Tripartite entanglement measure under local operation and classical communications

Multipartite entanglement is an indispensable resource in quantum communication and computation, however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work, we study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement for the three-qubit system in [S. Xie {\it et al.}, Phys. Rev. Lett. \textbf{127}. 040403 (2021)]. First, we use the well-known three-tangle and bipartite concurrence to reformulate this quantifier for all pure states. We then construct an explicit example to conclusively show the concurrence fill can be increased under local operation and classical communications (LOCCs) {\it on average}, implying it is not an entanglement monotone. Moreover, we give a simple proof of the LOCC-monotonicity of three-tangle and find that the bipartite concurrence and the squared can have distinct performances under the same LOCCs. Finally, we propose a reliable monotone to quantify genuine tripartite entanglement, which can also be easily generalised to the multipartite system. Our results shed light on studying genuine entanglement and also reveal the complex structure of multipartite systems.Comment: 6 pages and 1 figure; Comments are welcom

Ultrafast quantum state tomography with feed-forward neural networks

Reconstructing the state of many-body quantum systems is of fundamental importance in quantum information tasks, but extremely challenging due to the curse of dimensionality. In this work, we present a quantum tomography approach based on neural networks to achieve the ultrafast reconstruction of multi-qubit states. Particularly, we propose a simple 3-layer feed-forward network to process the experimental data generated from measuring each qubit with a positive operator-valued measure, which is able to reduce the storage cost and computational complexity. Moreover, the techniques of state decomposition and $P$-order absolute projection are jointly introduced to ensure the positivity of state matrices learned in the maximum likelihood function and to improve the convergence speed and robustness of the above network. Finally, it is tested on a large number of states with a wide range of purity to show that we can faithfully tomography 11-qubit states on a laptop within 2 minutes under noise. Our numerical results also demonstrate that more state samples are required to achieve the given tomography fidelity for the low-purity states, and the increased depolarizing noise induces a linear decrease in the tomography fidelity

Immunophenotyping in BK Virus Allograft Nephropathy Distinct from Acute Rejection

Differentiating BK virus nephropathy (BKVN) from acute rejection (AR) is crucial in clinical practice, as both of them have interstitial inflammation in the grafts. The purpose of the study is to describe the inflammatory cellular constituents of BKVN and to determine the clinical utility of immunophenotyping findings in distinguishing BKVN from AR. In addition, the expression of the HLA-DR was investigated. Sixty-five renal allograft recipients were included in this study, including 22 cases of BKVN, 31 cases of AR, and 12 cases of stable allograft. Immunostaining for infiltrating lymphocytes showed that the number of CD20 cells (P<0.001) and the percentages of CD3 (P<0.001), CD4 (P=0.004), CD8 (P=0.005), and CD20 (P=0.002) cells were all significantly different between BKVN and AR. Moreover, there were no statistically significant differences in tubule cell HLA-DR expression (P=0.156). This observation suggests that the number of CD20 cells and the percentages of CD3, CD4, CD8, and CD20 cells in renal biopsies would aid the distinction between BKVN and AR. On the other hand, the presence of HLA-DR upregulation may not only be specific for acute rejection but also be a response to BKVN

Differential expression of the catalytic subunits for PP-1 and PP-2A and the regulatory subunits for PP–2A in mouse eye

Purpose: Reversible protein phosphorylation is a fundamental regulatory mechanism in all biologic processes. Protein serine/threonine phosphatases-1 (PP-1) and 2A (PP-2A) account for 90% of serine/threonine phosphatase activity in eukaryote cells and play distinct roles in regulating multiple cellular processes and activities. Our previous studies have established the expression patterns of the catalytic subunits for PP-1 (PP-1cs) and PP-2A (PP-2Acs) in bovine and rat lenses. In the present study, we have determined the expression patterns of PP-1cs (PP-1α and PP-1β) and PP-2Acs (PP-2Aα and PP-2Aβ) in the retina and cornea along with the ocular lens of the mouse eye. Moreover, since the function of PP-2A is largely relied on its regulatory subunits, we have also analyzed the expression patterns of the genes encoding the scaffold A subunits of PP-2A, PP2A-Aα and PP2A-Aβ, and the regulatory B family subunits of PP-2A, PP2A-Bα, PP2A-Bβ, and PP2A-Bγ. In addition, we have also demonstrated the differential protections of PP-1 and PP-2A in mouse lens epithelial cell line, αTN4-1, against oxidative stress-induced apoptosis. Methods: Total RNAs and proteins were extracted from the retina, lens epithelium, lens fiber cells, and cornea of the mouse eye. Reverse transcription polymerase chain reaction (RT-PCR) and real time PCR were used to detect the mRNA expression. Western blot and immunohistochemistry analysis were applied to examine the protein expression and distribution. Stable clones of αTN4-1 cells expressing either PP-1α or PP-2Aα were used to analyze the differential protections against oxidative stress-induced apoptosis. Results: PP-1 is more abundant than PP-2A in the mouse eye. The catalytic subunits for PP-1 and PP-2A display similar expression patterns in the retina and cornea but much reduced in the lens. The mRNAs for all five isoforms of PP2A-A and PP2A-B subunits are highly expressed in the retina, but only three out of the five mRNAs are expressed in the cornea. In the ocular lens, only PP2A-Aβ and PP2A-Bγ mRNAs are clearly detectable. The A and B subunit proteins of PP-2A are highly expressed in the retina and cornea but are much reduced in the ocular lens. PP2A-Aα/β are differentially distributed in the mouse retina. When transfected into mouse lens epithelial cells, αTN4-1, PP-1α and PP-2Aα display differential protection against oxidative stress-induced apoptosis. Conclusions: Our results lead to the following conclusions regarding PP-1 and PP-2A in mouse eye: 1) PP1 is a more abundant phosphatase than PP-2A; 2) both PP-1 and PP-2A may play important roles, and the functions of PP-2A appear to be highly regulated by various regulatory subunits; and 3) the genes encoding PP-1α/β, PP-2Aα/ β, PP-2A-Aα/β, and PP-2A-B α/β/γ are all differentially expressed

Experimental verification of the steering ellipsoid zoo via two-qubit states

Quantum steering ellipsoid visualizes the set of all qubit states that can be steered by measuring on another correlated qubit in the Bloch picture. Together with local reduced states, it provides a faithful geometric characterization of the underlying two-qubit state so that almost all nonclassical state features can be reflected in its geometric properties. Consequently, the various types of quantum ellipsoids with different geometric properties form an ellipsoid zoo, which, in this work, is experimentally verified via measurements on many polarization-path photonic states. By generating two-qubit states with high fidelity, the corresponding ellipsoids are constructed to certify the presence of entanglement, one-way Einstein-Podolsky-Rosen steering, discord, and steering incompleteness. It is also experimentally verified that the steering ellipsoid can be reconstructed from using the twelve vertices of the icosahedron as measurement directions. Our results aid progress in applying the quantum steering ellipsoid to reveal nonclassical features of the multi-qubit system