Quantum Logic

**[General Information] **
**[Schedule] **
**[Prerequisites] **
**[Materials] **
**[Evaluation] **

## General Information
This general information (as well as the rest of the website) will be updated as more information becomes available. | ||||||||||||||||||||

## Schedule:
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## Prerequisites: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. | ||||||||||||||||||||

## Suggested reading:The following references are relevant to the topics this course aims to cover. As this list is very large (and may even grow), it is not expected that students read all of this material. Pointers will be given throughout the course as to what sections of which references are relevant to the particular subject matter we are covering at the time.General books and surveys: - J. Sack. Epicenter Quantum Logic Minicourse. pdf
- M. Nielsen and I. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
- B. Hall. Quantum Theory for Mathematicians. Springer, 2013. [doi]
- R.I.G. Hughes. The Structure and Interpretation of Quantum Mechanics. Harvard University Press. 1992.
- C. Piron. Foundations of Quantum Physics. W.A. Benjamin, Inc. 1976.
- T. Maudlin. Quantum Non-Locality and Relativity. Blackwell Publishing, 1994; second edition, 2002, third edition, 2011.
- M. Dalla Chiara, R. Giuntini, and R. Greechie. Reasoning in Quantum Theory: Sharp and unsharp quantum logics. Kluwer academic publisher, 2004. [doi]
- M.L. Dalla Chiara and R. Giuntini. Quantum Logics. In Handbook of Philosophical Logic Volume 6, pp. 129–228, 2002. [doi] [arXiv]
- A. Wilce. Quantum Logic and Probability Theory. Stanford Encyclopedia of Philosophy. [html (fulltext)]
- G. Birkhoff and J. von Neumann. The logic of quantum mechanics. Annals of Mathematics 37, pp. 823–843, 1936. [doi]
- J.M. Dunn, T. Hagge, L.S. Moss, Z. Wang. Quantum Logic as Motivated by Quantum Computing. The Journal of Symbolic Logic 70(2), pp. 353–359, 2005. [url]
- C. Herrmann and M. Ziegler. Computational Complexity of Quantum Satisfiability. In the proceedings of the 26th Anual IEEE Symposium on Logic in Computer Science (LICS), pp.175–184, 2011. [doi]
- Chapter 8 of M. Dalla Chiara, R. Giuntini, and R. Greechie. Reasoning in Quantum Theory: Sharp and unsharp quantum logics. Kluwer academic publisher, 2004. [doi]
- R.I. Goldblatt. Semantic Analysis of Orthologic. Journal of Philosophical Logic 3(1/2): 19–35, 1974. [url]
- Chapters 5 and 6 of M.L. Dalla Chiara and R. Giuntini. Quantum Logics. In Handbook of Philosophical Logic Volume 6, pp. 129–228, 2002. [doi] [arXiv]
- Chapter 17 of Dalla Chiara, R. Giuntini, and R. Greechie. Reasoning in Quantum Theory: Sharp and unsharp quantum logics. Kluwer academic publisher, 2004. [doi]
- A. Baltag and S. Smets. Complete axiomatizations for quantum actions. International Journal of Theoretical Physics 44: 2267–2282, 2005. [doi]
- A. Baltag and S. Smets. Correlated Knowledge, An Epistemic-Logic View on Quantum Entanglement. International Journal of Theoretical Physics 49(12): 3005–3021, 2010. [doi]
- A. Baltag and S. Smets. Correlated Information: A Logic for Multi-Partite Quantum Systems. Electronic Notes in Theoretical Computer Science 270(2): 3–14, 2011. [doi]
- S. Abramsky and L. Hardy. Logical Bell Inequalities. Phys. Rev. A 85, 062114, 2012. [doi]
- For game theoretic explanation of non-locality, see second half of Chapter 1 of: T. Maudlin. Quantum Non-Locality and Relativity. Blackwell Publishing, 1994; second edition, 2002, third edition, 2011.
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## Evaluation:Students will be evaluated by a combination of written homework sets and a short written report. There will be a homework set once every 1 to 2 weeks and the written report should provide either a survey of some of the literature with a new perspective or some (small) result. |