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 language | English (US) |
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Title of host publication | Asymptotic Theory of Quantum Statistical Inference |
Subtitle of host publication | Selected Papers |
Publisher | World Scientific Publishing Co. |
Pages | 509-538 |
Number of pages | 30 |
ISBN (Electronic) | 9789812563071 |
ISBN (Print) | 9812560157, 9789812560155 |
DOIs | |
State | Published - Jan 1 2005 |
ASJC Scopus subject areas
- General Physics and Astronomy