The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial transpose (PPT) criterion and the k-symmetric extendibility criterion to tackle this problem in practice, none of them enables a general, effective solution to the problem even for small dimensions. Explicitly, separable states form a high-dimensional convex set, which exhibits a vastly complicated structure. In this work, we build a new separability-entanglement classifier underpinned by machine learning techniques. Our method outperforms the existing methods in generic cases in terms of both speed and accuracy, opening up the avenues to explore quantum entanglement via the machine learning approach.

In this paper, we discuss the connection between two genuinely quantum phenomena-the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit.

Identification in a regression discontinuity (RD) research design hinges on the discontinuity in the probability of treatment when a covariate (assignment variable) exceeds a known threshold. When the assignment variable is measured with error, however, the discontinuity in the relationship between the probability of treatment and the observed mismeasured assignment variable may disappear. Therefore, the presence of measurement error in the assignment variable poses a direct challenge to treatment effect identification. This paper provides sufficient conditions to identify the RD treatment effect using the mismeasured assignment variable, the treatment status and the outcome variable. We prove identification separately for discrete and continuous assignment variables and study the properties of various estimation procedures. We illustrate the proposed methods in an empirical application, where we estimate Medicaid takeup and its crowdout effect on private health insurance coverage.JEL codes: C10, C18

Mammograms are difficult to interpret, especially of cancers at their early stages. In this paper, we analyze the effectiveness of our adaptive neighborhood contrast enhancement (ANCE) technique in increasing the sensitivity of breast cancer diagnosis. Seventy-eight screen-film mammograms of 21 difficult cases (14 benign and seven malignant), 222 screen-film mammograms of 28 interval cancer patients and six benign control cases were digitized with a high-resolution of about 4096 x 2048 x 10-bit pixels and then processed with the ANCE method. Unprocessed and processed digitized mammograms as well as the original films were presented to six experienced radiologists for a receiver operating characteristic (ROC) evaluation for the difficult case set and to three reference radiologists for the interval cancer set. The results show that the radiologists' performance with the ANCE-processed images is the best among the three sets of images (original, digitized, and enhanced) in terms of area under the ROC curve and that diagnostic sensitivity is improved by the ANCE algorithm. All of the 19 interval cancer cases not detected with the original films of earlier mammographic examinations were diagnosed as malignant with the corresponding ANCE-processed versions, while only one of the six benign cases initially labeled correctly with the original mammograms was interpreted as malignant after enhancement. McNemar's tests of symmetry indicated that the diagnostic confidence for the interval cancer cases was improved by the ANCE procedure with a high level of statistical significance (p-values of 0.0001-0.005) and with no significant effect on the diagnosis of the benign control cases (p-values of 0.08-0.1). This study demonstrates the potential for improvement of diagnostic performance in early detection of breast cancer with digital image enhancement.

Genuine multipartite entanglement is of great importance in quantum information, especially from the experimental point of view. Nevertheless, it is difficult to construct genuine multipartite entangled states systematically, because the genuine multipartite entanglement is unruly. We propose another product based on the Kronecker product in this paper. The Kronecker product is a common product in quantum information with good physical interpretation. We mainly investigate whether the proposed product of two genuine multipartite entangled states is still a genuine entangled one. We understand the entanglement of the proposed product better by characterizing the entanglement of the Kronecker product. Then we show the proposed product is a genuine multipartite entangled state in two cases. The results provide a systematical method to construct genuine multipartite entangled states of more parties. Contents