Reconstructing a pure state of a spin s through three Stern-Gerlach measurements

Consider a spin s prepared in a pure state. It is shown that, generically, the moduli of the spin components along three directions in space determine the state unambiguously. These probabilities are accessible experimentally by means of a standard Stern-Gerlach apparatus. It is therefore possible to reconstruct a generic pure state on the basis of 6s independent measured intensities.

[1]  Wolfgang Pauli,et al.  Handbuch der Physik , 1904, Nature.

[2]  Handbuch Der Physik/Encyclopedia of Physics , 1957 .

[3]  A. Wightman,et al.  PCT, spin and statistics, and all that , 1964 .

[4]  G. T. Trammell,et al.  Determination of the Quantum State by Measurements , 1968 .

[5]  Roger G. Newton,et al.  Measurability of the spin density matrix , 1968 .

[6]  H. Gould,et al.  Measurement of the Lamb shift in lithiumlike uranium (U89 , 1991 .

[7]  Pauli problem for a spin of arbitrary length: A simple method to determine its wave function. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[8]  Beck,et al.  Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum. , 1993, Physical review letters.

[9]  Leonhardt.  Quantum-state tomography and discrete Wigner function. , 1995, Physical review letters.

[10]  Walmsley,et al.  Experimental determination of the quantum-mechanical state of a molecular vibrational mode using fluorescence tomography. , 1995, Physical review letters.

[11]  Magnetic Tomography of a Cavity State. , 1996, Physical review letters.

[12]  King,et al.  Experimental Determination of the Motional Quantum State of a Trapped Atom. , 1996, Physical review letters.

[13]  Quantum state reconstruction and detection of quantum coherences on different observation levels. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[14]  R. Benner,et al.  Chemical composition of dissolved organic nitrogen in the ocean , 1997, Nature.

[15]  J. Amiet,et al.  Reconstructing the density matrix of a spin s through Stern - Gerlach measurements , 1998 .

[16]  D. Leibfried,et al.  Shadows and Mirrors: Reconstructing Quantum States of Atom Motion , 1998 .