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Knowledge in quantum systems (Extended Abstract

Ron van der Meyden, Manas Patra

Published Jan 1, 2003• 2 citations
OpenAlex

Abstract

This paper applies to quantum systems a modelling for the logic of knowledge, originally developed for reasoning about distributed systems, but since then applied to game theory, computer security and artificial intelligence. A formal model of quantum message passing systems is developed and the question of how one might define the semantics of a modal operator for knowledge in this model is considered. It is argued that there are at least two plausible semantics, depending on whether the agents are permitted to make use of their quantum state in determining what they know, and on whether one is dealing with single instances of quantum systems, or ensembles. The framework is illustrated using a number of examples from the quantum computing literature, including protocols for quantum key distribution and teleportation. 1

Related papers

Knowledge in quantum systems

Ron van der Meyden, Manas K. Patra

This paper applies to quantum systems a modelling for the logic of knowledge, originally developed for reasoning about distributed systems, but since then applied to game theory, computer security and artificial intelligence. A formal model of quantum message passing systems is developed and the question of how one might define the semantics of a modal operator for knowledge in this model is considered. It is argued that there are at least two plausible semantics, depending on whether the agents are permitted to make use of their quantum state in determining what they know, and on whether one is dealing with single instances of quantum systems, or ensembles. The framework is illustrated using a number of examples from the quantum computing literature, including protocols for quantum key distribution and teleportation.

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Knowledge in quantum systems

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This paper applies to quantum systems a modelling for the logic of knowledge, originally developed for reasoning about distributed systems, but since then applied to game theory, computer security and artificial intelligence. A formal model of quantum message passing systems is developed and the question of how one might define the semantics of a modal operator for knowledge in this model is considered. It is argued that there are at least two plausible semantics, depending on whether the agents are permitted to make use of their quantum state in determining what they know, and on whether one is dealing with single instances of quantum systems, or ensembles. The framework is illustrated using a number of examples from the quantum computing literature, including protocols for quantum key distribution and teleportation.

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We prove that quantum key distribution is secure against several types of attacks within the framework of classical knowledge knowledge for quantum systems, a formal model which was developed in [D'Hondt, E. and P. Panangaden, Reasoning about quantum knowledge, in: Proceedings of the 25th Conference on Foundations of Software Technology and Theoretical Computer Science, LNCS 3821, 2005, p. 0544c (to appear), quant-ph/0507176]. In particular we rephrase security as a logical property and use meta-logic reasoning on the finite state machine corresponding to the quantum key distribution protocol. While these security issues have been studied before, it is the logical-based approach that is original here.

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Abstract Quantum information gives rise to some puzzling epistemic problems that can be interestingly investigated from a logical point of view. A characteristic example is represented by teleportation phenomena, where knowledge and actions of observers (epistemic agents) play a relevant role. By abstracting from teleportation, we propose a simplified semantics for a language that consists of two parts: 1)the quantum computational sub-language, whose sentences α represent pieces of quantum information (which are supposed to be stored by some quantum systems)2)the classical epistemic sub-language, whose atomic sentences have the following forms: agent a has a probabilistic information about the sentence α; agent a knows the sentence α. Interestingly enough, some conceptual difficulties of standard epistemic logics can be avoided in this framework.

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Ellie D’Hondt, Mehrnoosh Sadrzadeh

We propose a decision procedure for analysing security of quantum cryptographic protocols, combining an algebraic logic rewrite system with an operational semantics for quantum distributed computations. We apply our approach to reasoning about security properties of a recently developed quantum secret sharing protocol.

Electronic Notes in Theoretical Computer Science•Feb 1, 2011•2 citations
This paper applies to quantum systems a modelling for the logic of knowledge, originally developed for reasoning about distributed systems, but since then applied to game theory, computer security and artificial intelligence. A formal model of quantum message passing systems is developed and the question of how one might define the semantics of a modal operator for knowledge in this model is considered. It is argued that there are at least two plausible semantics, depending on whether the agents are permitted to make use of their quantum state in determining what they know, and on whether one is dealing with single instances of quantum systems, or ensembles. The framework is illustrated using a number of examples from the quantum computing literature, including protocols for quantum key distribution and teleportation. 1
This paper applies to quantum systems a modelling for the logic of knowledge, originally developed for reasoning about distributed systems, but since then applied to game theory, computer security and artificial intelligence. A formal model of quantum message passing systems is developed and the question of how one might define the semantics of a modal operator for knowledge in this model is considered. It is argued that there are at least two plausible semantics, depending on whether the agents are permitted to make use of their quantum state in determining what they know, and on whether one is dealing with single instances of quantum systems, or ensembles. The framework is illustrated using a number of examples from the quantum computing literature, including protocols for quantum key distribution and teleportation.
This paper applies to quantum systems a modelling for the logic of knowledge, originally developed for reasoning about distributed systems, but since then applied to game theory, computer security and artificial intelligence. A formal model of quantum message passing systems is developed and the question of how one might define the semantics of a modal operator for knowledge in this model is considered. It is argued that there are at least two plausible semantics, depending on whether the agents are permitted to make use of their quantum state in determining what they know, and on whether one is dealing with single instances of quantum systems, or ensembles. The framework is illustrated using a number of examples from the quantum computing literature, including protocols for quantum key distribution and teleportation.
We construct a formal framework for investigating epistemic and temporal notions in the context of distributed quantum computation. While we rely on structures developed earlier, we stress that our notion of quantum knowledge makes sense more generally in any agent-based model for distributed quantum systems. Several arguments are given to support our view that an agent's possibility relation should not be based on the reduced density matrix, but rather on local classical states and local quantum operations. In this way, we are able to analyse distributed primitives such as superdense coding and teleportation, obtaining interesting conclusions as to how the knowledge of individual agents evolves. We show explicitly that the knowledge transfer in teleportation is essentially classical, in that eventually, the receiving agent knows that its state is equal to the initial state of the sender. The relevant epistemic statements for teleportation deal with this correlation rather than with the actual quantum state, which is unknown throughout the protocol.
We prove that quantum key distribution is secure against several types of attacks within the framework of classical knowledge knowledge for quantum systems, a formal model which was developed in [D'Hondt, E. and P. Panangaden, Reasoning about quantum knowledge, in: Proceedings of the 25th Conference on Foundations of Software Technology and Theoretical Computer Science, LNCS 3821, 2005, p. 0544c (to appear), quant-ph/0507176]. In particular we rephrase security as a logical property and use meta-logic reasoning on the finite state machine corresponding to the quantum key distribution protocol. While these security issues have been studied before, it is the logical-based approach that is original here.
Abstract Quantum information gives rise to some puzzling epistemic problems that can be interestingly investigated from a logical point of view. A characteristic example is represented by teleportation phenomena, where knowledge and actions of observers (epistemic agents) play a relevant role. By abstracting from teleportation, we propose a simplified semantics for a language that consists of two parts: 1)the quantum computational sub-language, whose sentences α represent pieces of quantum information (which are supposed to be stored by some quantum systems)2)the classical epistemic sub-language, whose atomic sentences have the following forms: agent a has a probabilistic information about the sentence α; agent a knows the sentence α. Interestingly enough, some conceptual difficulties of standard epistemic logics can be avoided in this framework.