Kolkata Paise Restaurant Problem

The players will measure the state in the <math>|0\rangle, |1\rangle </math> basis and interpret them as using roads A or B. In two cases out of 8 the first player will be in a minority; the same is true for the other players. Classically, each player will win with probability 1/8. Therefore, writing the rules of the game into an entanglement improves the probability of winning.

The players will measure the state in the <math>|0\rangle, |1\rangle </math> basis and interpret them as using roads A or B. In two cases out of 8 the first player will be in a minority; the same is true for the other players. Classically, each player will win with probability 1/8. Therefore, writing the rules of the game into an entanglement improves the probability of winning.

Similarly, Sharif and Heydari<ref name="SharifHeydari2011">{{cite arXiv |eprint=1111.1962 |author1=Sharif, P. |author2=Heydari, H. |title=Quantum solution to a three player Kolkata restaurant problem using entangled qutrits |class=quant-ph |year=2011}}</ref> used a qutrit to formulate the entanglement in a 3 player 3 roads/choice (<Math> N = 3, \lambda = 1 </Math>) KPR game; see also Ramzan.<ref name=Ramzan13/> Sharif and Heydari also generalized their results to multi-player multi-choice quantum games <ref name="SharifHeydari2013">{{cite book |last1=Sharif |first1=P. |title=Econophysics of Systemic Risk and Network Dynamics |last2=Heydari |first2=H. |publisher=Springer |year=2012 |isbn=9788847025523 |editor1-first=F.| editor1-last=Abergel |editor2-first=B. K. | editor2-last=Chakrabarti |editor3-first=A. |editor3-last=Chakraborti |editor4-first= A. | editor4-last=Ghosh | pages=217–236 |chapter=An introduction to multi-player multi-choice quantum games: Quantum minority games and Kolkata Restaurant Problems |doi=10.1007/978-88-470-2553-0_14 }}</ref>

Similarly, Sharif and Heydari<ref name="SharifHeydari2011">{{cite arXiv |eprint=1111.1962 |author1=Sharif, P. |author2=Heydari, H. |title=Quantum solution to a three player Kolkata restaurant problem using entangled qutrits |class=quant-ph |year=2011}}</ref> used a qutrit to formulate the entanglement in a 3 player 3 roads/choice (<Math> N = 3, \lambda = 1 </Math>) KPR game; see also Ramzan.<ref name=Ramzan13/> Sharif and Heydari also generalized their results to multi-player multi-choice quantum games <ref name="SharifHeydari2013">{{cite book |last1=Sharif |first1=P. |title=Econophysics of Systemic Risk and Network Dynamics |last2=Heydari |first2=H. |publisher=Springer |year=2012 |isbn=9788847025523 |editor1-first=F.| editor1-last=Abergel |editor2-first=B. K. | editor2-last=Chakrabarti |editor3-first=A. |editor3-last=Chakraborti |editor4-first= A. | editor4-last=Ghosh | pages=217–236 |chapter=An introduction to multi-player multi-choice quantum games: Quantum minority games and Kolkata Restaurant Problems |doi=10.1007/978-88-470-2553-0_14 }}</ref>

The problem will arise in the complexity of building the entanglement or scaling it to a KPR game. Also, the quantum minority game implicitly assumes all players cooperate in using the measurement, which will become hard to achieve when the group becomes large.

The problem will arise in the complexity of building the entanglement or scaling it to a KPR game. Also, the quantum minority game implicitly assumes all players cooperate in using the measurement, which will become hard to achieve when the group becomes large.