Dissertação de Mestrado #567: Jéssica Bavaresco

When Bob cannot trust Alice. A semi-device independent tale of quantum steering

Autor: Jéssica Bavaresco

Banca Avaliadora

Marcelo de Oliveira Terra Cunha (orientador)

IMECC/UNICAMP

Reinaldo de Oliveira Vianna

Física - UFMG

Rafael Luiz da Silva Rabelo (coorientador)

Matemática - UFMG

Orientadores

Marcelo de Oliveira Terra Cunha (orientador)

IMECC - UNICAMP

Resumo do Trabalho

Quantum steering is a form of quantum correlation intermediate between entanglement and Bell nonlocality. We say Alice can steer Bob when it is possible for her to prepare Bob’s state by interacting only with her part of the system, in such a way that the resulting correlation between her measurements, her outcomes, and Bob’s conditioned state exhibits nonlocal properties. In this setup, Alice’s apparatus is not trusted and she can only analyze raw statistical data. Bob, however, has complete knowledge over his setup, e.g., he is able to perform full state tomography. To demonstrate steering it is necessary for the shared state to be entangled. Hence, steering is a form of semi-device independent entanglement certification. However, not all entangled states can demonstrate steering and not all steerable states can demonstrate nonlocality. This work focuses mainly on the problem of quantifying the robustness of the steerability of quantum states when subjected to white noise. Exploring scenarios where Alice is allowed to perform a fixed and finite number of measurements, we investigate what is the family of measurements that reveals highest robustness. We develop and apply a variety of methods for estimating steerability based on semidefinite programming. Analytical solutions for a particular family of measurements are presented using the theory of joint measurability and providing explicit LHS models and steering inequalities. Finally, we study the relevance of general POVMs in exhibiting steering when compared to projective measurements.