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Junde Wu

Junde Wu appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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quant-phmath-phmath.MPComputer Visionmath.OAeess.IVmath.APArtificial IntelligenceMachine Learningmath.FA

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Published work

43 published item(s)

preprint2026arXiv

BioMedArena: An Open-source Toolkit for Building and Evaluating Biomedical Deep Research Agents

Building a deep research agent today is an exercise in glue code: the same backbone evaluated on the same benchmark can report different accuracies in different papers because harness and tool registry all differ, and integrating a new foundation model into a comparable evaluation surface costs weeks of model-specific engineering. We call this the per-paper engineering tax and release BioMedArena, an open-source toolkit that not only alleviates it but also provides an arena for fair comparison of different foundation models when evaluating them as deep-research agents. BioMedArena decouples six layers of biomedical agent evaluation -- benchmark loading, tool exposure, tool selection, execution mode, context management, and scoring -- and exposes 147 biomedical benchmarks and 75 biomedical tools across 9 functional families. Adding a new model, benchmark, or tool reduces to registering a few-line provider adapter. We further provide 6 agent harnesses with 6 context-management strategies, which provide 12 backbones with competitive research capabilities and significantly improved performance, achieving state-of-the-art (SOTA) results on 8 representative biomedical benchmarks, with an average lift of +15.03 percentage points over prior SOTA. The toolkit, configurations, and per-task traces are available at https://github.com/AI-in-Health/BioMedArena

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preprint2023arXiv

Medical SAM Adapter: Adapting Segment Anything Model for Medical Image Segmentation

The Segment Anything Model (SAM) has recently gained popularity in the field of image segmentation due to its impressive capabilities in various segmentation tasks and its prompt-based interface. However, recent studies and individual experiments have shown that SAM underperforms in medical image segmentation, since the lack of the medical specific knowledge. This raises the question of how to enhance SAM's segmentation capability for medical images. In this paper, instead of fine-tuning the SAM model, we propose the Medical SAM Adapter (Med-SA), which incorporates domain-specific medical knowledge into the segmentation model using a light yet effective adaptation technique. In Med-SA, we propose Space-Depth Transpose (SD-Trans) to adapt 2D SAM to 3D medical images and Hyper-Prompting Adapter (HyP-Adpt) to achieve prompt-conditioned adaptation. We conduct comprehensive evaluation experiments on 17 medical image segmentation tasks across various image modalities. Med-SA outperforms several state-of-the-art (SOTA) medical image segmentation methods, while updating only 2\% of the parameters. Our code is released at https://github.com/KidsWithTokens/Medical-SAM-Adapter.

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preprint2023arXiv

MedSegDiff: Medical Image Segmentation with Diffusion Probabilistic Model

Diffusion probabilistic model (DPM) recently becomes one of the hottest topic in computer vision. Its image generation application such as Imagen, Latent Diffusion Models and Stable Diffusion have shown impressive generation capabilities, which aroused extensive discussion in the community. Many recent studies also found it is useful in many other vision tasks, like image deblurring, super-resolution and anomaly detection. Inspired by the success of DPM, we propose the first DPM based model toward general medical image segmentation tasks, which we named MedSegDiff. In order to enhance the step-wise regional attention in DPM for the medical image segmentation, we propose dynamic conditional encoding, which establishes the state-adaptive conditions for each sampling step. We further propose Feature Frequency Parser (FF-Parser), to eliminate the negative effect of high-frequency noise component in this process. We verify MedSegDiff on three medical segmentation tasks with different image modalities, which are optic cup segmentation over fundus images, brain tumor segmentation over MRI images and thyroid nodule segmentation over ultrasound images. The experimental results show that MedSegDiff outperforms state-of-the-art (SOTA) methods with considerable performance gap, indicating the generalization and effectiveness of the proposed model. Our code is released at https://github.com/WuJunde/MedSegDiff.

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preprint2022arXiv

Calibrate the inter-observer segmentation uncertainty via diagnosis-first principle

On the medical images, many of the tissues/lesions may be ambiguous. That is why the medical segmentation is typically annotated by a group of clinical experts to mitigate the personal bias. However, this clinical routine also brings new challenges to the application of machine learning algorithms. Without a definite ground-truth, it will be difficult to train and evaluate the deep learning models. When the annotations are collected from different graders, a common choice is majority vote. However such a strategy ignores the difference between the grader expertness. In this paper, we consider the task of predicting the segmentation with the calibrated inter-observer uncertainty. We note that in clinical practice, the medical image segmentation is usually used to assist the disease diagnosis. Inspired by this observation, we propose diagnosis-first principle, which is to take disease diagnosis as the criterion to calibrate the inter-observer segmentation uncertainty. Following this idea, a framework named Diagnosis First segmentation Framework (DiFF) is proposed to estimate diagnosis-first segmentation from the raw images.Specifically, DiFF will first learn to fuse the multi-rater segmentation labels to a single ground-truth which could maximize the disease diagnosis performance. We dubbed the fused ground-truth as Diagnosis First Ground-truth (DF-GT).Then, we further propose Take and Give Modelto segment DF-GT from the raw image. We verify the effectiveness of DiFF on three different medical segmentation tasks: OD/OC segmentation on fundus images, thyroid nodule segmentation on ultrasound images, and skin lesion segmentation on dermoscopic images. Experimental results show that the proposed DiFF is able to significantly facilitate the corresponding disease diagnosis, which outperforms previous state-of-the-art multi-rater learning methods.

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preprint2022arXiv

Characterizing entanglement using quantum discord over state extensions

We propose a framework to characterize entanglement with quantum discord, both asymmetric and symmetric, over state extensions. In particular, we show that the minimal Bures distance of discord over state extensions is equivalent to Bures distance of entanglement. This equivalence places quantum discord at a more primitive position than entanglement conceptually in the sense that entanglement can be interpreted as an irreducible part of discord over all state extensions. Based on this equivalence, we also offer an operational meaning of Bures distance of entanglement by connecting it to quantum state discriminations. Moreover, for the relative entropy part, we prove that the entanglement measure introduced by Devi and Rajagopal [A. R. U. Devi and A. K. Rajagopal, Phys. Rev. Lett. 100, 140502 (2008)] is actually equivalent to the relative entropy of entanglement. We also provide several quantifications of entanglement based on discord measures.

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preprint2022arXiv

Contrastive Centroid Supervision Alleviates Domain Shift in Medical Image Classification

Deep learning based medical imaging classification models usually suffer from the domain shift problem, where the classification performance drops when training data and real-world data differ in imaging equipment manufacturer, image acquisition protocol, patient populations, etc. We propose Feature Centroid Contrast Learning (FCCL), which can improve target domain classification performance by extra supervision during training with contrastive loss between instance and class centroid. Compared with current unsupervised domain adaptation and domain generalization methods, FCCL performs better while only requires labeled image data from a single source domain and no target domain. We verify through extensive experiments that FCCL can achieve superior performance on at least three imaging modalities, i.e. fundus photographs, dermatoscopic images, and H & E tissue images.

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preprint2022arXiv

Dataset and Evaluation algorithm design for GOALS Challenge

Glaucoma causes irreversible vision loss due to damage to the optic nerve, and there is no cure for glaucoma.OCT imaging modality is an essential technique for assessing glaucomatous damage since it aids in quantifying fundus structures. To promote the research of AI technology in the field of OCT-assisted diagnosis of glaucoma, we held a Glaucoma OCT Analysis and Layer Segmentation (GOALS) Challenge in conjunction with the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI) 2022 to provide data and corresponding annotations for researchers studying layer segmentation from OCT images and the classification of glaucoma. This paper describes the released 300 circumpapillary OCT images, the baselines of the two sub-tasks, and the evaluation methodology. The GOALS Challenge is accessible at https://aistudio.baidu.com/aistudio/competition/detail/230.

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preprint2022arXiv

One Hyper-Initializer for All Network Architectures in Medical Image Analysis

Pre-training is essential to deep learning model performance, especially in medical image analysis tasks where limited training data are available. However, existing pre-training methods are inflexible as the pre-trained weights of one model cannot be reused by other network architectures. In this paper, we propose an architecture-irrelevant hyper-initializer, which can initialize any given network architecture well after being pre-trained for only once. The proposed initializer is a hypernetwork which takes a downstream architecture as input graphs and outputs the initialization parameters of the respective architecture. We show the effectiveness and efficiency of the hyper-initializer through extensive experimental results on multiple medical imaging modalities, especially in data-limited fields. Moreover, we prove that the proposed algorithm can be reused as a favorable plug-and-play initializer for any downstream architecture and task (both classification and segmentation) of the same modality.

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preprint2022arXiv

Progressive Hard-case Mining across Pyramid Levels for Object Detection

In object detection, multi-level prediction (e.g., FPN) and reweighting skills (e.g., focal loss) have drastically improved one-stage detector performance. However, the synergy between these two techniques is not fully explored in a unified framework. We find that, during training, the one-stage detector's optimization is not only restricted to the static hard-case mining loss (gradient drift) but also suffered from the diverse positive samples' proportions split by different pyramid levels (level discrepancy). Under this concern, we propose Hierarchical Progressive Focus (HPF) consisting of two key designs: 1) progressive focus, a more flexible hard-case mining setting calculated adaptive to the convergence progress, 2) hierarchical sampling, automatically generating a set of progressive focus for level-specific target optimization. Based on focal loss with ATSS-R50, our approach achieves 40.5 AP, surpassing the state-of-the-art QFL (Quality Focal Loss, 39.9 AP) and VFL (Varifocal Loss, 40.1 AP). Our best model achieves 55.1 AP on COCO test-dev, obtaining excellent results with only a typical training setting. Moreover, as a plug-and-play scheme, HPF can cooperate well with recent advances, providing a stable performance improvement on nine mainstream detectors.

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preprint2022arXiv

REFUGE2 Challenge: A Treasure Trove for Multi-Dimension Analysis and Evaluation in Glaucoma Screening

With the rapid development of artificial intelligence (AI) in medical image processing, deep learning in color fundus photography (CFP) analysis is also evolving. Although there are some open-source, labeled datasets of CFPs in the ophthalmology community, large-scale datasets for screening only have labels of disease categories, and datasets with annotations of fundus structures are usually small in size. In addition, labeling standards are not uniform across datasets, and there is no clear information on the acquisition device. Here we release a multi-annotation, multi-quality, and multi-device color fundus image dataset for glaucoma analysis on an original challenge -- Retinal Fundus Glaucoma Challenge 2nd Edition (REFUGE2). The REFUGE2 dataset contains 2000 color fundus images with annotations of glaucoma classification, optic disc/cup segmentation, as well as fovea localization. Meanwhile, the REFUGE2 challenge sets three sub-tasks of automatic glaucoma diagnosis and fundus structure analysis and provides an online evaluation framework. Based on the characteristics of multi-device and multi-quality data, some methods with strong generalizations are provided in the challenge to make the predictions more robust. This shows that REFUGE2 brings attention to the characteristics of real-world multi-domain data, bridging the gap between scientific research and clinical application.

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preprint2022arXiv

SeATrans: Learning Segmentation-Assisted diagnosis model via Transformer

Clinically, the accurate annotation of lesions/tissues can significantly facilitate the disease diagnosis. For example, the segmentation of optic disc/cup (OD/OC) on fundus image would facilitate the glaucoma diagnosis, the segmentation of skin lesions on dermoscopic images is helpful to the melanoma diagnosis, etc. With the advancement of deep learning techniques, a wide range of methods proved the lesions/tissues segmentation can also facilitate the automated disease diagnosis models. However, existing methods are limited in the sense that they can only capture static regional correlations in the images. Inspired by the global and dynamic nature of Vision Transformer, in this paper, we propose Segmentation-Assisted diagnosis Transformer (SeATrans) to transfer the segmentation knowledge to the disease diagnosis network. Specifically, we first propose an asymmetric multi-scale interaction strategy to correlate each single low-level diagnosis feature with multi-scale segmentation features. Then, an effective strategy called SeA-block is adopted to vitalize diagnosis feature via correlated segmentation features. To model the segmentation-diagnosis interaction, SeA-block first embeds the diagnosis feature based on the segmentation information via the encoder, and then transfers the embedding back to the diagnosis feature space by a decoder. Experimental results demonstrate that SeATrans surpasses a wide range of state-of-the-art (SOTA) segmentation-assisted diagnosis methods on several disease diagnosis tasks.

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preprint2022arXiv

Solvable dilation model of $\cal PT$-symmetric systems

The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present a simple yet non-trivial exactly solvable dilation problem with two dimensional time-dependent $\cal PT$-symmetric Hamiltonian. Our system is initially set in the unbroken $\cal PT$-symmetric phase and later goes across the so-called exceptional point and enters the broken $\cal PT$-symmetric phase. For this system, the dilated Hamiltonian and the evolution of $\cal PT$-symmetric system are analytically worked out. Our result clearly showed that the exceptional points do not have much physical relevance in a \textit{time-dependent} system.

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preprint2022arXiv

The Local Orthogonality between Quantum States and Entanglement Decomposition

In the paper, we show that when a quantum state can be decomposed as a convex combination of locally orthogonal mixed states, its entanglement can be decomposed into the entanglement of these mixed states without losing them. The obtained result generalizes a corresponding one proved by Horodecki [Acta Phys. Slov. 48, 141 (1998).]. But, for the entanglement cost it requires certain conditions for holding the decomposition, and the distillable entanglement only has a week result as inequality. Finally, we presented an example to show that the conditions of our conclusions are existence.

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preprint2022arXiv

Universal, transferable and targeted adversarial attacks

Deep Neural Networks have been found vulnerable re-cently. A kind of well-designed inputs, which called adver-sarial examples, can lead the networks to make incorrectpredictions. Depending on the different scenarios, goalsand capabilities, the difficulties of the attacks are different.For example, a targeted attack is more difficult than a non-targeted attack, a universal attack is more difficult than anon-universal attack, a transferable attack is more difficultthan a nontransferable one. The question is: Is there existan attack that can meet all these requirements? In this pa-per, we answer this question by producing a kind of attacksunder these conditions. We learn a universal mapping tomap the sources to the adversarial examples. These exam-ples can fool classification networks to classify all of theminto one targeted class, and also have strong transferability.Our code is released at: xxxxx.

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preprint2020arXiv

Leveraging Undiagnosed Data for Glaucoma Classification with Teacher-Student Learning

Recently, deep learning has been adopted to the glaucoma classification task with performance comparable to that of human experts. However, a well trained deep learning model demands a large quantity of properly labeled data, which is relatively expensive since the accurate labeling of glaucoma requires years of specialist training. In order to alleviate this problem, we propose a glaucoma classification framework which takes advantage of not only the properly labeled images, but also undiagnosed images without glaucoma labels. To be more specific, the proposed framework is adapted from the teacher-student-learning paradigm. The teacher model encodes the wrapped information of undiagnosed images to a latent feature space, meanwhile the student model learns from the teacher through knowledge transfer to improve the glaucoma classification. For the model training procedure, we propose a novel training strategy that simulates the real-world teaching practice named as 'Learning To Teach with Knowledge Transfer (L2T-KT)', and establish a 'Quiz Pool' as the teacher's optimization target. Experiments show that the proposed framework is able to utilize the undiagnosed data effectively to improve the glaucoma prediction performance.

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preprint2020arXiv

TR-GAN: Topology Ranking GAN with Triplet Loss for Retinal Artery/Vein Classification

Retinal artery/vein (A/V) classification lays the foundation for the quantitative analysis of retinal vessels, which is associated with potential risks of various cardiovascular and cerebral diseases. The topological connection relationship, which has been proved effective in improving the A/V classification performance for the conventional graph based method, has not been exploited by the deep learning based method. In this paper, we propose a Topology Ranking Generative Adversarial Network (TR-GAN) to improve the topology connectivity of the segmented arteries and veins, and further to boost the A/V classification performance. A topology ranking discriminator based on ordinal regression is proposed to rank the topological connectivity level of the ground-truth, the generated A/V mask and the intentionally shuffled mask. The ranking loss is further back-propagated to the generator to generate better connected A/V masks. In addition, a topology preserving module with triplet loss is also proposed to extract the high-level topological features and further to narrow the feature distance between the predicted A/V mask and the ground-truth. The proposed framework effectively increases the topological connectivity of the predicted A/V masks and achieves state-of-the-art A/V classification performance on the publicly available AV-DRIVE dataset.

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preprint2019arXiv

Integrating neural networks into the blind deblurring framework to compete with the end-to-end learning-based methods

Recently, end-to-end learning-based methods based on deep neural network (DNN) have been proven effective for blind deblurring. Without human-made assumptions and numerical algorithms, they are able to restore images with fewer artifacts and better perceptual quality. However, in practice, we also find some of their drawbacks. Without the theoretical guidance, these methods can not perform well when the motion is complex and sometimes generate unreasonable results. In this paper, for overcoming these drawbacks, we integrate deep convolution neural networks into conventional deblurring framework. Specifically, we build Stacked Estimation Residual Net (SEN) to estimate the motion flow map and Recurrent Prior Generative and Adversarial Net (RP-GAN) to learn the implicit image prior in the optimization model. Comparing with state-of-the-art end-to-end learning-based methods, our method restores reasonable details and shows better generalization ability.

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preprint2016arXiv

Analysis of a mathematical model for tumor growth with Gibbs-Thomson relation

In this paper we study a mathematical model for the growth of nonnecrotic solid tumor. The tumor is assumed to be radially symmetric and its radius R(t) is an unknown function of time t as tumor growth, and the model is in the form of a free boundary problem. The feature of the model is that a Gibbs-Thomson relation is taken into account, which resulting an interesting phenomenon that there exist two stationary solutions (depending on the model parameters). The global existence and uniqueness of solution are established. By denoting c the ratio of the diffusion time scale to the tumor doubling time scale, we prove that for sufficiently small c>0, the stationary solution with the larger radius is asymptotically stable, and the other smaller one is unstable.

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preprint2016arXiv

Asymptotic behavior of solutions of a free boundary problem modeling tumor spheroid with Gibbs-Thomson relation

In this paper we study a free boundary problem modeling the growth of solid tumor spheroid. It consists of two elliptic equations describing nutrient diffusion and pressure distribution within tumor, respectively. The new feature is that nutrient concentration on the boundary is less than external supply due to a Gibbs-Thomson relation and the problem has two radial stationary solutions, which differs from widely studied tumor spheroid model with surface tension effect. We first establish local well-posedness by using a functional approach based on Fourier multiplier method and analytic semigroup theory. Then we investigate stability of each radial stationary solution. By employing a generalized principle of linearized stability, we prove that the radial stationary solution with a smaller radius is always unstable, and there exists a positive threshold value $γ_*$ of cell-to-cell adhesiveness $γ$, such that the radial stationary solution with a larger radius is asymptotically stable for $γ>γ_*$, and unstable for $0<γ<γ_*$.

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preprint2016arXiv

Average distance of random pure states from maximally entangled and coherent states

It is well known that random bipartite pure states are typically maximally entangled within an arbitrarily small error. Showing that the marginals of random bipartite pure states are typically extremely close to the maximally mixed state, is a way to prove the above. However, a more direct way to prove the above is to estimate the distance of random bipartite pure states from the set of maximally entangled states. Here, we find the average distance between a random bipartite pure state and the set of maximally entanglement states as quantified by three different quantifiers of the distance and investigate the typical properties of the same. We then consider random pure states of a single quantum system and give an account of the typicality of the average $l_1$ norm of coherence for these states scaled by the maximum value of the $l_1$ norm of coherence. We also calculate the variance of the $l_1$ norm of coherence of random pure states to elaborate more on the typical nature of the scaled average $l_1$ norm of coherence. Moreover, We compute the distance of a random pure state from the set of maximally coherent states and obtain the average distance.

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preprint2016arXiv

Bell-type inequality in quantum coherence theory as an entanglement witness

Bell inequality is a mathematical inequality derived using the assumptions of locality and realism. Its violation guarantees the existence of quantum correlations in a quantum state. Bell inequality acts as an entanglement witness in the sense that a pure bipartite quantum state, having nonvanishing entanglement, always violates a Bell inequality. We construct Bell-type inequalities for product states in quantum coherence theory for different measures of coherence, and find that the maximally entangled states violate these inequalities. We further show that Bell-type inequalities for relative entropy of coherence is violated by all two-qubit pure entangled states, serving as an entanglement witness.

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preprint2016arXiv

Catalytic coherence transformations

Catalytic coherence transformations allow the otherwise impossible state transformations using only incoherent operations with the aid of an auxiliary system with finite coherence which is not being consumed in anyway. Here we find the necessary and sufficient conditions for the deterministic and stochastic catalytic coherence transformations between pair of pure quantum states. In particular, we show that the simultaneous decrease of a family of Rényi entropies of the diagonal parts of the states under consideration are necessary and sufficient conditions for the deterministic catalytic coherence transformations. Similarly, for stochastic catalytic coherence transformations we find the necessary and sufficient conditions for achieving higher optimal probability of conversion. We, thus, completely characterize the coherence transformations amongst pure quantum states under incoherent operations. We give numerous examples to elaborate our results. We also explore the possibility of the same system acting as a catalyst for itself and find that indeed {\it self catalysis} is possible. Further, for the cases where no catalytic coherence transformation is possible we provide entanglement assisted coherence transformations and find the necessary and sufficient conditions for such transformations.

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preprint2016arXiv

Coherence breaking channels and coherence sudden death

Quantum noise is ubiquitous to quantum systems as they incessantly interact with their surroundings and results in degrading useful resources such as coherence for single quantum systems and quantum correlations for multipartite systems. Given the importance of these resources in various quantum information processing protocols, it is of utmost importance to characterize how deteriorating is a particular noise scenario (quantum channel) in reference to a certain resource? Here we develop a theory of coherence breaking channels for single quantum systems. Any quantum channel on a single quantum system will be called a coherence breaking channel if it is an incoherent channel and maps any state to an incoherent state. We explicitly and exhaustively characterize these coherence breaking channels. Moreover, we define the coherence breaking indices for incoherent quantum channels and present various examples to elucidate this concept. We further introduce the concept of coherence sudden death under noisy evolutions and make an explicit connection of the phenomenon of coherence sudden death with the coherence breaking channels and the coherence breaking indices together with various suggestive examples. Furthermore, for higher dimensional Hilbert spaces, we establish the typicality of the dynamics of coherence under any incoherent quantum channel exploiting the concentration of measure phenomenon.

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preprint2016arXiv

Products of weak values: uncertainty relations, complementarity and incompatibility

The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the standard Heisenberg uncertainty relation to be derived from a classical uncertainty relation for complex random variables. We show this formula also leads to strong uncertainty relations for unitary operators, and underlies an interpretation of weak values as optimal (complex) estimates of quantum observables. Furthermore, we show that two incompatible observables that are weakly and strongly measured in a weak measurement context obey a complementarity relation under the interchange of these observables, in the form of an upper bound on the product of the corresponding weak values. Moreover, general tradeoff relations between weak purity, quantum purity and quantum incompatibility, and also between weak and strong joint probability distributions, are obtained based on products of real and imaginary components of weak values, where these relations quantify the degree to which weak probabilities can take anomalous values in a given context.

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preprint2016arXiv

Resource Theory of Special Antiunitary Asymmetry

We propose the resource theory of a special antiunitary asymmetry in quantum theory. The notion of antiunitary asymmetry, in particular, ${\cal PT}$-asymmetry is different from the usual resource theory for asymmetry about unitary representation of a symmetry group, as the ${\cal PT}$ operator is an antiunitary operator with ${\cal P}$ being any self-inverse unitary and ${\cal T}$ being the time-reversal operations. Here, we introduce the ${\cal PT}$-symmetric states, ${\cal PT}$-covariant operations and ${\cal PT}$-asymmetry measures. For single qubit system, we find duality relations between the ${\cal PT}$-asymmetry measures and the coherence. Moreover, for two-qubit states we prove the duality relations between the ${\cal PT}$-asymmetry measures and entanglement measure such as the concurrence. This gives a resource theoretic interpretation to the concurrence which is lacking till today. Thus, the ${\cal PT}$-asymmetry measure and entanglement can be viewed as two sides of an underlying resource. Finally, the ${\cal PT}$-symmetric dynamics is discussed and some open questions are addressed.

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preprint2015arXiv

The Continuity of Sequential Product of Sequential Quantum Effect Algebras

In order to study quantum measurement theory, sequential product defined for any two quantum effects is introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In this paper, we study the continuity problems of the sequential product with respect to the other important topologies, as norm topology, weak operator topology, order topology, interval topology, etc.

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preprint2014arXiv

Conditions for Anomalous Weak Value

We show that the weak value of any observable in pre- and post-selected states can be expressed as the sum of the average of the observable in the pre-selected state and an anomalous part. We argue that at a fundamental level the anomalous nature of the weak values arises due to the interference between the post-selected state and another quantum state which is orthogonal to the pre-selected state. This provides a necessary and sufficient condition for the anomalous nature of the weak value of a quantum observable. Furthermore, we prove that for two non-commuting observables the product of their anomalous parts cannot be arbitrarily large.

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preprint2014arXiv

Interference Visibility as a Witness of Entanglement and Quantum Correlation

In quantum information and communication one looks for the non-classical features like interference and quantum correlations to harness the true power of composite systems. We show how the concept akin to interference is, in fact, intertwined in a quantitative manner to entanglement and quantum correlation. In particular, we prove that the difference in the squared visibility for a density operator before and after a complete measurement, averaged over all unitary evolutions, is directly related to the quantum correlation measure based on the measurement disturbance. For pure and mixed bipartite states the unitary average of the squared visibility is related to entanglement measure. This may constitute direct detection of entanglement and quantum correlations with quantum interference setups. Furthermore, we prove that for a fixed purity of the subsystem state, there is a complementarity relation between the linear entanglement of formation and the measurement disturbance. This brings out a quantitative difference between two kinds of quantum correlations.

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preprint2014arXiv

Uncertainty and Complementarity Relations in Weak Measurement

We prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable operator whose average in the pre-selected quantum state gives the weak value, we show that one can have new uncertainty relations for variances of two such operators corresponding to two non-commuting observables. These generalize the recent stronger uncertainty relations that give non-trivial lower bounds for the sum of variances of two observables which fully capture the concept of incompatible observables. Furthermore, we show that weak values for two non-commuting projection operators obey a complementarity relation. Specifically, we show that for a pre-selected state if we measure a projector corresponding to an observable $A$ weakly followed by the strong measurement of another observable $B$ (for the post-selection) and, for the same pre-selected state we measure a projector corresponding to an observable $B$ weakly followed by the strong measurement of the observable $A$ (for the post-selection), then the product of these two weak values is always less than one. This shows that even though individually they are complex and can be large, their product is always bounded.

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preprint2013arXiv

A generalized family of discrete PT-symmetric square wells

N-site-lattice Hamiltonians H are introduced and perceived as a set of systematic discrete approximants of a certain PT-symmetric square-well-potential model with the real spectrum and with a non-Hermiticity which is localized near the boundaries of the interval. Its strength is controlled by one, two or three parameters. The problem of the explicit construction of a nontrivial metric which makes the theory unitary is then addressed. It is proposed and demonstrated that due to the not too complicated tridiagonal-matrix form of our input Hamiltonians the computation of the metric is straightforward and that its matrix elements prove obtainable, non-numerically, in elementary polynomial forms.

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preprint2012arXiv

Universal upper bound for the Holevo information induced by a quantum operation

Let $\cH_A\ot \cH_B$ be a bipartite system and $ρ_{AB}$ a quantum state on $\cH_A\ot \cH_B$, $ρ_A = \Ptr{B}{ρ_{AB}}$, $ρ_B = \Ptr{A}{ρ_{AB}}$. Then each quantum operation $Φ_B$ on the quantum system $\cH_B$ can induce a quantum ensemble $\set{(p_μ,ρ_{A,μ})}$ on quantum system $\cH_A$. In this paper, we show that the Holevo quantity $χ\set{(p_μ,ρ_{A,μ})}$ of the quantum ensemble $\set{(p_μ,ρ_{A,μ})}$ can be upper bounded by both subsystem entropies. By using the result, we answer partly a conjecture of Fannes, de Melo, Roga and Życzkowski.

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preprint2011arXiv

On Conjectures of Classical and Quantum Correlations in Bipartite States

In this paper, two conjectures which were proposed in [Phys. Rev. A \textbf{82}, 052122(2010)] on the correlations in a bipartite state $ρ^{AB}$ are studied. If the mutual information $I\Pa{ρ^{AB}}$ between two quantum systems $A$ and $B$ before any measurement is considered as the total amount of correlations in the state $ρ^{AB}$, then it can be separated into two parts: classical correlations and quantum correlations. The so-called classical correlations $C\Pa{ρ^{AB}}$ in the state $ρ^{AB}$, defined by the maximizing mutual information between two quantum systems $A$ and $B$ after von Neumann measurements on system $B$, we show that it is upper bounded by the von Neumann entropies of both subsystems $A$ and $B$, this answered the conjecture on the classical correlation. If the quantum correlations $Q\Pa{ρ^{AB}}$ in the state $ρ^{AB}$ is defined by $Q\Pa{ρ^{AB}}= I\Pa{ρ^{AB}} - C\Pa{ρ^{AB}}$, we show also that it is upper bounded by the von Neumann entropy of subsystem $B$. It is also obtained that $Q\Pa{ρ^{AB}}$ is upper bounded by the von Neumann entropy of subsystem $A$ for a class of states.

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preprint2011arXiv

Von Neumann Entropy-Preserving Quantum Operations

For a given quantum state $ρ$ and two quantum operations $Φ$ and $Ψ$, the information encoded in the quantum state $ρ$ is quantified by its von Neumann entropy $§(ρ)$. By the famous Choi-Jamiołkowski isomorphism, the quantum operation $Φ$ can be transformed into a bipartite state, the von Neumann entropy $§^{\mathrm{map}}(Φ)$ of the bipartite state describes the decoherence induced by $Φ$. In this Letter, we characterize not only the pairs $(Φ, ρ)$ which satisfy $§(Φ(ρ))=§(ρ)$, but also the pairs $(Φ, Ψ)$ which satisfy $§^{\mathrm{map}}(Φ\circΨ) = §^{\mathrm{map}}(Ψ)$.

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