Experimental characterization of qutrits using symmetric, informationally complete positive operator-valued measures

Abstract

Generalized quantum measurements (also known as positive operator-valued measures or POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform arbitrary POVMs in a linear-optical context. One of the most interesting POVMs, the symmetric, informationally complete-POVM (or SIC-POVM), is the most compact set of measurements that can be used to fully describe a quantum state. We use our technique to carry out the first experimental characterization of the state of a qutrit using SIC-POVMs. Because of the highly symmetric nature of this measurement, such a representation has the unique property that it permits all other measurement outcomes to be predicted by a simple extension of the classical Bayesian sum rule, making no use of complex amplitudes or Hilbert-space operators. We demonstrate this approach on several qutrit states encoded in single photons.

Symmetric informationally complete measurements identify the irreducible difference between classical and quantum systems

“…where P (D|H) is a matrix of conditional probabilities. A SIC [16][17][18][19][20][21][22][23][24][25] is a MIC for which all the H i are rank-1 and SICs have yet to be proven to exist in all finite dimensions d, but they are widely believed to [24] and have even been experimentally demonstrated in some low dimensions [26][27][28][29]. The SIC projectors associated with a SIC are the pure states ρ i = dH i .…”

“…SICs have yet to be proven to exist in all finite dimensions d, but they are widely believed to [24] and have even been experimentally demonstrated in some low dimensions [26][27][28][29]. The SIC projectors associated with a SIC are the pure states ρ i = dH i .…”