It is known that Eisert–Wilkens–Lewenstein scheme and Marinatto–Weber scheme are widely used to quantize simultaneous games. Further, distributed quantum game can be implemented in quantum networks using the schemes based on client–server model and peer-to-peer model. While most of the research works focus on simultaneous games, in this work, we propose the quantum circuit implementation of sequential game, namely cop and robber game using peer-to-peer model. Thus we have made a modest attempt to show the possibility of implementing sequential games in quantum circuits. Further, quantum version of cop and robber game is analyzed. Implications of the results are discussed from the game-theoretic point of view and quantum circuit point of view.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Wiley, New York (1967)
Guo, H., Zhang, J., Koehler, G.J.: A survey of quantum games. Decis. Support Syst. 46, 318 (2008)
Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83, 3077 (1999)
Marinatto, L., Weber, T.: A quantum approach to static games of complete information. Phys. Letts. A. 272, 291 (2000)
Gisin, N., Thew, R.: Quantum communication. Nat. Photonics 1, 165 (2007)
Kimble, H.J.: The quantum internet. Nature (London) 453, 1023 (2008)
Pirandola, S.: A quantum teleportation game. Int. J. Quantum Inf. 03, 239 (2005)
Rass, S., Schartner, P.: Game-theoretic security analysis of quantum networks. In: Third International Conference on Quantum, Nano and Micro Technologies (2009)
Liu, B., Dai, H., Zhang, M.: Playing distributed two-party quantum games on quantum networks. Quantum Inf. Process. 16, 290 (2017)
Nowakowski, R.J., Winkler, P.: Vertex-to-vertex pursuit in graph. Discrete Math. 43(2–3), 235–239 (1983)
Quilliot, A.: A short note about pursuit games played on a graph with a given genus. J. Comb. Theory 38(1), 89–92 (1985)
Rezakhani, A.T.: Characterization of two-qubit perfect entanglers. Phys. Rev. A 70, 052313 (2004)
Zhang, J., Vala, J., Whaley, K.B., Sastry, S.: Geometric theory of non-local two-qubit operations. Phys. Rev. A 67, 042313 (2003)
Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Acin, A., Cirac, J.I., Lewenstein, M.: Entanglement percolation in quantum networks. Nat. Phys. 3, 256 (2007)
Vidal, G., Dawson, C.M.: Universal quantum circuit for two-qubit transformations with three controlled-NOT gates. Phys. Rev. A 69, R010301 (2004)
Sankrith, S., Dave, B., Balakrishnan, S.: Significance of entangling operators in quantum two penny flip game. Braz. J. Phys. 49, 859 (2019)
Iqbal, A., Toor, A.H.: Backwards-induction outcome in a quantum game. Phys. Rev. A 65, 052328 (2002)
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Dhiman, A., Uttam, T. & Balakrishnan, S. Implementation of sequential game on quantum circuits. Quantum Inf Process 19, 109 (2020). https://doi.org/10.1007/s11128-020-2607-9
- Quantum games
- Quantization scheme
- Quantum circuits
- Quantum network