On the measurement of qubits

Daniel F.V. James, Paul G. Kwiat, William J. Munro, Andrew G. White

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (“qubits”). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction (in which the density matrix is linearly related to a set of measured quantities) and a maximum likelihood technique which requires numerical optimization (but has the advantage of producing density matrices which are always non-negative definite). In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results.

Original languageEnglish (US)
Title of host publicationAsymptotic Theory of Quantum Statistical Inference
Subtitle of host publicationSelected Papers
PublisherWorld Scientific Publishing Co.
Pages509-538
Number of pages30
ISBN (Electronic)9789812563071
ISBN (Print)9812560157, 9789812560155
DOIs
StatePublished - Jan 1 2005

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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    James, D. F. V., Kwiat, P. G., Munro, W. J., & White, A. G. (2005). On the measurement of qubits. In Asymptotic Theory of Quantum Statistical Inference: Selected Papers (pp. 509-538). World Scientific Publishing Co.. https://doi.org/10.1142/9789812563071_0035