Projects in Previous Years

1st Semester 2014/15: Quantum Logic

Joshua Sack
If you are interested in this project, please contact the instructor by email.
This project introduces students to logics for reasoning about quantum theory, quantum information, and quantum computation. Work on quantum logic started with Birkoff and von Neumann as a tool for studying relationships among physical observables. The language of this logic is the same as for propositional logic, but the semantics is different. Later developments focused not just on the observables, but also the dynamics of a quantum system: for example what happens to a quantum system when certain actions are made, such as a measurement. Early development of quantum logic avoided the use of probability, though probability has been receiving an increasing amount of attention in quantum logics. We will explore some recently proposed probabilistic extensions of those logics. Quantum systems can be combined. Some states in the composed system can be separated into a composition of states from the subsystems, while others may be entangled. We will study how to reason about these concepts using logic, and explore certain protocols that make use of such compositionality, such as the quantum teleportation protocol or a quantum key distribution protocol.
The course will be a mixture of introductory lectures by the instructor and group discussion. The overall aim of the project is to provide students with an overview of the theory and applications of quantum logic so that students can incorporate quantum reasoning in their own research if they so desire.
Familiarity with propositional modal logic and first-order logic will be helpful. Although this course does not assume knowledge of linear algebra, some familiarity with vector spaces would be helpful too. This course will be self-contained, and will not assume familiarity with quantum physics, quantum information, or quantum computation.
Students will be evaluated by a combination of written homework sets and a short written report. The written report should provide either a survey of some of the literature with a new perspective or some (small) original result.
Website: Further information is available at the project website.