Quantification of quantum entanglement in mixed quantum states: from two qubits to the Kondo effect

Abstract

Quantum entanglement is the core concept in quantum information science and also a state-of-the-art tool to understand many-body systems in condensed matter physics. In both fields, the entanglement in mixed quantum states is an important issue. For the former, it describes the realistic situation with decoherence and exhibits the structure of entanglement. For the latter, it encodes how the ground-state quantum nature (e.g., quantum criticality and topological order) evolves at finite temperature and how the many-body state extends spatially. The quantitative analysis of mixed-state entanglement, however, becomes less feasible due to the heavy computational cost even for three-qubit full-rank states. Moreover, the direct determination of the mixed-state entanglement in experiment without {\it a priori} knowledge nor the full state reconstruction is an open problem, including the simplest two-qubit case, since the entanglement is not defined by physical observables.

In this dissertation, we illustrate a series of our researches resolving the aforementioned problems. We develop the optimal witness approach which reduces the computational cost in optimization and affords the experimental realization, and apply this approach to the qubit systems and the Kondo physics. First, we construct the optimal witness in quantum optics experiment to determine the entanglement of an arbitrary two-qubit mixed state. The optimal witness directly accesses to the entanglement-related properties of the state and is more accurate and efficient than the conventional approach using the full state reconstruction. Second, we study the Greenberger-Horne-Zeilinger entanglement of three qubits and the four-qubit entanglement of the noisy Smolin states, which is the first analytic quantification of multipartite entanglement of full-rank states. The global optimality of our solution is verified quantitatively by formulating the witness optimization as the minimax problem. Our latest work ...