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Junde Wu

Publications and source records attributed to Junde Wu.

At least 109 records · Page 6Linked to original sources

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.

cs.CV↗

Duistermaat-Heckman measure and the mixture of quantum states

In this paper, we present a general framework to solve a fundamental problem in Random Matrix Theory (RMT), i.e., the problem of describing the joint distribution of eigenvalues of the sum $\bsA+\bsB$ of two independent random Hermitian matrices $\bsA$ and $\bsB$. Some considerations about the mixture of quantum states are basically subsumed into the above mathematical problem. Instead, we focus on deriving the spectral density of the mixture of adjoint orbits of quantum states in terms of Duistermaat-Heckman measure, originated from the theory of symplectic geometry. Based on this method, we can obtain the spectral density of the mixture of independent random states. In particular, we obtain explicit formulas for the mixture of random qubits. We also find that, in the two-level quantum system, the average entropy of the equiprobable mixture of $n$ random density matrices chosen from a random state ensemble (specified in the text) increases with the number $n$. Hence, as a physical application, our results quantitatively explain that the quantum coherence of the mixture monotonously decreases statistically as the number of components $n$ in the mixture. Besides, our method may be used to investigate some statistical properties of a special subclass of unital qubit channels.

quant-ph↗

Quantumness of Relative Incompatibility

We propose a new measure of relative incompatibility for a quantum system with respect to two non-commuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is inconsequential, hence probability distribution of outcomes of any observable remains undisturbed. We define relative entropy of the two marginal probability distributions as a measure of quantumness in the state, which is revealed only in presence of two non-commuting observables. Like all other measures, we show that the proposed measure satisfies some basic axioms. Also, we find that this measure depicts complementarity with quantum coherence. The relation is more vivid when we choose one of the observables in such a way that its eigen basis matches with the basis in which the coherence is measured. Our result indicates that the quantumness in a single system is still an interesting question to explore and there can be an inherent feature of the state which manifests beyond the idea of quantum coherence.

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Simulating broken $\cal PT$-symmetric Hamiltonian systems by weak measurement

By embedding a $\cal PT$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $\cal{PT}$-symmetric Hamiltonians and weak measurement theory. We show that the amplification effect in weak measurement on a conventional quantum system can be used to effectively simulate a local broken $\cal PT$-symmetric Hamiltonian system, with the pre-selected state in the $\cal PT$-symmetric Hamiltonian system and its post-selected state resident in the dilated Hamiltonian system.

quant-ph↗

The geometry properties of parity and time reversal operators in two dimensional spaces

The parity operator $\cal P$ and time reversal operator $\cal T$ are two important operators in the quantum theory, in particular, in the $\cal PT$-symmetric quantum theory. By using the concrete forms of $\cal P$ and $\cal T$, we discuss their geometrical properties in two dimensional spaces. It is showed that if $\cal T$ is given, then all $\cal P$ links with the quadric surfaces; if $\cal P$ is given, then all $\cal T$ links with the quadric curves. Moreover, we give out the generalized unbroken $\cal PT$-symmetric condition of an operator. The unbroken $\cal PT$-symmetry of a Hermitian operator is also showed in this way.

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Discrete-Time Modelling of Quantum Evolutions, the Energy-Time Uncertainty Relation and General Extensions in the Entangled History Formalism

Time evolution is an indivisible part in any physics theory. Usually, people are accustomed to think that the universe is a fixed background and the system itself evolves step by step in time. However, Yakir Aharonov challenges this view using his two-vector formalism. In this paper, using the entangled history formalism, we attain three achievements.

quant-ph↗

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.

cs.CV↗

Partial coherence and quantum correlation with fidelity and affinity distances

A fundamental task in any physical theory is to quantify certain physical quantity in a meaningful way. In this paper we show that both fidelity distance and affinity distance satisfy the strong contractibility, and the corresponding resource quantifiers can be used to characterize a large class of resource theories. Under two assumptions, namely, convexity of "free states" and closure of free states under "selective free operations", our general framework of resource theory includes quantum resource theories of entanglement, coherence, partial coherence and superposition. In partial coherence theory, we show that fidelity partial coherence of a bipartite state is equal to the minimal error probability of a mixed quantum state discrimination (QSD) task and vice versa, which complements the main result in [Xiong and Wu, J. Phys. A: Math. Theor. 51, 414005 (2018)]. We also compute the analytic expression of fidelity partial coherence for $(2,n)$ bipartite X-states. At last, we study the correlated coherence in the framework of partial coherence theory. We show that partial coherence of a bipartite state, with respect to the eigenbasis of a subsystem, is actually a measure of quantum correlation.

quant-ph↗

A Unified Convergence Theorem

We prove a unified convergence theorem, which presents in four equivalent forms of the famous Antosik-Mikusinski Theorems. In particular, we show that Swartz' three uniform convergence principles are all equivalent to the Antosik-Mikusinski Theorems.

quant-ph↗

Family of coherence measures and duality between quantum coherence and path distinguishability

Coherence measures and their operational interpretations lay the cornerstone of coherence theory. In this paper, we introduce a class of coherence measures with $α$-affinity, say $α$-affinity of coherence for $α\in (0, 1)$. Furthermore, we obtain the analytic formulae for these coherence measures and study their corresponding convex roof extension. We provide an operational interpretation for $1/2$-affinity of coherence by showing that it is equal to the error probability to discrimination a set of pure states with the least square measurement. Employing this relationship we regain the optimal measurement for equiprobable quantum state discrimination. Moreover, we compare these coherence quantifiers, and establish a complementarity relation between $1/2$-affinity of coherence and path distinguishability for some special cases.

quant-ph↗

Geometric coherence and quantum state discrimination

The operational meaning of coherence measure lies at very heart of the coherence theory. In this paper, we provide an operational interpretation for geometric coherence, by proving that the geometric coherence of a quantum state is equal to the minimum error probability to discriminate a set of pure states with von Neumann measurement. On the other hand, we also show that a task to ambiguously discriminate a set of linearly independent pure states can be also regards as a problem of calculating geometric coherence. That is, we reveal an equivalence relation between ambiguous quantum state discrimination and geometric coherence. Based on this equivalence, moreover, we improve the upper bound for geometric coherence and give the explicit expression of geometric coherence for a class of states. Besides, we establish a complementarity relation of geometric coherence and path distinguishability, with which the relationship between $l_1$-norm of coherence and geometric coherence is obtained. Finally, with geometric coherence, we study multiple copies quantum state discrimination and give an example to show how to discriminate two pure states.

quant-ph↗

Demi-linear Analysis II -- Demi-distributions

In this paper, we establish a demi-distributions theory which develops the usual distribution theory, in particular, we show that many conclusions as differentiations, Fourier transforms and convolutions can be generalized to the demi-distributions theory.

math.FA↗

Interrelation between Partial Coherence and Quantum Correlations

Both coherence and entanglement stem from the superposition principle, capture quantumness of a physical system, and play a central role in quantum physics. In a multipartite quantum system, coherence and quantum correlations are closely connected. In particular, it has been established that quantum coherence of a bipartite state is an important resource for its conversion to entanglement [A. Streltsov {\it et al.}, Phys. Rev. Lett. {\bf 115}, 020403 (2015)] and to quantum discord [J. Ma {\it et al}., Phys. Rev. Lett. {\bf 116}, 160407 (2016)]. We show here that there is a very close association between partial coherence introduced by Luo and Sun [S. Luo and Y. Sun, Phys. Rev. A {\bf 96}, 022136 (2017)] and quantum correlations (quantified by quantum discord) in both directions. Furthermore, we propose families of coherence measures in terms of quantum correlations and quantum Fisher information.

quant-ph↗

Embedding, simulation and consistency of $\cal PT$ -symmetric quantum Theory

A physical requirement on the Hamiltonian operator in quantum mechanics is that it must generate real energy spectrum and unitary time evolution. While the Hamiltonians are Dirac Hermitian in conventional quantum mechanics, they observe $\cal PT$-symmetry in $\cal PT$-symmetric quantum theory. The embedding property was first studied by Günther and Samsonov to visualize the evolution of unbroken $\cal PT$-symmetric Hamiltonians on $\mathbb C^2$ by Hermitian Hamiltonians on $\mathbb C^4$. This paper investigates the properties of $\cal PT$-symmetric quantum systems including the embedding property. We provide a full characterization of the embedding property in the general case and show that only unbroken $\cal PT$-symmetric quantum systems admit this property in a finite dimensional space. Furthermore, utilizing this property, we establish a physically realizable simulation process of the unbroken $\cal PT$-symmetric Hamiltonians. An observation that the unbroken $\cal PT$-symmetric quantum systems can be viewed as open systems in the conventional quantum mechanics accounts for the consistency of $\cal PT$-symmetric quantum theory.

math-ph↗

Manifestation of Superposition and Coherence in $\cal PT$-symmetry through the $η$-inner Product

Through the $η$-inner product, we investigate $\cal PT$-symmetric quantum mechanics from the viewpoint of superposition and coherence theory. It is argued that $\cal PT$-symmetric quantum systems are endowed with stationary superposition or superposition-free properties. A physical interpretation of $η$-inner product in $\mathbb C^2$ is given through the Stokes parameters, showing the difference between broken and unbroken $\cal PT$-symmetric quantum systems.

quant-ph↗

Field extension of real values of physical observables in classical theory can help attain quantum results

Physical quantities are assumed to take real values, which stems from the fact that an usual measuring instrument that measures a physical observable always yields a real number. Here we consider the question of what will happen if physical observables are allowed to take complex values. In this paper, we show that by allowing observables in the Bell inequality to take complex values, a classical physical theory can actually get the same upper bound of the Bell expression as quantum theory. Also, by extending the real field to the quaternionic field, we can puzzle out the GHZ problem using local hidden variable model. Furthermore, we try to build a new type of hidden-variable theory of a single qubit based on the result.

quant-ph↗

Characterizing nonclassical correlations via local quantum Fisher information

We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in Lu et al. [X. M. Lu, S. Luo, and C. H. Oh, Phys Rev. A 86, 022342 (2012)], we show that the presence of quantum correlation can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord for pure quantum states.

quant-ph↗

Quantum Observable Generalized Orthoalgebras

Let ${\cal S}(\mathcal{H})$ denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space $\mathcal{H}$, which is the set of all physical quantities on a quantum system $\mathcal{H}$. We introduce a binary relation $\bot$ on ${\cal S}(\mathcal{H})$. We show that if $A\bot B$, then $A$ and $B$ are affiliated with some abelian von Neumann algebra. The relation $\bot$ induces a partial algebraic operation $\oplus$ on ${\cal S}(\mathcal{H})$. We prove that $({\cal S}({\mathcal{H}}), \bot, \oplus, 0)$ is a generalized orthoalgebra. This algebra is a generalization of the famous Birkhoff\,--\,von Neumann quantum logic model. It establishes a mathematical structure on all physical quantities on $\mathcal{H}$. In particular, we note that $({\cal S}({\mathcal{H}}), \bot, \oplus, 0)$ has a partial order $\preceq$, and prove that $A\preceq B$ if and only if $A$ has a value in $Δ$ implies that $B$ has a value in $Δ$ for every Borel set $Δ$ not containing $0$. Moreover, the existence of the infimum $A\wedge B$ and supremum $A\vee B$ for $A,B\in \mathcal{S}(\mathcal{H})$ (with respect to $\preceq$) is studied, and it is shown at the end that the position operator $Q$ and momentum operator $P$ in the Heisenberg commutation relation satisfy $Q\wedge P=0$.

math-ph↗