Search

In the neutral hydrogen (HI) intensity mapping (IM) survey, the foreground contamination on the cosmological signals is extremely severe, and the systematic effects caused by radio telescopes themselves further aggravate the difficulties in subtracting foreground. In this work, we investigate whether the deep learning method, concretely the 3D U-Net algorithm here, can play a crucial role in foreground subtraction when considering the systematic effect caused by the telescope's primary beam. We consider two beam models, i.e., the Gaussian beam model as a simple case and the Cosine beam model as a sophisticated case. The traditional principal component analysis (PCA) method is employed as a comparison and, more importantly, as the preprocessing step for the U-Net method to reduce the sky map dynamic range. We find that in the case of the Gaussian beam, the PCA method can effectively clean the foreground. However, the PCA method cannot handle the systematic effect induced by the Cosine beam, and the additional U-Net method can improve the result significantly. In order to show how well the PCA and U-Net methods can recover the HI signals, we also derive the HI angular power spectra, as well as the HI 2D power spectra, after performing the foreground subtractions. It is found that, in the case of Gaussian beam, the concordance with the original HI map using U-Net is better than that using PCA by $27.4\%$, and in the case of Cosine beam, the concordance using U-Net is better than that using PCA by $144.8\%$. Therefore, the U-Net based foreground subtraction can efficiently eliminate the telescope primary beam effect and shed new light on recovering the HI power spectrum for future HI IM experiments., Comment: 19 pages, 13 figures

We prove that the canonical sub-Laplacian on $SU(2)$ admits a uniform modified log-Sobolev inequality for all its matrix-valued functions, independent of the matrix dimension. This is the first example of sub-Laplacian that a matrix-valued modified log-Sobolev inequality has been obtained. We also show that on Lie groups, the heat kernel measure $p_t$ at time $t$ admits matrix-valued modified log-Sobolev constants of order $O(t^{-1})$., Comment: v2, 30 pages, Section 4 added. Comments are welcome!

We study quantum soft covering and privacy amplification against quantum side information. The former task aims to approximate a quantum state by sampling from a prior distribution and querying a quantum channel. The latter task aims to extract uniform and independent randomness against quantum adversaries. For both tasks, we use trace distance to measure the closeness between the processed state and the ideal target state. We show that the minimal amount of samples for achieving an $\varepsilon$-covering is given by the $(1-\varepsilon)$-hypothesis testing information (with additional logarithmic additive terms), while the maximal extractable randomness for an $\varepsilon$-secret extractor is characterized by the conditional $(1-\varepsilon)$-hypothesis testing entropy. When performing independent and identical repetitions of the tasks, our one-shot characterizations lead to tight asymptotic expansions of the above-mentioned operational quantities. We establish their second-order rates given by the quantum mutual information variance and the quantum conditional information variance, respectively. Moreover, our results extend to the moderate deviation regime, which are the optimal asymptotic rates when the trace distances vanish at sub-exponential speed. Our proof technique is direct analysis of trace distance without smoothing.

How well can we approximate a quantum channel output state using a random codebook with a certain size? In this work, we study the quantum soft covering problem. Namely, we use a random codebook with codewords independently sampled from a prior distribution and send it through a classical-quantum channel to approximate the target state. When using a random codebook sampled from an independent and identically distributed prior with a rate above the quantum mutual information, we show that the expected trace distance between the codebook-induced state and the target state decays with exponent given by the sandwiched R\'enyi information. On the other hand, when the rate of the codebook size is below the quantum mutual information, the trace distance converges to one exponentially fast. We obtain similar results when using a random constant composition codebook, whereas the sandwiched Augustin information expresses the error exponent. In addition to the above large deviation analysis, our results also hold in the moderate deviation regime. That is, we show that even when the rate of the codebook size approaches the quantum mutual information moderately quickly, the trace distance still vanishes asymptotically.

The deep reinforcement learning-based energy management strategies (EMS) have become a promising solution for hybrid electric vehicles (HEVs). When driving cycles are changed, the neural network will be retrained, which is a time-consuming and laborious task. A more efficient way of choosing EMS is to combine deep reinforcement learning (DRL) with transfer learning, which can transfer knowledge of one domain to the other new domain, making the network of the new domain reach convergence values quickly. Different exploration methods of DRL, including adding action space noise and parameter space noise, are compared against each other in the transfer learning process in this work. Results indicate that the network added parameter space noise is more stable and faster convergent than the others. In conclusion, the best exploration method for transferable EMS is to add noise in the parameter space, while the combination of action space noise and parameter space noise generally performs poorly. Our code is available at https://github.com/BIT-XJY/RL-based-Transferable-EMS.git.

We establish a one-shot strong converse bound for privacy amplification against quantum side information using trace distance as a security criterion. This strong converse bound implies that in the independent and identical scenario, the trace distance exponentially converges to one in every finite blocklength when the rate of the extracted randomness exceeds the quantum conditional entropy. The established one-shot bound has an application to bounding the information leakage of classical-quantum wiretap channel coding and private communication over quantum channels. That is, the trace distance between Alice and Eavesdropper's joint state and its decoupled state vanishes as the rate of randomness used in hashing exceeds the quantum mutual information. On the other hand, the trace distance converges to one when the rate is below the quantum mutual information, resulting in an exponential strong converse. Our result also leads to an exponential strong converse for entropy accumulation, which complements a recent result by Dupuis [arXiv:2105.05342]. Lastly, our result and its applications apply to the moderate deviation regime. Namely, we characterize the asymptotic behaviors of the trace distances when the associated rates approach the fundamental thresholds with speeds slower than $O(1/\sqrt{n})$.

Quantum communication networks are connected by various devices to achieve communication or distributed computing for users in remote locations. In order to solve the problem of generating temporary session key for secure communication in optical-ring quantum networks, a quantum key agreement protocol is proposed. In the key agreement protocols, an attacker can impersonate a legal user to participate in the negotiation process and eavesdrop the agreement key easily. This is often overlooked in most quantum key agreement protocols, which makes them insecure in practical implementation. Considering this problem, the function of authenticating the user's identity is added in the proposed protocol. Combining classical hash function with identity information, we design the authentication operation conforming to the characteristics of quantum search algorithm. In the security analysis of the proposed protocol, quantum state discrimination is utilized to show that the protocol is secure against common attacks and impersonation attack. In addition, only single photons need to be prepared and measured, which makes our protocol feasible with existing technology.

Given a finite-range, translation-invariant commuting system Hamiltonians on a spin chain, we show that the Davies semigroup describing the reduced dynamics resulting from the joint Hamiltonian evolution of a spin chain weakly coupled to a large heat bath thermalizes rapidly at any temperature. More precisely, we prove that the relative entropy between any evolved state and the equilibrium Gibbs state contracts exponentially fast with an exponent that scales logarithmically with the length of the chain. Our theorem extends a seminal result of Holley and Stroock to the quantum setting, up to a logarithmic overhead, as well as provides an exponential improvement over the non-closure of the gap proved by Brandao and Kastoryano. This has wide-ranging applications to the study of many-body in and out-of-equilibrium quantum systems. Our proof relies upon a recently derived strong decay of correlations for Gibbs states of one dimensional, translation-invariant local Hamiltonians, and tools from the theory of operator spaces., Comment: 44 pages, 6 figures

We prove that spin chains weakly coupled to a large heat bath thermalize rapidly at any temperature for finite-range, translation-invariant commuting Hamiltonians, reaching equilibrium in a time which scales logarithmically with the system size. Our main result is a generalization to the quantum setting of a seminal result of Holley and Stroock for classical spin chains and represents an exponential improvement over bounds based on the non-closure of the spectral gap. From a physical point of view, our result rigorously establishes the absence of dissipative phase transition for Davies evolutions over translation-invariant spin chains. The result also applies in the case of Symmetry Protected Topological phases where the evolution is respecting the symmetry of the phase. This has wide-ranging applications to the study of many-body in and out-of-equilibrium quantum systems., Comment: 5 pages + 3 pages, 3 figures