Normal product form of two-mode Wigner operator

In the context of normal product, we use the method of the integration within an ordered product (IWOP) of operators to derive three representations of the two-mode Wigner operator: SU (2) symmetric description, SU (1, 1) symmetric description and polar coordinate form. We find that two-mode Wigner operator has multiple potential degrees of freedom. As the physical meaning of the selected integral variable changes, Wigner operator shows different symmetries. In particular, in the case of polar coordinates, we reveal the natural connection between the two-mode Wigner operator and the entangled state representation.

Hardy type inequalities for the fractional relativistic operator

<abstract><p>We prove Hardy type inequalities for the fractional relativistic operator by using two different techniques. The first approach goes through trace Hardy inequalities. In order to get the latter, we study the solutions of the associated extension problem. The second develops a non-local version of the ground state representation in the spirit of Frank, Lieb, and Seiringer.</p></abstract>

Model Reference Tracking Control Solutions for a Visual Servo System Based on a Virtual State from Unknown Dynamics

This paper focuses on validating a model-free Value Iteration Reinforcement Learning (MFVI-RL) control solution on a visual servo tracking system in a comprehensive manner starting from theoretical convergence analysis to detailed hardware and software implementation. Learning is based on a virtual state representation reconstructed from input-output (I/O) system samples under nonlinear observability and unknown dynamics assumptions, while the goal is to ensure linear output reference model (ORM) tracking. Secondary, a competitive model-free Virtual State-Feedback Reference Tuning (VSFRT) is learned from the same I/O data using the same virtual state representation, demonstrating the framework’s learning capability. A model-based two degrees-of-freedom (2DOF) output feedback controller serving as a comparisons baseline is designed and tuned using an identified system model. With similar complexity and linear controller structure, MFVI-RL is shown to be superior, confirming that the model-based design issue of poor identified system model and control performance degradation can be solved in a direct data-driven style. Apart from establishing a formal connection between output feedback control, state feedback control and also between classical control and artificial intelligence methods, the results also point out several practical trade-offs, such as I/O data exploration quality and control performance leverage with data volume, control goal and controller complexity.

Experimental classical entanglement in a 16 acoustic qubit-analogue

The possibility of achieving and controlling scalable classically entangled, i.e., inseparable, multipartite states, would fundamentally challenge the advantages of quantum systems in harnessing the power of complexity in information science. Here, we investigate experimentally the extent of classical entanglement in a $$16$$ 16 acoustic qubit-analogue platform. The acoustic qubit-analogue, a.k.a., logical phi-bit, results from the spectral partitioning of the nonlinear acoustic field of externally driven coupled waveguides. Each logical phi-bit is a two-level subsystem characterized by two independently measurable phases. The phi-bits are co-located within the same physical space enabling distance independent interactions. We chose a vector state representation of the $$16$$ 16 -phi-bit system which lies in a $${2}^{16}$$ 2 16 -dimensional Hilbert space. The calculation of the entropy of entanglement demonstrates the possibility of achieving inseparability of the vector state and of navigating the corresponding Hilbert space. This work suggests a new direction in harnessing the complexity of classical inseparability in information science.

An Experimental Study on State Representation Extraction for Vision-Based Deep Reinforcement Learning

Scaling end-to-end learning to control robots with vision inputs is a challenging problem in the field of deep reinforcement learning (DRL). While achieving remarkable success in complex sequential tasks, vision-based DRL remains extremely data-inefficient, especially when dealing with high-dimensional pixels inputs. Many recent studies have tried to leverage state representation learning (SRL) to break through such a barrier. Some of them could even help the agent learn from pixels as efficiently as from states. Reproducing existing work, accurately judging the improvements offered by novel methods, and applying these approaches to new tasks are vital for sustaining this progress. However, the demands of these three aspects are seldom straightforward. Without significant criteria and tighter standardization of experimental reporting, it is difficult to determine whether improvements over the previous methods are meaningful. For this reason, we conducted ablation studies on hyperparameters, embedding network architecture, embedded dimension, regularization methods, sample quality and SRL methods to compare and analyze their effects on representation learning and reinforcement learning systematically. Three evaluation metrics are summarized, including five baseline algorithms (including both value-based and policy-based methods) and eight tasks are adopted to avoid the particularity of each experiment setting. We highlight the variability in reported methods and suggest guidelines to make future results in SRL more reproducible and stable based on a wide number of experimental analyses. We aim to spur discussion about how to assure continued progress in the field by minimizing wasted effort stemming from results that are non-reproducible and easily misinterpreted.