A theory of communicating processes with value passing
Information and Computation
A calculus for cryptographic protocols: the spi calculus
Proceedings of the 4th ACM conference on Computer and communications security
Topology in process calculus: approximate correctness and infinite evolution of concurrent programs
Topology in process calculus: approximate correctness and infinite evolution of concurrent programs
Communication and Concurrency
Quantum computation and quantum information
Quantum computation and quantum information
Bisimulation indexes and their applications
Theoretical Computer Science
Weak Bisimulation is Sound and Complete for PCTL*
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
Weak Bisimulation for Fully Probabilistic Processes
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Domain equations for probabilistic processes
Mathematical Structures in Computer Science
Toward a quantum process algebra
Proceedings of the 1st conference on Computing frontiers
Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
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
Remarks on Testing Probabilistic Processes
Electronic Notes in Theoretical Computer Science (ENTCS)
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)
Metrics for Action-labelled Quantitative Transition Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Bisimulation for quantum processes
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Compositional reasoning for probabilistic finite-state behaviors
Processes, Terms and Cycles
Reachability probabilities of quantum markov chains
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
Hi-index | 0.00 |
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 more faults than classical protocol designers since human intuition is poorly adapted to the quantum world. To offer formal techniques for modeling and verification of quantum protocols, several quantum extensions of process algebra have been proposed. An important issue in quantum process algebra is to discover a quantum generalization of bisimulation preserved by various process constructs, in particular, parallel composition, where one of the major differences between classical and quantum systems, namely quantum entanglement, is present. 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 communication is involved. Many quantum cryptographic protocols, however, employ the LOCC (Local Operations and Classical Communication) scheme, where classical communication must be explicitly specified. So, a notion of bisimulation preserved by parallel composition in the circumstance of both classical and quantum communication is crucial for process algebra approach to verification of quantum cryptographic protocols. In this article we introduce novel notions of strong bisimulation and weak bisimulation for quantum processes, and prove that they are congruent with respect to various process algebra combinators including parallel composition even when both classical and quantum communication are present. We also establish some basic algebraic laws for these bisimulations. In particular, we show the uniqueness of the solutions to recursive equations of quantum processes, which proves useful in verifying complex quantum protocols. To capture the idea that a quantum process approximately implements its specification, and provide techniques and tools for approximate reasoning, a quantified version of strong bisimulation, which defines for each pair of quantum processes a bisimulation-based distance characterizing the extent to which they are strongly bisimilar, is also introduced.