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- W4385152322 abstract "The classical combinatorial problem of 36 officers has no solution, as there are no Graeco-Latin squares of order six. The situation changes if one works in a quantum setup and allows for superpositions of classical objects and admits entangled states. We analyze the recently found solution to the quantum version of the Euler’s problem from a geometric point of view. The notion of a non-displaceable manifold embedded in a larger space is recalled. This property implies that any two copies of such a manifold, like two great circles on a sphere, do intersect. The existence of a quantum Graeco-Latin square of size six, equivalent to a maximally entangled state of four subsystems with d = 6 levels each, implies that three copies of the manifold U(36)∕U(1) of maximally entangled states of the 36 × 36 system, embedded in the complex projective space $$mathbb {C}P^{36times 36 -1}$$ , do intersect simultaneously at a certain point." @default.
- W4385152322 created "2023-07-23" @default.
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- W4385152322 date "2023-01-01" @default.
- W4385152322 modified "2023-10-14" @default.
- W4385152322 title "Quantum Version of Euler’s Problem: A Geometric Perspective" @default.
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- W4385152322 doi "https://doi.org/10.1007/978-3-031-30284-8_12" @default.
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