Abstract
For every rule of a single penny flip game, there exists a unitary operation as a winning strategy for a quantum player. Now, in the two penny flip game, an extra option is available, viz. the use of entangling operators. However, it is known that entangling operators are not useful in this case, and a tensor product of unitary operators works just fine. In this work, we look for the significance of the entangling operators, if any, under the situation that the options available to the classical player are expanded. We extend the problem to a more general case and it is shown that there is no entangling operator capable of guaranteeing the victory of the quantum player. Eventually, we reach the classical game situation in a quantum setup of a game.
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References
J. Von Neumann, O. Morgenstern, Theory of Games and Economic Behavior (Wiley, New York, 1967)
J. Nash, Equilibrium points in n-person games. Proc. Natl. Acad. Sci. 36, 48–49 (1950)
D.A. Meyer, Quantum strategies. Phys. Rev. Lett. 82, 1052–1055 (1999)
H. Gui, J. Zhang, G.J. Koehler, Dec. Supp. Sys 46, 318 (2008)
M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)
J. Eisert, M. Wilkens, M. Lewenstein, Quantum games and quantum strategies. Phys. Rev. Lett. 83, 3077–3080 (1999)
L. Marinatto, T. Weber, A quantum approach to static games of complete information. Phys. Letts. A. 272, 291–303 (2000)
J. Du, X. Xu, H. Li, X. Zhou, R. Han, Entanglement playing a dominating role in quantum games. Phys. Letts. A. 289, 9–15 (2001)
A.P. Flitney, D. Abbott, Advantage of a quantum player over a classical one in 2 × 2 quantum games. Proc. R. Soc. London. 459, 2463–2474 (2003)
A. Barenco, C.H. Bennett, R. Cleve, D.P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J.A. Smolin, H. Weinfurter, Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995)
D.P. DiVincenzo, Two-bit gates are universal for quantum computation. Phys. Rev. A 51, 1015–1022 (1995)
S. Balakrishnan, R. Sankaranarayanan, Classical rules and quantum strategies in penny flip game. Quantum Inf. Process 12, 1261–1268 (2013)
J.M. Chappell, A. Iqbal, M.A. Lohe, L.V. Smekal, An Analysis of the quantum penny flip game using geometric algebra. J. Phys. Soc. Jpn. 78, 054801 (2009)
R. Heng-Feng, W. Qing-Liang, Int. J. Theor.Phys. 47, 1828 (2008)
X.-B. Wang, L.C. Kwek, C.H. Oh, Phys. Lett. A 278, 44 (2009)
N. Anand, C. Benjamin, Do quantum strategies always win? Quantum Inf. Process 14, 4027–4038 (2015)
A.T. Rezakhani, Characterization of two-qubit perfect entanglers. Phys. Rev. A 70, 052313 (2004)
J. Zhang, J. Vala, K.B. Whaley, S. Sastry, Geometric theory of nonlocal two-qubit operations. Phys. Rev. A 67, 042313 (2003)
S. Balakrishnan, R. Sankaranarayanan, Operator-Schmidt decomposition and the geometrical edges of two-qubit gates. Quantum Inf. Process 10(4), 449–461 (2011)
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Sankrith, S., Dave, B. & Balakrishnan, S. Significance of Entangling Operators in Quantum Two Penny Flip Game. Braz J Phys 49, 859–863 (2019). https://doi.org/10.1007/s13538-019-00698-x
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DOI: https://doi.org/10.1007/s13538-019-00698-x