Prostate cancer affects a large part of the western male population. The need for an early and accurate detection is thus a great challenge in common clinical practice, but the lack of specificity of the serum marker PSA (Prostate Specific Antigen) is a serious problem since its increased concentration can be related to several abnormalities. PSA, however, is found in serum in both a free and a complexed form with other proteins and the percentage amount of unbound PSA (the free-to-total PSA ratio) can be employed to distinguish prostate cancer from benign prostatic conditions, and also to predict the future risk of prostate cancer. To improve the operating characteristics of current PSA tests and to provide a clinical tool able to run label-free and sensitive analysis, we thus developed a biosensing platform based on Electrochemical Impedance Spectroscopy (EIS), which allows the contemporary detection of free and total PSA on a single biochip, enabling a quick screening for the risk of prostate cancer thanks to the presence of two different immobilized antibodies specific for the different antigens researched.

We show how the resource theory of magic quantifies the hardness of quantum certification protocols. In particular, the resources needed for a direct fidelity estimation grow exponentially with the stabilizer Rényi entropy[1]: the more the magic, the harder the certification. Remarkably, the verification turns out to be polynomially feasible only for those states which are shown to be useless to attain any quantum advantage. We then extend our results to quantum evolutions, showing that the resources needed to certify the quality of the application of a given unitary U are governed by the magic in the Choi state associated with U, which is shown to possess a profound connection with out-of-time order correlators.

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Magic states are the resource that allows quantum computers to attain an advantage over classical computers. This resource consists in the deviation from a property called stabilizerness which in turn implies that stabilizer circuits can be efficiently simulated on a classical computer. Without magic, no quantum computer can do anything that a classical computer cannot do. Given the importance of magic for quantum computation, it would be useful to have a method for measuring the amount of magic in a quantum state. In this work, we propose and experimentally demonstrate a protocol for measuring magic based on randomized measurements. Our experiments are carried out on two IBM Quantum Falcon processors. This protocol can provide a characterization of the effectiveness of a quantum hardware in producing states that cannot be effectively simulated on a classical computer. We show how from these measurements one can construct realistic noise models affecting the hardware.