TY - JOUR

T1 - Measurement of qubits

AU - James, Daniel F.V.

AU - Kwiat, Paul G.

AU - Munro, William J.

AU - White, Andrew G.

PY - 2001

Y1 - 2001

N2 - 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 that 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.

AB - 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 that 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.

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U2 - 10.1103/PhysRevA.64.052312

DO - 10.1103/PhysRevA.64.052312

M3 - Article

AN - SCOPUS:84861524885

SN - 1050-2947

VL - 64

SP - 15

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 5

ER -