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Springer eBooks

Theoretical Response

Jan C. A. Boeyens

Published Jan 1, 2013• 0 citations
Publisher
DOI
10.1007/978-94-007-7578-7_4

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Response-register quantum oracles admit two complementary operational interpretations: value readout and phase kickback. Although their computational equivalence is well understood, the quantitative relation between these two operational interpretations has lacked an exact characterization. We prove that, for finite Abelian response groups, the optimal single-query value-readout probability is exactly the normalized Rényi-1/2 effective Fourier support of the response state. This identity provides an exact information-theoretic characterization of optimal value-readout capability, gives the Rényi-1/2 effective Fourier support a direct operational interpretation in the oracle setting, and yields a tight phase--value complementarity theorem together with an explicit family of saturating response states.
The coherent response in the forward direction to the almost stepwise -pulse (hereafter one supposes that the pure stepwise -pulse is described by a step function) is theoretically analysed. In this way, first of all the analytical form of the -pulse has been obtained when remagnetization of the `magnetic shutter' takes place. The problem is solved by employing the semiclassical Maxwell - Bloch formalism. Then the time evolution of the coherent response to that -pulse is calculated when it propagates through a two-level resonant medium. Finally the theoretical results are used to describe the experiment quantitatively.