Physics:Quantum pseudo-telepathy - Revision history

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	{{hatnote\|This article uses quantum theoretical concepts and terminology. For a generally accessible introduction to quantum mechanics, see Introduction to quantum mechanics.}}		{{hatnote\|This article uses quantum theoretical concepts and terminology. For a generally accessible introduction to quantum mechanics, see Introduction to quantum mechanics.}}
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	~~{{Quantum mechanics\|cTopic=Fundamental concepts}}~~
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	{{reflist}}		{{reflist}}

	~~[[Category:Concepts in physics]]~~
	~~[[Category:Quantum information science]]~~
	~~[[Category:Quantum measurement]]~~
	~~[[Category:Thought experiments in quantum mechanics]]~~

	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

	{{Sourceattribution\|Physics:Quantum pseudo-telepathy\|1}}		{{Sourceattribution\|Physics:Quantum pseudo-telepathy\|1}}

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	===Pseudo-telepathic strategies===		===Pseudo-telepathic strategies===
	Use of quantum pseudo-telepathy would enable Alice and Bob to win the game 100% of the time ''without'' any communication once the game has begun.		Use of quantum pseudo-telepathy would enable Alice and Bob to win the game 100% of the time ''without'' any communication once the game has begun.


	However, the process of measuring the particles imposes sufficient structure on the joint probability distribution of the results of the measurement such that if Alice and Bob choose their actions based on the results of their measurement, then there will exist a set of strategies and measurements allowing the game to be won with probability 1.		However, the process of measuring the particles imposes sufficient structure on the joint probability distribution of the results of the measurement such that if Alice and Bob choose their actions based on the results of their measurement, then there will exist a set of strategies and measurements allowing the game to be won with probability 1.
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	If question 0 is received, the player makes a measurement in the X basis <math display="inline">\{\|+\rangle,\|-\rangle\}</math>. If question 1 is received, the player makes a measurement in the Y basis <math display="inline">\left\{\frac{1}{\sqrt 2}(\|0\rangle+i\|1\rangle), \frac{1}{\sqrt 2}(\|0\rangle-i\|1\rangle)\right\}</math>. In both cases, the players give answer 0 if the result of the measurement is the first state of the pair, and answer 1 if the result is the second state of the pair. With this strategy the players win the game with probability 1.		If question 0 is received, the player makes a measurement in the X basis <math display="inline">\{\|+\rangle,\|-\rangle\}</math>. If question 1 is received, the player makes a measurement in the Y basis <math display="inline">\left\{\frac{1}{\sqrt 2}(\|0\rangle+i\|1\rangle), \frac{1}{\sqrt 2}(\|0\rangle-i\|1\rangle)\right\}</math>. In both cases, the players give answer 0 if the result of the measurement is the first state of the pair, and answer 1 if the result is the second state of the pair. With this strategy the players win the game with probability 1.

	==See also==		== See also ==
	{{~~cols~~\|~~colwidth=26em}}~~		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}
	*Quantum game theory
	*Quantum refereed game
	*GHZ state – an entangled 3-particle state.
	*EPR paradox
	*Kochen–Specker theorem
	*Quantum ~~information science~~
	*Qubit
	*Tsirelson's bound
	~~{{colend~~}}

	==Notes==		==Notes==

	~~== See also ==~~
	~~{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}~~
	== References ==		== References ==

	{{reflist}}		{{reflist}}


	[[Category:Concepts in physics]]		[[Category:Concepts in physics]]

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	Effectively, while it is not possible to construct a 3×3 table with entries +1 and −1 such that the product of the elements in each row equals +1 and the product of elements in each column equals −1, it is possible to do so with the richer algebraic structure based on spin matrices.		Effectively, while it is not possible to construct a 3×3 table with entries +1 and −1 such that the product of the elements in each row equals +1 and the product of elements in each column equals −1, it is possible to do so with the richer algebraic structure based on spin matrices.

	The play proceeds by having each player make one measurement on their part of the entangled state per round of play. Each of Alice's measurements will give her the values for a row, and each of Bob's measurements will give him the values for a column. It is possible to do that because all observables in a given row or column commute, so there exists a basis in which they can be measured simultaneously. For Alice's first row she needs to measure both her particles in the <math>Z</math> basis, for the second row she needs to measure them in the <math>X</math> basis, and for the third row she needs to measure them in an entangled basis. For Bob's first column he needs to measure his first particle in the <math>X</math> basis and the second in the <math>Z</math> basis, for second column he needs to measure his first particle in the <math>Z</math> basis and the second in the <math>X</math> basis, and for his third column he needs to measure both his particles in a different entangled basis, the ~~[[Bell state#Bell basis\|~~Bell basis]]. As long as the table above is used, the measurement results are guaranteed to always multiply out to +1 for Alice along her row, and −1 for Bob down his column. Of course, each completely new round requires a new entangled state, as different rows and columns are ''not'' compatible with each other.		The play proceeds by having each player make one measurement on their part of the entangled state per round of play. Each of Alice's measurements will give her the values for a row, and each of Bob's measurements will give him the values for a column. It is possible to do that because all observables in a given row or column commute, so there exists a basis in which they can be measured simultaneously. For Alice's first row she needs to measure both her particles in the <math>Z</math> basis, for the second row she needs to measure them in the <math>X</math> basis, and for the third row she needs to measure them in an entangled basis. For Bob's first column he needs to measure his first particle in the <math>X</math> basis and the second in the <math>Z</math> basis, for second column he needs to measure his first particle in the <math>Z</math> basis and the second in the <math>X</math> basis, and for his third column he needs to measure both his particles in a different entangled basis, the Bell basis. As long as the table above is used, the measurement results are guaranteed to always multiply out to +1 for Alice along her row, and −1 for Bob down his column. Of course, each completely new round requires a new entangled state, as different rows and columns are ''not'' compatible with each other.

	==Current research==		==Current research==

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	==Notes==		==Notes==

			== See also ==
			{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}
			== References ==

	{{reflist}}		{{reflist}}

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	[[Category:Thought experiments in quantum mechanics]]		[[Category:Thought experiments in quantum mechanics]]

	{{Sourceattribution\|Quantum pseudo-telepathy}}		{{Author\|Harold Foppele}}

			{{Sourceattribution\|Physics:Quantum pseudo-telepathy\|1}}

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	{{About\|quantum mechanics' application in game theory\|quantum mechanics-related pseudoscience\|Quantum mysticism}}		{{About\|quantum mechanics' application in game theory\|quantum mechanics-related pseudoscience\|Quantum mysticism}}