Mathematics for Quantum Information Processing

Jonathan A. Jones

Emanuel H. Knill, Michael A. Nielsen

Short review article on quantum information processing accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM

Shikhar Uttam

Giovanni Francesco Mascari

This paper presents first steps of an approach to quantum information processing in the framework of higher category theory from a noncommutative mathematics perspective. The aim is to provide a unifying theory for the structure and dynamics of composite quantum information processing systems, such that states, evolution, entanglement, decoherence are modeled by abstract categorical constructions and vice versa new mathematical structures arising from higher dimensional algebra could be "tested" as computational schemes and possibly realized by physical experiments.

Osamu Hirota

Preethi Nanjundan, Jossy Paul George, S Chandrasekaran +1 more

The objective of the research work is to propose a quantum information processing model (QIP) for legal applications including litigation and investigation phases. The quantum information processing and quantum computing concepts can be visualized within a Bloch Sphere of Law (BSL) as legal Bloch vectors (LBV) as quantum computing entities. This quantum approach is needed since the complexity of legalities and the legal objects involved in the final judgement are to be reversible with a lot of uncertainties. The reasoning and prosecution through various trials and investigations are to be considered as mathematical matrix or unitary operations in this muti dimensional legal space. The mapping of legal information into technical and then vectorial representations are deployed through a glossary of legal terms in this quantum paradigm. As a forerunning study and application in the quantum paradigm, mathematical and computational models have been proposed in the work with a case study of a recent civil case.