The quantum Fisher information (QFI) represents a fundamental concept in quantum physics. On the one hand, it quantifies the metrological potential of quantum states in quantum-parameter-estimation measurements. On the other hand, it is intrinsically
related to the quantum geometry and multipartite entanglement of many-body systems. Here, we explore how the QFI can be estimated via randomized measurements, an approach which has the advantage of being applicable to both pure and mixed quantum states. In the latter case, our method gives access to the sub-quantum Fisher information, which sets a lower bound on the QFI. We experimentally validate this approach using two platforms: a nitrogen-vacancy center spin in diamond and a 4-qubit state provided by a superconducting quantum computer. We further perform a numerical study on a many-body spin system to illustrate the advantage of our randomized-measurement approach in estimating multipartite entanglement, as compared to quantum state tomography. Our results highlight the general applicability of our method to general quantum platforms, including solid-state spin systems, superconducting quantum computers and trapped ions, hence providing a versatile tool to explore the essential role of the QFI in quantum physics.
In this paper, we propose FairCrowd, a private, fair, and verifiable framework for aggregate statistics in mobile crowdsensing based on the public blockchain. In specific, mobile users are incentivized to collect and share private data values (e.g.,
current locations) to fufill a commonly interested task released by a customer, and the crowdsensing server computes aggregate statistics over the values of mobile users (e.g., the most popular location) for the customer. By utilizing the ElGamal encryption, the server learns nearly nothing about the private data or the statistical result. The correctness of aggregate statistics can be publicly verified by using a new efficient and verifiable computation approach. Moreover, the fairness of incentive is guaranteed based on the public blockchain in the presence of greedy service provider, customers, and mobile users, who may launch payment-escaping, payment-reduction, free-riding, double-reporting, and Sybil attacks to corrupt reward distribution. Finally, FairCrowd is proved to achieve verifiable aggregate statistics with privacy preservation for mobile users. Extensive experiments are conducted to demonstrate the high efficiency of FairCrowd for aggregate statistics in mobile crowdsensing.
