A theory of communicating processes with value passing
Information and Computation
Quantum computation and quantum information
Quantum computation and quantum information
Domain equations for probabilistic processes
Mathematical Structures in Computer Science
Toward a quantum process algebra
Proceedings of the 1st conference on Computing frontiers
Towards a quantum programming language
Mathematical Structures in Computer Science
Communicating quantum processes
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Relations among quantum processes: bisimilarity and congruence
Mathematical Structures in Computer Science
Probabilistic bisimulations for quantum processes
Information and Computation
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
An algebra of quantum processes
ACM Transactions on Computational Logic (TOCL)
Floyd--hoare logic for quantum programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Bisimulation for Quantum Processes
ACM Transactions on Programming Languages and Systems (TOPLAS)
Reachability and termination analysis of concurrent quantum programs
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
Open bisimulation for quantum processes
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
Equivalence checking of quantum protocols
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Reachability probabilities of quantum markov chains
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
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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 other hand, quantum protocol designers may commit much more faults than classical protocol designers since human intuition is much better adapted to the classical world than the quantum world. To offer formal techniques for modeling and verification of quantum protocols, several quantum extensions of process algebra have been proposed. One of the most serious issues in quantum process algebra is to discover a quantum generalization of the notion of bisimulation, which lies in a central position in process algebra, preserved by parallel composition in the presence of quantum entanglement, which has no counterpart in classical computation. Quite a few versions of bisimulation have been defined for quantum processes in the literature, but in the best case they are only proved to be preserved by parallel composition of purely quantum processes where no classical communications are involved. Many quantum cryptographic protocols, however, employ the LOCC (Local Operations and Classical Communications) scheme, where classical communications must be explicitly specified. So, a notion of bisimulation preserved by parallel composition in the circumstance of both classical and quantum communications is crucial for process algebra approach to verification of quantum cryptographic protocols. In this paper we introduce a novel notion of bisimulation for quantum processes and prove that it is congruent with respect to various process algebra combinators including parallel composition even when both classical and quantum communications are present. We also establish some basic algebraic laws for this bisimulation. In particular, we prove uniqueness of the solutions to recursive equations of quantum processes, which provides a powerful proof technique for verifying complex quantum protocols.