Volkert, Georg Friedrich (2011) Quantum Information in Geometric Quantum Mechanics. [Tesi di dottorato] (Unpublished)


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Item Type: Tesi di dottorato
Lingua: English
Title: Quantum Information in Geometric Quantum Mechanics
Volkert, Georg Friedrichvolkert@na.infn.it
Date: 30 November 2011
Number of Pages: 144
Institution: Università degli Studi di Napoli Federico II
Department: Scienze fisiche
Scuola di dottorato: Scienze fisiche
Dottorato: Fisica fondamentale ed applicata
Ciclo di dottorato: 23
Coordinatore del Corso di dottorato:
Velotta, Raffaelevelotta@na.infn.it
Marmo, Giuseppemarmo@na.infn.it
Date: 30 November 2011
Number of Pages: 144
Uncontrolled Keywords: Quantum Information Geometry
Settori scientifico-disciplinari del MIUR: Area 02 - Scienze fisiche > FIS/02 - Fisica teorica, modelli e metodi matematici
Area 01 - Scienze matematiche e informatiche > MAT/07 - Fisica matematica
Date Deposited: 15 Dec 2011 17:45
Last Modified: 30 Apr 2014 19:49
URI: http://www.fedoa.unina.it/id/eprint/8930
DOI: 10.6092/UNINA/FEDOA/8930


A fundamental starting point in quantum information theory is the consideration of the von Neumann entropy and its generalization to relative quantum entropies. A particular feature of quantum relative entropies is their relation via their Hessian to monotonic Riemannian metrics on the dense set of invertible mixed quantum states (Lesniewski and Ruskai 1999). These metrics are also known as quantum Fisher information metrics and provide a direct link to quantum estimation theory (Helstrom 1969). Quantum Fisher information metrics which are extendable to pure states coincide all with the Fubini Study metric of the projective Hilbert space of complex rays. This theses outlines possible advantages of an inverse approach to quantum information theory, by starting with the Fubini Study metric rather then with the von Neumann entropy. This is done in a first step by associating to the Fubini Study metric a covariant and a contra-variant structure on the punctured Hilbert space as being available in the geometric formulation of quantum mechanics. While the contra-variant structure leads to a quantum version of the Cramér-Rao inequality for general 1-dimensional submanifolds of pure states, the covariant structure provides alternative entanglement monotones by identifying an inner product on the pullback tensor fields on local unitary group orbits of quantum states. It is shown in the case of two qubits that these monotones yield a more efficient estimation of entanglement than standard measures from the literature as those associated with the linearization of the von Neumann entropy.

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