Partial entanglement, complementary, and simultaneous measurement of discrete observables

Different quantum information schemes, such as eavesdropping in quantum cryptography, dictate the necessity of extracting information about pair conjugate observables from a single copy of a quantum system. Mathematically, quantum measurements are usually described by an uncertainty relation. The difference between the simultaneous measurement uncertainty relation form those known from the textbooks on quantum mechanics is the additional uncertainty associated with the measurement procedure itself in contrast to the state preparation uncertainties described by the Schroedinger-Robertson type uncertainty relations. We present here an overview of our approach based on the state estimation theory and maximum likelihood strategy. We make a theoretical analysis and an experimental verification of minimum-uncertainty product of the two-states quantum system simultaneous measurement based on partially entangled photon pairs.