Lin, H.-C.; (2009) Local approach to quantum entanglement. Doctoral thesis , UCL (University College London).

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Abstract

Quantum entanglement is the key property that makes quantum information theory different from its classical counterpart and is also a valuable physical resource with massive potential for technological applications. However, our understanding of entanglement is still far from complete despite intense research activities. Like other physical resources, the first step towards exploiting them fully is to know how to quantify. There are many reasons to focus on the entanglement of continuous-variable states since the underlying degrees of freedom of physical systems carrying quantum information are frequently continuous, rather than discrete. Much of the effort has been concentrated on Gaussian states, because these are common as the ground or thermal states of optical modes. Within this framework, many interesting topics have been studied and some significant progress made. Nevertheless, non-Gaussian states are also extremely important; this is especially so in condensed-phase systems, where harmonic behaviour in any degree of freedom is likely to be only an approximation. So far, there is little knowledge about the quantification of entanglement in non-Gaussian states. This thesis aims to contribute to the active field of research in quantum entanglement by introducing a new approach to the analysis of entanglement, especially in continuous-variable states, and shows that it leads to the first systematic quantification of the (local) entanglement in arbitrary bipartite non-Gaussian states. By applying this local approach, many new insights can be gained. Notably, local entanglements of systems with smooth wavefunctions are fully characterised by the derived simple expressions, provided the wavefunction is known. The local (logarithmic) negativity of any two-mode mixed states can be directly computed from the closed-form formulae given. For multi-mode mixed states, this approach provides a scheme that permits much simpler numerical computation for quantifying entanglement than is generally possible from directly computing the full entanglement of the system.

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