Tensor Norms and the Classical Communication Complexity of Nonlocal Quantum Measurement

We initiate the study of quantifying nonlocalness of a bipartite measurement by the minimum amount of classical communication required to simulate the measurement. We derive general upper bounds, which are expressed in terms of certain tensor norms of the measurement operator. As applications, we show that (a) If the amount of communication is constant, quantum and classical communication protocols with unlimited amount of shared entanglement or shared randomness compute the same set of functions; (b) A local hidden variable model needs only a constant amount of communication to create, within an arbitrarily small statistical distance, a distribution resulted from local measurements of an entangled quantum state, as long as the number of measurement outcomes is constant.Comment: A preliminary version of this paper appears as part of an article in Proceedings of the the 37th ACM Symposium on Theory of Computing (STOC 2005), 460--467, 200

Quantum Communication Complexity and Nonlocality of Bipartite Quantum Operations.

This dissertation is motivated by the following fundamental questions: (a) are there any exponential gaps between quantum and classical communication complexities? (b) what is the role of entanglement in assisting quantum communications? (c) how to characterize the nonlocality of quantum operations? We study four specific problems below. 1. The communication complexity of the Hamming Distance problem. The Hamming Distance problem is for two parties to determine whether or not the Hamming distance between two n-bit strings is more than a given threshold. We prove tighter quantum lower bounds in the general two-party, interactive communication model. We also construct an efficient classical protocol in the more restricted Simultaneous Message Passing model, improving previous results. 2. The Log-Equivalence Conjecture. A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical ones for computing a total Boolean function in the two-party, interactive model. The answer is believed to be No. Razborov proved this conjecture for the most general class of functions so far. We prove this conjecture for a broader class of functions that we called block-composed functions. Our proof appears to be the first demonstration of the dual approach of the polynomial method in proving new results. 3. Classical simulations of bipartite quantum measurement. We define a new ix concept that measures the nonlocality of bipartite quantum operations. From this measure, we derive an upper bound that shows the limitation of entanglement in reducing communication costs. 4. The maximum tensor norm of bipartite superoperators. We define a maximum tensor norm to quantify the nonlocality of bipartite superoperators. We show that a bipartite physically realizable superoperator is bi-local if and only if its maximum tensor norm is 1. Furthermore, the estimation of the maximum tensor norm can also be used to prove quantum lower bounds on communication complexities.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58538/1/yufanzhu_1.pd

Trifolirhizin relieves renal injury in a diabetic nephropathy model by inducing autophagy and inhibiting oxidative stress through the regulation of PI3K/AKT/mTOR pathway

Purpose: To evaluate the effects of trifolirhizin on diabetic nephropathy (DN), and the mechanism of action. Methods: Male db/db mice (8 weeks, n = 24) and age-matched control mice (n = 6) were obtained. The mice were further divided into four groups and administered increasing doses of trifolirhizin (0, 12.5, 25 and 50 mg/kg). Histological analysis of renal tissues were performed by H & E staining. Blood urea nitrogen (BUN) and creatinine were determined using enzyme-linked immunosorbent assay (ELISA). Immunoblot and TUNEL assay were performed to investigate the effect of trifolirhizin on autophagy and apoptosis, while ELISA and dihydroethidium (DHE) staining were conducted to evaluate reactive oxygen species (ROS), malondialdehyde (MDA) and superoxide dismutase (SOD) levels. The effect of trifolirhizin on PI3K/AKT/mTOR pathway was determined using Immunoblot assays. Results: Trifolirhizin alleviated renal injury in diabetic mice, and also activate autophagy and inhibited apoptosis in the renal tissues in diabetic mice (p < 0.001). In addition, trifolirhizin inhibited the oxidative stress response in the renal tissue in diabetic mice (p < 0.001). Trifolirhizin further inhibited PI3K/AKT/mTOR pathway and therefore relieved renal injury in the diabetic nephropathy model (p < 0.001). Conclusion: Trifolirhizin alleviates renal injury in diabetic mice, activates autophagy, and inhibits apoptosis in renal tissue of diabetic mice. Therefore, trifolirhizin is a promising a promising drug for the treatment of DN

The Communication Complexity of the Hamming Distance Problem

We investigate the randomized and quantum communication complexity of the Hamming Distance problem, which is to determine if the Hamming distance between two n-bit strings is no less than a threshold d. We prove a quantum lower bound of \Omega(d) qubits in the general interactive model with shared prior entanglement. We also construct a classical protocol of O(d \log d) bits in the restricted Simultaneous Message Passing model, improving previous protocols of O(d^2) bits (A. C.-C. Yao, Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, pp. 77-81, 2003), and O(d\log n) bits (D. Gavinsky, J. Kempe, and R. de Wolf, quant-ph/0411051, 2004).Comment: 8 pages, v3, updated reference. to appear in Information Processing Letters, 200

Shifted Diffusion for Text-to-image Generation

We present Corgi, a novel method for text-to-image generation. Corgi is based on our proposed shifted diffusion model, which achieves better image embedding generation from input text. Unlike the baseline diffusion model used in DALL-E 2, our method seamlessly encodes prior knowledge of the pre-trained CLIP model in its diffusion process by designing a new initialization distribution and a new transition step of the diffusion. Compared to the strong DALL-E 2 baseline, our method performs better in generating image embedding from the text in terms of both efficiency and effectiveness, resulting in better text-to-image generation. Extensive large-scale experiments are conducted and evaluated in terms of both quantitative measures and human evaluation, indicating a stronger generation ability of our method compared to existing ones. Furthermore, our model enables semi-supervised and language-free training for text-to-image generation, where only part or none of the images in the training dataset have an associated caption. Trained with only 1.7% of the images being captioned, our semi-supervised model obtains FID results comparable to DALL-E 2 on zero-shot text-to-image generation evaluated on MS-COCO. Corgi also achieves new state-of-the-art results across different datasets on downstream language-free text-to-image generation tasks, outperforming the previous method, Lafite, by a large margin