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.
Interference phenomena lead to a wealth of applications in many areas of physics. Entangled quantum states allow one to surpass the classical measurement sensitivity or resolution in polarimetry, interferometry, and imaging. In this paper we shall review, in some depth, polarization properties of quantized two-mode electromagnetic fields and show how interference and quantum entanglement lead to new phenomena. We shall also briefly discuss subwavelength quantum lithography.