Enhancing Pseudo-Telepathy in the Magic Square Game

We study the possibility of reversing an action of a quantum channel. Our principal objective is to find a specific channel that reverses as accurately as possible an action of a given quantum channel. To achieve this goal we use semidefinite programming. We show the benefits of our method using the quantum pseudo-telepathy Magic Square game with noise. Our strategy is to move the pseudo-telepathy region to higher noise values. We show that it is possible to reverse the action of a noise channel using semidefinite programming.

[1]  Mermin,et al.  Simple unified form for the major no-hidden-variables theorems. , 1990, Physical review letters.

[2]  Jaroslaw Adam Miszczak,et al.  NOISE EFFECTS IN QUANTUM MAGIC SQUARES GAME , 2008, 0801.4848.

[3]  J. Schwinger THE GEOMETRY OF QUANTUM STATES. , 1960, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Piotr Gawron,et al.  Qubit flip game on a Heisenberg spin chain , 2011, Quantum Inf. Process..

[5]  Edward W. Piotrowski,et al.  An Invitation to Quantum Game Theory , 2002, ArXiv.

[6]  P. K. Aravind Quantum mysteries revisited again , 2004 .

[7]  G. Brassard,et al.  Quantum Pseudo-Telepathy , 2004, quant-ph/0407221.

[8]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[9]  Ryszard Winiarczyk,et al.  Noise effects in the quantum search algorithm from the viewpoint of computational complexity , 2011, Int. J. Appl. Math. Comput. Sci..

[10]  P. Gawron NOISY QUANTUM MONTY HALL GAME , 2009, 0907.1381.

[11]  D. Abbott,et al.  Quantum version of the Monty Hall problem , 2001, quant-ph/0109035.

[12]  A. Schmidt,et al.  Quantum Russian roulette , 2013 .

[13]  Silvio Simani International Journal of Applied Mathematics and Computer Sciences , 2013 .

[14]  Piotr Gawron,et al.  Experimentally feasible measures of distance between quantum operations , 2009, Quantum Inf. Process..

[15]  Mermin Nd Simple unified form for the major no-hidden-variables theorems. , 1990 .

[16]  Piotr Frackiewicz,et al.  Quantum information approach to normal representation of extensive games , 2011, ArXiv.

[17]  E. W. Piotrowski,et al.  Quantum Auctions: Facts and Myths ⋆ , 2007, 0709.4096.

[18]  Karol Życzkowski,et al.  Random quantum operations , 2008, 0804.2361.

[19]  J. Eisert,et al.  Quantum Games and Quantum Strategies , 1998, quant-ph/9806088.

[20]  Renato D. C. Monteiro,et al.  A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization , 2003, Math. Program..

[21]  Renato D. C. Monteiro,et al.  Digital Object Identifier (DOI) 10.1007/s10107-004-0564-1 , 2004 .