Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.600535
Title: Quantum information, Bell inequalities and the no-signalling principle
Author: Pitalúa-García, Damián
ISNI:       0000 0004 5351 5702
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2014
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Abstract:
This PhD thesis contains a general introduction and three main chapters. Chapter 2 investigates Bell inequalities that generalize the CHSH and Braunstein-Caves inequalities. Chapter 3 shows a derivation of an upper bound on the success probability of a class of quantum teleportation protocols, denoted as port-based teleportation, from the no-cloning theorem and the no-signalling principle. Chapter 4 introduces the principle of quantum information causality. Chapter 2 considers the predictions of quantum theory and local hidden variable theories (LHVT) for the correlations obtained by measuring a pair of qubits by projections defined by randomly chosen axes separated by a given angle θ. The predictions of LHVT correspond to binary colourings of the Bloch sphere with antipodal points oppositely coloured. We show a Bell inequality for all θ, which generalizes the CHSH and the Braunstein-Caves inequalities in the sense that the measurement choices are not restricted to be in a finite set, but are constrained only by the angle θ. We motivate and explore the hypothesis that for a continuous range of θ > 0, the maximum correlation (anticorrelation) is obtained by assigning to one qubit the colouring with one hemisphere black and the other white, and assigning the same (reverse) colouring to the other qubit. We describe numerical tests that are consistent with this hypothesis and bound the range of θ. Chapter 3 shows a derivation of an upper bound on the success probability of port-based teleportation from the no-cloning theorem and the no-signalling principle. Chapter 4 introduces the principle of quantum information causality, a quantum version of the information causality principle. The quantum information causality principle states the maximum amount of quantum information that a transmitted quantum system can communicate as a function of its dimension, independently of any quantum physical resources previously shared by the communicating parties. These principles reduce to the no-signalling principle if no systems are transmitted. We present a new quantum information task, the quantum information causality game, whose success probability is upper bounded by the new principle, and show that an optimal strategy to perform it combines the quantum teleportation and superdense coding protocols with a task that has classical inputs.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.600535  DOI: Not available
Keywords: Quantum information ; Quantum foundations
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