We show that the density matrix of a spin- $l$ system can be described entirely in terms of the measurement statistics of projective spin measurements along a minimum of $4l+1$ different spin directions. It is thus possible to represent the complete quantum statistics of any $N$ -level system within the spherically symmetric three-dimensional space defined by the spin vector. An explicit method for reconstructing the density matrix of a spin-1 system from the measurement statistics of five nonorthogonal spin directions is presented and the generalization to spin- $l$ systems is discussed.We show that the density matrix of a spin-$l$ system can be described entirely in terms of the measurement statistics of projective spin measurements along a minimum of $4l+1$ different spin directions. It is thus possible to represent the complete quantum statistics of any $N$-level system within the spherically symmetric three-dimensional space defined by the spin vector. An explicit method for reconstructing the density matrix of a spin-1 system from the measurement statistics of five nonorthogonal spin directions is presented and the generalization to spin-$l$ systems is discussed.

arXiv:quant-ph/0310003Physical Review AApr 23, 200436 citations

Reconstructing the density matrix of a spinsthrough Stern - Gerlach measurements

Jean-Pierre Amiet, Stefan Weigert

The Pauli problem is solved for a spin of length s prepared in an arbitrary (unnormalized) mixed state which has free real parameters. The reconstruction of its density operator is possible if one knows the probabilities of the spin components along each of directions in space. These probabilties are directly accessible through measurements performed with a Stern - Gerlach apparatus. A multipole expansion of the density operator establishes the link between the matrix elements of and the measured intensities.The Pauli problem is solved for a spin of length s prepared in an arbitrary (unnormalized) mixed state which has free real parameters. The reconstruction of its density operator is possible if one knows the probabilities of the spin components along each of directions in space. These probabilties are directly accessible through measurements performed with a Stern - Gerlach apparatus. A multipole expansion of the density operator establishes the link between the matrix elements of and the measured intensities.

Journal of Physics A Mathematical and GeneralAug 7, 199819 citations

Spin Density Matrices

Alan McLachlan

NatureDec 5, 19700 citations

We show that the density matrix of a spin-

l

system can be described entirely in terms of the measurement statistics of projective spin measurements along a minimum of

4l+1

different spin directions. It is thus possible to represent the complete quantum statistics of any

N

-level system within the spherically symmetric three-dimensional space defined by the spin vector. An explicit method for reconstructing the density matrix of a spin-1 system from the measurement statistics of five nonorthogonal spin directions is presented and the generalization to spin-

l

systems is discussed.