MoL201703: Coopmans, Tim (2017) Robust selftesting of (almost) all pure twoqubit states. [Report]

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Abstract
In a nonlocal scenario, physically isolated players each have a device that inputs and outputs classical information. Certain correlations between the joint input and output of the devices almost uniquely identify the quantum state that they share. This phenomenon is known as selftesting and has applications in quantum cryptography with untrusted devices. It was for example shown that for every pure twoqubit state, there exists a twoplayer Bell experiment whose correlations, or rather the Bell value that is computed from the correlations, can be used here to selftest that state; the Bell value that is used stems from a family of Bell inequalities called tilted CHSH inequalities. A special case is the regular CHSH inequality, which is used to selftest the singlet, a maximally entangled state of two qubits. For practical applications, estimation errors and the presence of external noise require selftesting statements to be robust to errors. In this thesis, we extend previous work on selftesting of the singlet with the CHSH game. First, we use tilted CHSH inequalities to improve the robustness of previously found selftesting statements for (almost) all pure partially entangled states. Our result consists of the explicit construction of local quantum channels for the two players, from which we derive operator inequalities that we verify numerically. Using a recently developed method, the improved bounds can be inferred. Furthermore, we construct a state that violates the CHSH inequality but for which there exist no local quantum channels that achieve greater fidelity than a trivial lower bound (i.e. achieve fidelity with the singlet greater than what is achievable using a separable state). This result implies that CHSH violation is not sufficient for the two players to `extract' a singlet from their actual state by just local operations. Future research could focus on extending our results to different selftestable states such as the GHZstates and on selftesting in the scenario where only one of the two players has a potentially untrusted device (quantum steering).
Item Type:  Report 

Report Nr:  MoL201703 
Series Name:  Master of Logic Thesis (MoL) Series 
Year:  2017 
Uncontrolled Keywords:  selftesting, extractability, deviceindependence, quantum cryptography 
Subjects:  Computation Logic 
Depositing User:  Dr Marco Vervoort 
Date Deposited:  22 Jun 2017 15:34 
Last Modified:  13 Jul 2017 13:27 
URI:  https://eprints.illc.uva.nl/id/eprint/1539 
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