Qsquare quantum pseudo-telepathy
Part of a work-in-progress "Agrippa Algorithm"; Supposing my Magic Qsquare employed in a quantum pseudo-telepathy game. for exposition, its semi modeled after the Mermin-Peres magic square game. It takes some imagination i guess to picture this complete with switches & grids (or just a simulation). but for the time being, it's a peek into stuff that goes on in my brain. Regarding quantum pseudo-telepathy, in game theory, and so often does it seem like it is easier to oversimplify quantum computing and emulate the effects of a hypothetical magical power. Here, in that you could fool a person into thinking you were a telepath by using a quantum computer employing some quantum strategy. Eventually, i'll have to start thinking about relating the Qsquare system of inequalities to something like the "parity conditions" of mermin-peres, unsatisfiable situations, and hence magical nonetheless. The players naturally, Alice and Bob, are separated by distance and having no prior communication Alice receives only the row information, Bob only the column information from a referee. linear combinations of number presses have a corresponding vector on a 3x3 grid and, basically only one will be "true" at a time but are (here) just randomly assigned to one of 8 different outcomes of a 3x3 magic square with a different 3 bit label themselves, and not all possible combs of number presses are shown, though i have a bunch of game scenarios etc it is not realistic nor even necessary because like grover's algorithm, most possibilities exhibit interference. Same deal for the ones that u can barely see shaded here in the color coded boxes up top, only one combination is successful - two of ea. color that represent some # on the quantum register are still viable, but it would be a "needy" phase flip situation, collapsing to one or another based on player choice, thus it can't be read until the program is run and revealed (aka measured) - except for the case of the "centered square number" of what would be a 3x3 (row2,col2)..for uh...reasons that lead to one of 8 (technically 1 of 4, and reflections of those) equally possible solutions to a traditional 3x3 magic square. The centered square number in this case being the number 5 essentially translates into a minimum of 5 comparisons before the magic square can uniquely be determined. In other words, which possible arrangement of a 3x3 magic square will result. Notice it is not a question of will this or will this not be a magic square, as a classical computer might ask. A better question might be how did it form? The color coded logic described in this circuit is such that it will always be 'magic'. The quantum strategy then, becomes only in taking of all of those possibilities at once and predetermining the most logically efficient "superposition" of them. The super-permuted output will always be one of the 8 possible arrangements that exactly correspond to one of the 8 possible arrangements of 3 bits: 000, 001, 010, 011, 100, 101, 110, 111.