text: Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with what we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical computer science that aims at quantifying the amount of communication necessary to solve distributed computational problems. Quantum communication complexity uses quantum mechanics to reduce the amount of communication that would be classically required.
  @cite_31: A proof of Bell's theorem using two maximally entangled states of two qubits is presented. It exhibits a similar logical structure to Hardy's argument of nonlocality without inequalities''. However, it works for 100 of the runs of a certain experiment. Therefore, it can also be viewed as a Greenberger-Horne-Zeilinger-like proof involving only two spacelike separated regions.
  @cite_26: Bell’s theorem [1] refutes local theories based on Einstein, Podolsky, and Rosen’s (EPR’s) “elements of reality” [2]. A recently introduced proof without inequalities [3] presents the same logical structure as that of Hardy’s proof [4], but exhibits a greater contradiction between EPR local elements of reality and quantum mechanics. Here a simpler version of the proof in [3] will be introduced. This new version parallels Mermin’s reformulation [5] of Greenberger, Horne, and Zeilinger’s (GHZ’s) proof [6] and, besides being simpler, it emphasizes the fact that [3] is also an “all versus nothing” [7] or GHZ-type proof of Bell’s theorem, albeit with only two observers. In addition, this new approach will allow us to derive an inequality between correlation functions which is violated by quantum mechanics. Moreover, this new version will also constitute the basis for a new stateindependent proof of the Kochen-Specker (KS) theorem [8]. The whole set of new results provides a wider perspective on the relations between the most relevant proofs of no hidden variables. Consider four qubits, labeled 1, 2, 3, 4, prepared in the state jc1234 1 j0011 2 j0110 2 j1001 1 j1100 , (1) which, as can be easily checked, is the product of two singlet states, jc 2 13 ≠j c 2 24. Let us suppose that qubits 1 and 2 fly apart from qubits 3 and 4, and that an observer, Alice, performs measurements on qubits 1 and 2, while in a spacelike separated region a second observer, Bob, performs measurements on qubits 3
summary: There are other pseudo-telepathy games that are related to the magic square game. Ad 'an Cabello's game @cite_31 @cite_26 does not resembles the magic square game on first approach. However, closer analysis reveals that the two games are totally equivalent!