Reformulating and Reconstructing Quantum Theory
By Lucien Hardy. 2011
175 citations recorded by the source corpus.
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the following: [Axiom 1] Operations correspond to operators. [Axiom 2] Every complete set of physical operators corresponds to a complete set of operations. The following operational postulates are shown to be equivalent to these mathematical axioms: [P1] Sharpness. Associated with any given pure state is a unique maximal effect giving probability equal to one. This maximal effect does not give probability equal to one for any other pure state. [P2] Information locality. A maximal measurement on a composite system is effected if we perform maximal measurements on each of the components. [P3] Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components. [P4] Compound permutability. There exists a compound reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. [P5] Sturdiness. Filters are non-flattening. Hence, from these postulates we can reconstruct all the usual features of quantum theory: States are represented by positive operators, transformations by completely positive trace non-increasing maps, and effects by positive operators. The Born rule (i.e. the trace rule) for calculating probabilitieso follows. A more detailed abstract is provided in the paper.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/b0f8427eae5f1b133ad508bea8b55c2a9b680fbd
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In Artificial Intelligence
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Citations in the corpus
- Quantum theory cannot consistently describe the use of itself (2016, background): “Similarly, many of the modern arguments in quantum foundations employ probabilistic frameworks [55, 56, 57, 58, 59, 60, 61, 62].”