84,305 research outputs found
Automated Verification of Quantum Protocols using MCMAS
We present a methodology for the automated verification of quantum protocols
using MCMAS, a symbolic model checker for multi-agent systems The method is
based on the logical framework developed by D'Hondt and Panangaden for
investigating epistemic and temporal properties, built on the model for
Distributed Measurement-based Quantum Computation (DMC), an extension of the
Measurement Calculus to distributed quantum systems. We describe the
translation map from DMC to interpreted systems, the typical formalism for
reasoning about time and knowledge in multi-agent systems. Then, we introduce
dmc2ispl, a compiler into the input language of the MCMAS model checker. We
demonstrate the technique by verifying the Quantum Teleportation Protocol, and
discuss the performance of the tool.Comment: In Proceedings QAPL 2012, arXiv:1207.055
Fitch's knowability axioms are incompatible with quantum theory
How can we consistently model the knowledge of the natural world provided by
physical theories? Philosophers frequently use epistemic logic to model
reasoning and knowledge abstractly, and to formally study the ramifications of
epistemic assumptions. One famous example is Fitch's paradox, which begins with
minimal knowledge axioms and derives the counter-intuitive result that "every
agent knows every true statement." Accounting for knowledge that arises from
physical theories complicates matters further. For example, quantum mechanics
allows observers to model other agents as quantum systems themselves, and to
make predictions about measurements performed on each others' memories.
Moreover, complex thought experiments in which agents' memories are modelled as
quantum systems show that multi-agent reasoning chains can yield paradoxical
results.
Here, we bridge the gap between quantum paradoxes and foundational problems
in epistemic logic, by relating the assumptions behind the recent
Frauchiger-Renner quantum thought experiment and the axioms for knowledge used
in Fitch's knowability paradox. Our results indicate that agents' knowledge of
quantum systems must violate at least one of the following assumptions: it
cannot be distributive over conjunction, have a kind of internal continuity,
and yield a constructive interpretation all at once. Indeed, knowledge provided
by quantum mechanics apparently contradicts traditional notions of how
knowledge behaves; for instance, it may not be possible to universally assign
objective truth values to claims about agent knowledge. We discuss the
relations of this work to results in quantum contextuality and explore possible
modifications to standard epistemic logic that could make it consistent with
quantum theory.Comment: 22 + 7 page
On Weak Values and Feynman's Blind Alley
Feynman famously recommended accepting the basic principles of quantum
mechanics without trying to guess the machinery behind the law. One of the
corollaries of the Uncertainty Principle is that the knowledge of probability
amplitudes does not allow one to make meaningful statements about the past of
an unobserved quantum system. A particular type of reasoning, based on weak
values, appears to do just that. Has Feynman been proven wrong by the more
recent developments? Most likely not
On Weak Values and Feynman's Blind Alley
Feynman famously recommended accepting the basic principles of quantum mechanics without trying to guess the machinery behind the law. One of the corollaries of the Uncertainty Principle is that the knowledge of probability amplitudes does not allow one to make meaningful statements about the past of an unobserved quantum system. A particular type of reasoning, based on weak values, appears to do just that. Has Feynman been proven wrong by the more recent developments? Most likely not.Quanta 2023; 12: 180–189
Classical Knowledge for Quantum Cryptographic Reasoning
AbstractWe 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
A Framework for Understanding the Patterns of Student Reasoning Difficulties in Quantum Mechanics
Compared with introductory physics, relatively little is known about the
development of expertise in advanced physics courses, especially in the case of
quantum mechanics. Here, we describe a framework for understanding the patterns
of student reasoning difficulties and how students develop expertise in quantum
mechanics. The framework posits that the challenges many students face in
developing expertise in quantum mechanics are analogous to the challenges
introductory students face in developing expertise in introductory classical
mechanics. This framework incorporates both the diversity in upper-level
students' prior preparation, goals, and motivation in general (i.e., the facts
that even in upper-level courses, students may be inadequately prepared, have
unclear goals, and have insufficient motivation to excel) as well as the
"paradigm shift" from classical mechanics to quantum mechanics. The framework
is based on empirical investigations demonstrating that the patterns of
reasoning, problem-solving, and self-monitoring difficulties in quantum
mechanics bear a striking resemblance to those found in introductory classical
mechanics. Examples from research in quantum mechanics and introductory
classical mechanics are discussed to illustrate how the patterns of
difficulties are analogous as students learn to unpack the respective
principles and grasp the formalism in each knowledge domain during the
development of expertise. Embracing such a framework and contemplating the
parallels between the difficulties in these two knowledge domains can enable
researchers to leverage the extensive literature for introductory physics
education research to guide the design of teaching and learning tools for
helping students develop expertise in quantum mechanics
A Review of Student Difficulties in Upper-Level Quantum Mechanics
Learning advanced physics, in general, is challenging not only due to the
increased mathematical sophistication but also because one must continue to
build on all of the prior knowledge acquired at the introductory and
intermediate levels. In addition, learning quantum mechanics can be especially
challenging because the paradigms of classical mechanics and quantum mechanics
are very different. Here, we review research on student reasoning difficulties
in learning upper-level quantum mechanics and research on students'
problem-solving and metacognitive skills in these courses. Some of these
studies were multi-university investigations. The investigations suggest that
there is large diversity in student performance in upper-level quantum
mechanics regardless of the university, textbook, or instructor and many
students in these courses have not acquired a functional understanding of the
fundamental concepts. The nature of reasoning difficulties in learning quantum
mechanics is analogous to reasoning difficulties found via research in
introductory physics courses. The reasoning difficulties were often due to
over-generalizations of concepts learned in one context to another context
where they are not directly applicable. Reasoning difficulties in
distinguishing between closely related concepts and in making sense of the
formalism of quantum mechanics were common. We conclude with a brief summary of
the research-based approached that take advantage of research on student
difficulties in order to improve teaching and learning of quantum mechanics
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