Abstract
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
- Received 26 April 2016
DOI:https://doi.org/10.1103/PhysRevLett.117.120401
© 2016 American Physical Society
Physics Subject Headings (PhySH)
Viewpoint
Mapping Out the State of a Quantum System
Published 12 September 2016
Researchers have developed a new technique to measure the density matrix—a more general way of characterizing the state of a quantum system than that provided by the wave function.
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