Abstract
With the previous notions of bisimulation presented in the literature, to check if two quantum processes are bisimilar, we have to instantiate their free quantum variables with arbitrary quantum states, and verify the bisimilarity of the resulting configurations. This makes checking bisimilarity infeasible from an algorithmic point of view, because quantum states constitute a continuum. In this article, we introduce a symbolic operational semantics for quantum processes directly at the quantum operation level, which allows us to describe the bisimulation between quantum processes without resorting to quantum states. We show that the symbolic bisimulation defined here is equivalent to the open bisimulation for quantum processes in previous work, when strong bisimulations are considered. An algorithm for checking symbolic ground bisimilarity is presented. We also give a modal characterisation for quantum bisimilarity based on an extension of Hennessy-Milner logic to quantum processes.
- C. H. Bennett and G. Brassard. 1984. Quantum cryptography: Public-key distribution and coin tossing. In Proceedings of the IEEE International Conference on Computer, Systems and Signal Processing. 175--179.Google Scholar
- C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. Wootters. 1993. Teleporting an unknown quantum state via dual classical and EPR channels. Phys. Rev. Lett. 70, 1895--1899.Google ScholarCross Ref
- C. H. Bennett and S. J. Wiesner. 1992. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 20, 2881--2884.Google ScholarCross Ref
- J. R. Burch, E. M. Clarke, K. L. McMillan, D. L. Dill, and L. J. Hwang. 1992. Symbolic model checking: 1020 states and beyond. Inf. Comput. 98, 2, 142--170. Google ScholarDigital Library
- J. Cheriyan, T. Hagerup, and K. Mehlhorn. 1990. Can a maximum flow be computed in o(nm) time? In Automata, Languages and Programming, M. Paterson, Ed., Lecture Notes in Computer Science, vol. 443, Springer, 235--248. Google ScholarDigital Library
- T. A. S. Davidson. 2011. Formal verification techniques using quantum process calculus. PhD thesis, University of Warwick.Google Scholar
- Y. Deng and W. Du. 2011. Logical, metric, and algorithmic characterisations of probabilistic bisimulation. arXiv:1103.4577v1 {cs.LO}. Tech. rep. CMU-CS-11-110, Carnegie Mellon University.Google Scholar
- Y. Deng and Y. Feng. 2012. Open bisimulation for quantum processes. In Theoiretical Computer Science, Lecture Notes in Computer Science, vol. 7604, Springer, 119--133. (Full version available at http://arxiv.org/abs/1202.3484). Google ScholarDigital Library
- Y. Feng, R. Duan, Z. Ji, and M. Ying. 2007. Probabilistic bisimulations for quantum processes. Inf. Comput. 205, 11, 1608--1639. Google ScholarDigital Library
- Y. Feng, R. Duan, and M. Ying. 2011. Bisimulation for quantum processes. In Proceedings of the 38th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, 523--534. Google ScholarDigital Library
- Y. Feng, R. Duan, and M. Ying. 2012. Bisimulation for quantum processes. ACM Trans. Program. Lang. Syst. 34, 4, 1--43. Google ScholarDigital Library
- Y. Feng, N. Yu, and M. Ying. 2013. Model checking quantum Markov chains. J. Comput. Syst. Sci. 79, 7, 1181--1198.Google ScholarCross Ref
- S. Gay, R. Nagarajan, and N. Papanikolaou. 2006. Probabilistic model-checking of quantum protocols. In Proceedings of the 2nd International Workshop on Developments in Computational Models.Google Scholar
- S. Gay, R. Nagarajan, and N. Papanikolaou. 2008. QMC: A model checker for quantum systems. In Proceedings of the International Conference on Computer Aided Verification. Springer, 543--547. Google ScholarDigital Library
- S. Gay and R. Nagarajan. 2005. Communicating quantum processes. In Proceedings of the 32nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. J. Palsberg and M. Abadi, Eds., 145--157. Google ScholarDigital Library
- M. Hennessy and A. Ingolfsdotir. 1993. A theory of communicating processes value-passing. Inf. Comput. 107, 2, 202--236. Google ScholarDigital Library
- M. Hennessy and H. Lin. 1995. Symbolic bisimulations. Theor. Comput. Sci. 138, 2, 353--389. Google ScholarDigital Library
- P. Jorrand and M. Lalire. 2004. Toward a quantum process algebra. In Proceedings of the 2nd International Workshop on Quantum Programming Languages. P. Selinger, Ed., 111. Google ScholarDigital Library
- K. Kraus. 1983. States, Effects and Operations: Fundamental Notions of Quantum Theory. Springer.Google Scholar
- T. Kubota, Y. Kakutani, G. Kato, Y. Kawano, and H. Sakurada. 2012. Application of a process calculus to security proofs of quantum protocols. In Proceedings of the International Conference on Foundations of Computer Science (FCS'12).Google Scholar
- M. Lalire. 2006. Relations among quantum processes: Bisimilarity and congruence. Math. Structures Comput. Sci. 16, 3, 407--428. Google ScholarDigital Library
- R. Milner. 1989. Communication and Concurrency. Prentice Hall, Englewood Cliffs, NJ. Google ScholarDigital Library
- M. Nielsen and I. Chuang. 2000. Quantum Computation and Quantum Information. Cambridge University Press. Google ScholarDigital Library
- N. K. Papanikolaou. 2008. Model checking quantum protocols. Ph.D. thesis, University of Warwick.Google Scholar
- D. Sangiorgi. 1996. A theory of bisimulation for the pi-calculus. Acta Informatica 33, 1, 69--97. Google ScholarDigital Library
- Neumann, J. 1955. States, Effects and Operations: Fundamental Notions of Quantum Theory. Princeton University Press.Google Scholar
- M. Ying, Y. Feng, R. Duan, and Z. Ji. 2009. An algebra of quantum processes. ACM Trans. Comput. Log. 10, 3, 1--36. Google ScholarDigital Library
Index Terms
- Symbolic Bisimulation for Quantum Processes
Recommendations
Bisimulation for Quantum Processes
Quantum cryptographic systems have been commercially available, with a striking advantage over classical systems that their security and ability to detect the presence of eavesdropping are provable based on the principles of quantum mechanics. On the ...
Bisimulation for quantum processes
POPL '11Quantum cryptographic systems have been commercially available, with a striking advantage over classical systems that their security and ability to detect the presence of eavesdropping are provable based on the principles of quantum mechanics. On the ...
Bisimulation for quantum processes
POPL '11: Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languagesQuantum cryptographic systems have been commercially available, with a striking advantage over classical systems that their security and ability to detect the presence of eavesdropping are provable based on the principles of quantum mechanics. On the ...
Comments