A Partial Order on Classical and Quantum States (2002) [11 citations — 5 self]
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Abstract:
We introduce a partial order on classical and quantum states which reveals that these sets are actually domains: Directed complete partially ordered sets with an intrinsic notion of approximation. The operational significance of the orders involved conclusively establishes that physical information has a natural domain theoretic structure. In the same way that the order on a domain provides a rigorous qualitative definition of information, a special type of mapping on a domain called a measurement provides a formal account of the intuitive notion `information content.' Not only is physical information domain theoretic, but so too is physical entropy: Shannon entropy is a measurement on the domain of classical states; von Neumann entropy is a measurement on the domain of quantum states. These results yield a foundation for problem solving in computer science, quantum information and physics.
Citations
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| 3 | The majorization arrow in quantum algorithm design – Latorre, Martn-Delgado |
