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Quantum Information

In: Mathematics Unlimited — 2001 and Beyond

Author

Listed:
  • Ole E. Barndorff-Nielsen
  • Richard D. Gill
  • Peter E. Jupp

Abstract

In the last two decades, developments of an axiomatic type in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical stochastics1. On the other hand, the unique character of quantum physics sets many of the questions addressed apart from those met classically in stochastics. The key mathematical notion is that of a quantum instrument, which we shall describe in Sect. 2 and which, for arbitrary quantum experiments, specifies both the observational outcome of the experiment and the state of the physical system after the experiment. Concurrently with these theoretical developments, major advances in experimental techniques have opened many possibilities for studying small quantum systems and this has led to considerable current interest in a range of questions that in essence belong to statistical inference and are concerned with the amount of information about unknown parameters in given observational data or accessible through various possible types of measurements.

Suggested Citation

  • Ole E. Barndorff-Nielsen & Richard D. Gill & Peter E. Jupp, 2001. "Quantum Information," Springer Books, in: Björn Engquist & Wilfried Schmid (ed.), Mathematics Unlimited — 2001 and Beyond, pages 83-107, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56478-9_6
    DOI: 10.1007/978-3-642-56478-9_6
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