### Max Tegmark's quantum mechanics library: radon

**Figure 1: The wavefunction measurement apparatus.**

**Figure 2: How phase-space tomography works.**
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##
Measuring quantum states:

an experimental setup for measuring
the spatial density
matrix

### Author:

Max Tegmark
### Abstract:

To quantify the effect of decoherence in quantum measurements,
it is desirable to measure not merely the square modulus
of the spatial wavefunction, but the entire density matrix,
whose phases carry information about momentum and
how pure the state is.
An experimental setup is presented which can measure
the density matrix (or equivalently, the Wigner function)
of a beam of identically prepared charged particles
to an arbitrary accuracy, limited only by count statistics
and detector resolution.
The particles enter into
an electric field causing simple harmonic oscillation in
the transverse direction.
This corresponds to rotating the Wigner function in phase space.
With a slidable
detector, the
marginal distribution of the Wigner function can
be measured from all angles.
Thus the phase-space tomography formalism can be used to
recover the Wigner function by
the standard inversion of the Radon transform.
By applying this technique to for instance
double-slit experiments with various degrees of
environment-induced decoherence, it should be possible to
make our understanding of decoherence and apparent
wave-function collapse less qualitative and more quantitative.
### Reference info:

*Phys. Rev. A.*, **54**, 2703-2706 (1996)
### Online references:

This site also contains the latest versions of some other recent
quantum mechanics papers of mine; a paper on
decoherence,
one on how this produces coherent states,
one on quantum heat baths
and one about the .
information content of the Universe.

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This page was last modified July 1, 1998.
max@ias.edu