19 July 2010
New ICFO PhD Graduate

Dr. Mafalda Almeida

Thesis Committee

Dr. Mafalda Almeida obtained her PhD with a thesis on resources for quantum information tasks.
Dr. Mafalda Almeida graduated in Physics & Technology Engineering from Instituto Superior Técnico, Universidade Técnica de Lisboa, in 2004. Next year she joined ICFO to work in the field of Quantum Information Theory.

Dr. Almeida\'s thesis, \'Resources for Quantum Information Tasks: from the Bipartite to the Multipartite Scenario’ was supervised by ICFO Group Leader and ICREA Prof. Antonio Acin.

ABSTRACT

Quantum information theory shows that encoding information in quantum systems achieves results unattainable by any classical means. The aim of the present thesis is to contribute to the identification and characterization of quantum entanglement and quantum non-locality, the resources believed to underlie the power of quantum physics at information-processing tasks.

We address the question of designing better direct methods of entanglement detection. For that, we study physical approximations to positive (non-physical) maps, which are used in the most efficient criterion of identification of entangled quantum states. In all considered cases, physical approximations to optimal positive maps define entanglement-breaking channels. These channels are useless for entanglement distribution and can be replaced by measurement and state-preparation protocols. Hence, physical approximations to optimal positive maps have a simple practical implementation and might contribute for improved entanglement-detection schemes.

Concerning the characterization of quantum non-locality, we start by considering the bipartite scenario. We study the relation between non-locality, entanglement and noise. In particular, we study the robustness of nonlocal correlations under the action of depolarizing noise, in a regime where entanglement is still present. We show that, for a generic class of quantum states, noise completely destroys the nonlocal properties of states, before entanglement is also lost. More specifically, we provide bounds on the amount of noise that transforms nonlocal entangled quantum states into local entangled quantum states. This means that local entanglement can be found frequently, and is not a particular property of highly symmetric mixed states.

Then we move into the multipartite scenario, where quantum correlations are shared by more than two subsystems. We define the following multipartite strategy for the study of non-locality. Local measurements are performed on a subset of the parties, which leave the remaining ones in given quantum state. If this state violates a Bell inequality, it implies that the original state (held by all the parties) necessarily contains nonlocal correlations. This procedure reveals itself very useful for the study of non-locality in a broad sense.

First, we prove that there exist multipartite quantum states, pure and mixed, which contain fully-nonlocal multipartite correlations. This consists of the strongest form of multipartite non-locality. Then, we take copies of bipartite states and distribute them by several parties, in such a way that the whole system is in some multipartite state. We are then able to apply our multipartite strategy. Our second result is a direct link between quantum non-locality and one-way entanglement distillability.

And third, we prove that nonlocal resources can be activated. Performing collective local measurements on N copies of a bipartite local quantum state reveals its bipartite nonlocal content. Analogously, there exist genuine multipartite quantum states composed by N copies of some quantum state that individually does not contain any genuine multipartite non-locality.

THESIS COMMITTEE

Dr. Almeida\'s thesis, \'Resources for Quantum Information Tasks: from the Bipartite to the Multipartite Scenario’ was supervised by ICFO Group Leader and ICREA Prof. Antonio Acin.

ABSTRACT

Quantum information theory shows that encoding information in quantum systems achieves results unattainable by any classical means. The aim of the present thesis is to contribute to the identification and characterization of quantum entanglement and quantum non-locality, the resources believed to underlie the power of quantum physics at information-processing tasks.

We address the question of designing better direct methods of entanglement detection. For that, we study physical approximations to positive (non-physical) maps, which are used in the most efficient criterion of identification of entangled quantum states. In all considered cases, physical approximations to optimal positive maps define entanglement-breaking channels. These channels are useless for entanglement distribution and can be replaced by measurement and state-preparation protocols. Hence, physical approximations to optimal positive maps have a simple practical implementation and might contribute for improved entanglement-detection schemes.

Concerning the characterization of quantum non-locality, we start by considering the bipartite scenario. We study the relation between non-locality, entanglement and noise. In particular, we study the robustness of nonlocal correlations under the action of depolarizing noise, in a regime where entanglement is still present. We show that, for a generic class of quantum states, noise completely destroys the nonlocal properties of states, before entanglement is also lost. More specifically, we provide bounds on the amount of noise that transforms nonlocal entangled quantum states into local entangled quantum states. This means that local entanglement can be found frequently, and is not a particular property of highly symmetric mixed states.

Then we move into the multipartite scenario, where quantum correlations are shared by more than two subsystems. We define the following multipartite strategy for the study of non-locality. Local measurements are performed on a subset of the parties, which leave the remaining ones in given quantum state. If this state violates a Bell inequality, it implies that the original state (held by all the parties) necessarily contains nonlocal correlations. This procedure reveals itself very useful for the study of non-locality in a broad sense.

First, we prove that there exist multipartite quantum states, pure and mixed, which contain fully-nonlocal multipartite correlations. This consists of the strongest form of multipartite non-locality. Then, we take copies of bipartite states and distribute them by several parties, in such a way that the whole system is in some multipartite state. We are then able to apply our multipartite strategy. Our second result is a direct link between quantum non-locality and one-way entanglement distillability.

And third, we prove that nonlocal resources can be activated. Performing collective local measurements on N copies of a bipartite local quantum state reveals its bipartite nonlocal content. Analogously, there exist genuine multipartite quantum states composed by N copies of some quantum state that individually does not contain any genuine multipartite non-locality.

THESIS COMMITTEE

**Chair**Prof. Artur Ekert, Mathematical Institute, University of Oxford / University of Singapore, SINGAPORE.**Secretary**Prof. Ramon Muñoz Tapia, Department of Physics, Universitat Autonoma Barcelona, SPAIN**Member**Prof. Andreas Winter, Department of Mathematics, University of Bristol, U.K.