Deriving Bell inequalities for target states and measurements

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ID: 810 6760 4076

Code: 628975

Abstract

Bell inequalities play a key role in certifying quantum properties for device-independent quantum information protocols. It is still a major challenge, however, to devise Bell inequalities tailored for an arbitrary given quantum state and/or measurement. In this presentation, we will dive into two methods aiming at two sightly different tasks. First, we will focus on the use of the variational method in order to restrict the range of relevant inequalities for a fixed choice of state and measurements. This method can allow for the derivations of all possible self-test for a given realization. Second, we will show how a sum of square property can be enforced for an arbitrary target state by making an appropriate choice of nullifiers, which is made possible by leaving freedom in the choice of measurement. Using this method allows finding simple Bell inequalities for several families of quantum states, including partially entangled multipartite GHZ states and qutrit states. In most cases, we are able to prove that the constructed Bell inequalities achieve self-testing of the target state.

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