Five Measurement Bases Determine Pure Quantum States on Any Dimension
Abstract
A longstanding problem in quantum mechanics is the minimum number of observables required for the characterization of unknown pure quantum states. The solution to this problem is especially important for the developing field of highdimensional quantum information processing. In this work we demonstrate that any pure d dimensional state is unambiguously reconstructed by measuring five observables, that is, via projective measurements onto the states of five orthonormal bases. Thus, in our method the total number of different measurement outcomes (5 d ) scales linearly with d . The state reconstruction is robust against experimental errors and requires simple postprocessing, regardless of d . We experimentally demonstrate the feasibility of our scheme through the reconstruction of eightdimensional quantum states, encoded in the momentum of single photons.
 Publication:

Physical Review Letters
 Pub Date:
 August 2015
 DOI:
 10.1103/PhysRevLett.115.090401
 arXiv:
 arXiv:1411.2789
 Bibcode:
 2015PhRvL.115i0401G
 Keywords:

 03.65.Wj;
 03.65.Aa;
 03.65.Fd;
 03.67.a;
 State reconstruction quantum tomography;
 Algebraic methods;
 Quantum information;
 Quantum Physics
 EPrint:
 Comments are very welcome