Some New Properties of Quantum Correlations

Lê Phuc Thinh

Margarita A. Man’ko, Vladimir I. Man’ko

The approach to extend the notion of entanglement for characterizing the properties of quantum correlations in the state of a single qudit is presented. New information and entropic inequalities, such as the subadditivity condition, strong subadditivity condition, and monotonicity of relative entropy for a single qudit corresponding to an arbitrary spin state with spin j are discussed. The idea to employ quantum correlations in the single-qudit state, such as the entanglement, for developing a new quantum technique in quantum computing and quantum communication is proposed. Examples of qutrit and qudit with j = 3/2 are considered.

Ajoy Sen

Margarita A. Man’ko, Vladimir I. Man’ko

The approach to extend the notion of entanglement for characterizing the properties of quantum correlations in the state of a single qudit is presented. New information and entropic inequalities, such as the subadditivity condition, strong subadditivity condition, and monotonicity of relative entropy for a single qudit corresponding to an arbitrary spin state with spin j are discussed. The idea to employ quantum correlations in the single-qudit state, such as the entanglement, for developing a new quantum technique in quantum computing and quantum communication is proposed. Examples of qutrit and qudit with j = 3/2 are considered.

Guido Bellomo, A. P. Majtey, Angel Ricardo Plastino +1 more

Kristian Patrick

Full knowledge of the entanglement properties of quantum systems can be used to identify different phases in condensed matter. Quantum correlations serve as a fingerprint for universal behaviours, leading to the discovery of new phases and new tools for probing them. In this thesis we use quantum correlations, as witnessed by the entanglement spectrum of a bipartitioned state, to probe the phases and behaviours of various one-dimensional quantum systems. In an era when novel quantum technologies are at the forefront of research it is important to find new models and new methods that may be applicable to the field. This thesis is a composition of two main works. The first is a study of a topological phase with non-local couplings, where we find that protected midgap states are split from zero energy whilst retaining their topological properties. The second aims to quantify the applicability of a known approximate method through the optimality of its entanglement spectrum. We determine bounds that confirm regions of applicability and suggest a new model that is by construction always optimal.