Experimentally-friendly methods of generation and detection of quantum correlations

Abstract

One of the most relevant problems in the quantum theory is the question whether the appropriate state of the system can be described within a classical theory. The famous examples of nonclassical states are Schrodinger-cats states or entanglement states. In spite of many practical applications of entanglement as a special kind of nonclassicality (like quantum teleportation [1], dense coding [2], or implementation of super-fast [3] and fast algorithms [4]), we still have difficulties with describing and specifying it. One cannot find such an operational optimal method, which would allow us to maximally use the technological and scientific potential arising from the adaptation properties of quantum correlations. Thus, my thesis is focused on giving a proposal of a theoretical recipe for constructing experimentally achievable procedures for the study of quantum correlations. In my thesis I have focused on quantum correlations described in terms of nonclassicality (quantumness) and specific kind of it,i.e., entanglement. The nonclassicality definition, used by me in the thesis, is based on the Glauber-Sudarshan function (P -function). One can assume, that a state is nonclassical, if its P -function is negative or more singular than Dirac’s delta [5]. As follows, the state is nonclassical, when its P -function cannot be treated as a “real” probabilistic distribution. Based on specific properties of the P -function, Agarwal and Tara [6], as well as, Shchukin, Richter and Vogel [7, 8] proposed nonclassicality and entanglement [9] criteria based on matrices of moments of annihilation and creation operators. The operational procedures for analyzing nonclassicality and an efficient method for measuring such moments developed by Shchukin and Vogel [10] creates basis for my thesis. It can be seen that the nonclassicality criteria based on matrices of moments offer an effective way of deriving specific inequalities, which might be useful in the verification of nonclassicality of particular states generated in experiments. Therefore, criteria constructed based on the above definition of nonclassicality can be used to find practical and effective methods of generating and testing nonclassicality and, therefore, also quantum entanglement of optical fields. The results presented in my thesis can be divided into three main groups: 1. Finding operational and practical criteria to classify states in terms of nonclassicality and entanglement based on fundamental classical inequalities like Cauchy-Schwarz inequality. It was also shown how some known entanglement inequalities can be derived as nonclassicality inequalities or as sums of more than one inequality [Bartkowiak2010a]. 2. Describing properties and behaviour of quantum correlations for different optical fields (e.g. for multiand single-mode systems, for interacting and noninteracting modes). In particular, general occurrence of sudden vanishing of nonclassicality, which can be observed not only for twoor multimode but also for single-mode fields, was proven [Bartkowiak2011]. 3. Finding the methods of generating and testing of quantum correlations, which would be practical and easy to implement with available resources in both linear and nonlinear optics.