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I'm struggling in order to understand the meaning of the following expression:

aᵢ ⊕ bᵢ = xᵢ ∧ yᵢ

I know the symbol ⊕ is actually an exclusive OR, and the ∧ is an and symbol.

But I cannot grasp the overall meaning. What does that mean in simple words? The context is what is stated here. Can someone help me?

Thanks a lot

Mariia Mykhailova
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terence
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  • I think that the ∧ symbol here is being used as Bitwise AND, i.e. the number such that for each binary digit, that digit is a 1 if and only if that digit is a 1 in both xi and yi. – The Zach Man Dec 15 '19 at 22:39
  • You are more likely to get an answer to this question on https://cs.stackexchange.com/ or https://quantumcomputing.stackexchange.com/ – The Zach Man Dec 15 '19 at 22:41

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The paper you reference uses notation a⊕b = x·y, but · and ∧ mean the same in this context: logical AND operation on single-bit variables.

This equality describes the requirement of the CHSH game. The game involves two players, Alice and Bob, who cannot communicate with one another. They are each given a single random bit (Alice gets X and Bob gets Y). Alice and Bob then output a single bit they choose independently based on their input bits (A from Alice and B from Bob) with the goal of satisfying the formula X · Y = A ⊕ B.

This game illustrates that quantum entanglement enables strategies that are dramatically better than the purely classical strategies. The best classical strategy is for Alice and Bob to output 0 regardless of the input - this strategy wins the game 75% of the time. But a quantum strategy exists that allows them to win 85% of the time if they share an entangled pair of qubits before the start of the game.

You can read more on the CHSH game here.

Mariia Mykhailova
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  • actually I would like to ask you a few more questions about the paper ...something I don't really understand ...rounds for example...does that mean input? Then.... If this fraction is smaller than...a formula...I think I'm not allowed to ask these questions here... – terence Dec 16 '19 at 20:54
  • This kind of questions are really better received at https://quantumcomputing.stackexchange.com/ - as an extra benefit, you'll get attention of people who know a lot more about quantum computing than I do! – Mariia Mykhailova Dec 17 '19 at 01:45
  • I did what you suggested but so far nobody has replied to my questions... – terence Dec 26 '19 at 16:58
  • It might take more than 6 hours... :-) Quantum computing is a much smaller community than general StackOverflow, and on top of that it's Christmas week. – Mariia Mykhailova Dec 26 '19 at 17:45
  • thanks a lot . what I asked...it might sound trivial but not for me... – terence Dec 26 '19 at 21:50