Entropy最新文献

In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in (1+1)-d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of (1+1)-d theories with categorical symmetries.

In the wake of quantum computing advancements and quantum algorithmic progress, quantum algorithms are increasingly being employed to address a myriad of combinatorial optimization problems. Among these, the Independent Domination Problem (IDP), a derivative of the Domination Problem, has practical implications in various real-world scenarios. Despite this, existing classical algorithms for the IDP are plagued by high computational complexity, and quantum algorithms have yet to tackle this challenge. This paper introduces a Quantum Approximate Optimization Algorithm (QAOA)-based approach to address the IDP. Utilizing IBM's qasm_simulator, we have demonstrated the efficacy of the QAOA in solving the IDP under specific parameter settings, with a computational complexity that surpasses that of classical methods. Our findings offer a novel avenue for the resolution of the IDP.

This paper investigated a non-orthogonal multiple access (NOMA)-based integrated satellite-terrestrial network (ISTN), where each user can select to access a terrestrial base station (BS) or the satellite according to the capacity of BS and their individual transmission requirements. A two-stage algorithm is proposed to solve the achievable sum rate maximizing resource optimization problem. In the first stage, user associations are determined based on individual preference lists and the backhaul capacities of the access points (APs). In the second stage, the power allocation, and the receiving beamforming vectors are optimized alternately. Within each iteration, the closed-form solution for the transmit power is derived. Simulation results show the effectiveness of the proposed algorithm and the benefits brought by NOMA. When the backhaul link capacity of terrestrial BSs is sufficient, users (UEs) prefer to access these BSs. Otherwise, the satellite can offer QoS guarantees to UEs. Furthermore, the overall system performance reaches its optimum when the number of UEs in the system matches the number of receive antennas at the APs.

This paper investigates the design of active and passive beamforming in a reconfigurable intelligent surface (RIS)-aided multi-user multiple-input single-output (MU-MISO) system with the objective of maximizing the sum rate. We propose a deep evolution policy (DEP)-based algorithm to derive the optimal beamforming strategy by generating multiple agents, each utilizing distinct deep neural networks (DNNs). Additionally, a random subspace selection (RSS) strategy is incorporated to effectively balance exploitation and exploration. The proposed DEP-based algorithm operates without the need for alternating iterations, gradient descent, or backpropagation, enabling simultaneous optimization of both active and passive beamforming. Simulation results indicate that the proposed algorithm can bring significant performance enhancements.

In this paper, we study the equivalence problem for quantum circuits: Given two quantum circuits, are they equivalent? We reduce this problem to the contraction problem of a tensor network. The order in which the contraction operations between tensors are applied has a crucial impact on efficiency, which is why many heuristics have been proposed. In this work, we use an efficient representation of tensors as a tensor decision diagram. Since existing contraction heuristics do not perform well in combination with these diagrams, we propose two new contraction heuristics. We demonstrate experimentally that our heuristics outperform other state-of-the-art heuristics. We also demonstrate that our framework yields state-of-the-art performance for equivalence checking.

Complex networks, from neuronal assemblies to social systems, can exhibit abrupt, system-wide transitions without external forcing. These endogenously generated "noise-induced transitions" emerge from the intricate interplay between network structure and local dynamics, yet their underlying mechanisms remain elusive. Our study unveils two critical roles that nodes play in catalyzing these transitions within dynamical networks governed by the Boltzmann-Gibbs distribution. We introduce the concept of "initiator nodes", which absorb and propagate short-lived fluctuations, temporarily destabilizing their neighbors. This process initiates a domino effect, where the stability of a node inversely correlates with the number of destabilized neighbors required to tip it. As the system approaches a tipping point, we identify "stabilizer nodes" that encode the system's long-term memory, ultimately reversing the domino effect and settling the network into a new stable attractor. Through targeted interventions, we demonstrate how these roles can be manipulated to either promote or inhibit systemic transitions. Our findings provide a novel framework for understanding and potentially controlling endogenously generated metastable behavior in complex networks. This approach opens new avenues for predicting and managing critical transitions in diverse fields, from neuroscience to social dynamics and beyond.

Random number generators (RNGs) are notoriously challenging to build and test, especially for cryptographic applications. While statistical tests cannot definitively guarantee an RNG's output quality, they are a powerful verification tool and the only universally applicable testing method. In this work, we design, implement, and present various post-processing methods, using randomness extractors, to improve the RNG output quality and compare them through statistical testing. We begin by performing intensive tests on three RNGs-the 32-bit linear feedback shift register (LFSR), Intel's 'RDSEED,' and IDQuantique's 'Quantis'-and compare their performance. Next, we apply the different post-processing methods to each RNG and conduct further intensive testing on the processed output. To facilitate this, we introduce a comprehensive statistical testing environment, based on existing test suites, that can be parametrised for lightweight (fast) to intensive testing.

All characterizations of the Shannon entropy include the so-called chain rule, a formula on a hierarchically structured probability distribution, which is based on at least two elementary distributions. We show that the chain rule can be split into two natural components, the well-known additivity of the entropy in case of cross-products and a variant of the chain rule that involves only a single elementary distribution. The latter is given as a proportionality relation and, hence, allows a vague interpretation as self-similarity, hence intrinsic property of the Shannon entropy. Analogous characterizations are given for the Rényi entropy and its limits, the min-entropy and the Hartley entropy.

We present the results from kinetic theory for a system of self-propelled particles with alignment interactions of higher-order symmetry, particularly nematic ones. To this end, we use the Landau equation approach, a systematic approximation to the BBGKY hierarchy for small effective couplings. Our calculations are presented in a pedagogical way with the explicit goal of serving as a tutorial from a physicists' perspective into applying kinetic theory ideas beyond mean-field to active matter systems with essentially no prerequisites and yield predictions without free parameters that are in quantitative agreement with direct agent-based simulations.

By utilizing chirp-BOK (binary orthogonal keying) modulation into a troposphere scattering communication system, a lower demodulation threshold can be achieved with excellent linear frequency modulation properties in a strong noise and weak signal environment. Firstly, the bit error rate (BER) formula of chirp-BOK modulation over a Rayleigh fading channel was derived theoretically. Then, the BER performance with different chirp-BOK parameters were numerically calculated. In order to investigate the performance of chirp-BOK over deeping fading troposphere scattering link, a seven-path equal-delay Rayleigh fading model was employed. Finally, the system BER performance was simulated under different tap delay and time-bandwidth product parameters. The results demonstrate that when BER reaches 10-4, the optimal configuration of the system achieves a gains approximately from 1.7 dB to 10 dB compared to non-optimized configuration under different Path-Gain-Vector with varying tap delays.