46 research outputs found
Bisimulation for quantum processes
In this paper we introduce a novel notion of probabilistic 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.Comment: Journal versio
Symbolic bisimulation for quantum processes
With the previous notions of bisimulation presented in literature, to check
if two quantum processes are bisimilar, we have to instantiate the free quantum
variables of them with arbitrary quantum states, and verify the bisimilarity of
resultant configurations. This makes checking bisimilarity infeasible from an
algorithmic point of view because quantum states constitute a continuum. In
this paper, 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 the previous work, when strong
bisimulations are considered. An algorithm for checking symbolic ground
bisimilarity is presented. We also give a modal logical characterisation for
quantum bisimilarity based on an extension of Hennessy-Milner logic to quantum
processes.Comment: 30 pages, 7 figures, comments are welcom
Open Bisimulation for Quantum Processes
Quantum processes describe concurrent communicating systems that may involve quantum information. We propose a notion of open bisimulation for quantum processes and show that it provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between quantum processes. We also give a modal characterisation of open bisimulation, by extending the Hennessy-Milner logic to a quantum setting
Observational Equivalence Using Schedulers for Quantum Processes
In the study of quantum process algebras, researchers have introduced
different notions of equivalence between quantum processes like bisimulation or
barbed congruence. However, there are intuitively equivalent quantum processes
that these notions do not regard as equivalent. In this paper, we introduce a
notion of equivalence named observational equivalence into qCCS. Since quantum
processes have both probabilistic and nondeterministic transitions, we
introduce schedulers that solve nondeterministic choices and obtain probability
distribution of quantum processes. By definition, the restrictions of
schedulers change observational equivalence. We propose some definitions of
schedulers, and investigate the relation between the restrictions of schedulers
and observational equivalence.Comment: In Proceedings QPL 2014, arXiv:1412.810
Toward Automatic Verification of Quantum Cryptographic Protocols.
Several quantum process algebras have been proposed and successfully applied
in verification of quantum cryptographic protocols. All of the bisimulations
proposed so far for quantum processes in these process algebras are
state-based, implying that they only compare individual quantum states, but not
a combination of them. This paper remedies this problem by introducing a novel
notion of distribution-based bisimulation for quantum processes. We further
propose an approximate version of this bisimulation that enables us to prove
more sophisticated security properties of quantum protocols which cannot be
verified using the previous bisimulations. In particular, we prove that the
quantum key distribution protocol BB84 is sound and (asymptotically) secure
against the intercept-resend attacks by showing that the BB84 protocol, when
executed with such an attacker concurrently, is approximately bisimilar to an
ideal protocol, whose soundness and security are obviously guaranteed, with at
most an exponentially decreasing gap.Comment: Accepted by Concur'1