Quantum state nullifiers as an alternative to fidelity

Abstract:

Quantum technologies, the practical application of quantum information theory, employ quantum systems in specific quantum states to achieve effects surpassing classical methods. IT therefore follows that quantum states serve as the main resource and a great deal of research goes into theoretical design and experimental preparation of specific states. With this also comes the task of telling whether some unknown quantum state is what we need it to be, a task traditionally fulfilled by fidelity.

However, fidelity has some drawbacks, especially for continuous variable systems. Even when it is not ill defined, it requires a full quantum state tomography, making it problematic for rigorous verification. In this talk we show that these drawbacks can be removed by replacing fidelity by quantum state nullifiers - mean values of suitably chosen positive semi-definite hermitian operators.