TY - GEN
T1 - Logic of local inference for contextuality in quantum physics and beyond
AU - Kishida, Kohei
N1 - Publisher Copyright:
© Kohei Kishida.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - Contextuality in quantum physics provides a key resource for quantum information and computation. The topological approach in [Abramsky and Brandenburger, New J. Phys., 2011, Abramsky et al., CSL 2015, 2015] characterizes contextuality as "global inconsistency" coupled with "local consistency", revealing it to be a phenomenon also found in many other fields. This has yielded a logical method of detecting and proving the "global inconsistency" part of contextuality. Our goal is to capture the other, "local consistency" part, which requires a novel approach to logic that is sensitive to the topology of contexts. To achieve this, we formulate a logic of local inference by using context-sensitive theories and models in regular categories. This provides a uniform framework for local consistency, and lays a foundation for high-level methods of detecting, proving, and moreover using contextuality as computational resource.
AB - Contextuality in quantum physics provides a key resource for quantum information and computation. The topological approach in [Abramsky and Brandenburger, New J. Phys., 2011, Abramsky et al., CSL 2015, 2015] characterizes contextuality as "global inconsistency" coupled with "local consistency", revealing it to be a phenomenon also found in many other fields. This has yielded a logical method of detecting and proving the "global inconsistency" part of contextuality. Our goal is to capture the other, "local consistency" part, which requires a novel approach to logic that is sensitive to the topology of contexts. To achieve this, we formulate a logic of local inference by using context-sensitive theories and models in regular categories. This provides a uniform framework for local consistency, and lays a foundation for high-level methods of detecting, proving, and moreover using contextuality as computational resource.
KW - Contextuality
KW - Quantum mechanics
KW - Regular category
KW - Regular logic
KW - Separated presheaf
UR - http://www.scopus.com/inward/record.url?scp=85012917754&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85012917754&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ICALP.2016.113
DO - 10.4230/LIPIcs.ICALP.2016.113
M3 - Conference contribution
AN - SCOPUS:85012917754
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016
A2 - Rabani, Yuval
A2 - Chatzigiannakis, Ioannis
A2 - Sangiorgi, Davide
A2 - Mitzenmacher, Michael
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016
Y2 - 12 July 2016 through 15 July 2016
ER -