example is that of Schrodinger’s cat. Repeating the experiment with an identical set of boxes, can result in the reverse colours immediately. The strange thing about this state is that opening the Chennai box can randomly reveal it to contain a blue or red cube and the nature of entanglement is to ensure that the other distant box contains a cube of the opposite colour. A quantum entangled state, is a weird “superposition” of these two which physicists represent by RB+BR. We think of the state as RB or BR depending on if the Chennai box contains a red or blue cube. To get an idea, take 2 boxes, one in Chennai and other in Shopian, one containing a red (R) cube and other a blue (B) one. Here, it is necessary to understand “quantum entanglement”. But suppose the officers were not classical objects but were quantum entities, would this still be true? This is what physicists who joined the group of problem solvers started asking.Ĭlassically, this problem cannot be solved, but what if the officers were quantum entities? Now Tarry had explicitly shown that n = 6 (36 officers puzzle) has no solution. In this case, OLS solutions exist for all values of n except 2 and 6. Euler’s 36 officers problem (for which n=6) and generalisations of it to other values of n = 2,3, etc are examples of Orthogonal Latin Squares (OLS). Squares such as this are often encountered in Sudoku and other magic squares of size n. Parker proved that solutions exist for all n except for two and six. Later these two mathematicians along with E. Shrikhande constructed solutions for n = 22, earning themselves the description “Euler spoilers”. This was reinforced when Tarry showed that the case of n=6, the original problem of 36 officers had no solution. Euler himself believed solutions do not exist for those even numbers, n, which took the form n = 2+ 4k, for k taking values 1,2,3, etc. For the case of four officers, to be arranged in a two by two matrix, it was easily seen that no possible solution could be found. Tarry in 1901.Įuler was able to show that when you have odd number of rows and columns, as for example, 25 officers belonging to five regiments of five ranks each, the solution was easy to find. This puzzle was guessed to be unsolvable by Euler in 1779 and proven to be so by the French amateur mathematician G. The question is, can you place the 36 officers in a square arrangement with six rows and six columns such that no row or column repeats an officer’s rank or regiment? There are six regiments, each containing six officers of six different ranks. The 36 officers puzzle was first posed by Swiss mathematician Leonhard Euler. Numerical puzzles often appear simple when phrased but can occupy mathematicians for hundreds of years. This could potentially be used in quantum secret sharing protocols – which will be useful when quantum computers come into play parallel teleportation, which is a way to transferring information across distances and even perhaps may come in useful in solving the problem of quantum gravity. The researchers have solved using matrix methods, the quantum equivalent of the classical problem. A famous problem that has perplexed mathematicians since 1779 has been settled, but with a quantum twist, by a collaboration of six Indian and Polish researchers, two of whom are from Indian Institute of Technology (IIT) Madras.
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