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


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.
Number of pages30
ISBN (Electronic)9789812563071
ISBN (Print)9812560157, 9789812560155
StatePublished - Jan 1 2005

ASJC Scopus subject areas

  • General Physics and Astronomy


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