Certifying the dimension of classical and quantum systems in a prepare-and-measure scenario with independent devices.
We consider the problem of testing the dimension of uncharacterized classical and quantum systems in a prepare-and-measure setup. Here we assume the preparation and measurement devices to be independent, thereby making the problem nonconvex. We present a simple method for generating nonlinear dimension witnesses for systems of arbitrary dimension. The simplest of our witnesses is highly robust to technical imperfections, and can certify the use of qubits in the presence of arbitrary noise and arbitrarily low detection efficiency. Finally, we show that this witness can be used to certify the presence of randomness, suggesting applications in quantum information processing.
Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland.
Joseph
J
Bowles
Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland.
Marco Túlio
MT
Quintino
Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland and H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom.
Nicolas
N
Brunner