Search Results (781)

The final goal of this paper is to organize the tools needed to study digital Quantum Communications, where classical information is entrusted to quantum states represented by density operators. A density operator is usually defined starting from a set of kets in the Hilbert space and a probability distribution. A fundamental problem in Quantum Communications is the factorization of such operators of the form $\rho =\gamma {\gamma }^{*}$, where $\gamma$ is a matrix called a density factor (DF). The environments considered are finite dimensional Hilbert space (discrete variables) and infinite dimensional Hilbert space (continuous variables). Using discrete variables, the multiplicity and the variety of DFs are investigated using the tools of matrix analysis, arriving in particular to establish the DF with minimal size. With continuous variables, the target is the closed-form factorization, which is achieved with recent results for the important class of Gaussian states. Finally, an application is carried out in Quantum Communications with noisy Gaussian states. Full article

There has been strong interest in the fate of relativistic symmetries in some quantum spacetimes, partly because of its possible relevance for high-precision experimental tests of relativistic properties. However, the main technical results obtained so far concern the description of suitably deformed relativistic symmetry transformation rules, whereas the properties of the associated Noether charges, which are crucial for the phenomenology, are still poorly understood. Here, we tackle this problem focusing on first-quantized particles described within a Hamiltonian framework and using as a toy model the so-called “spatial kappa-Minkowski noncommutative spacetime”, where all the relevant conceptual challenges are present but, as here shown, in technically manageable fashion. We derive the Noether charges, including the much-debated total momentum charges, and we reveal a strong link between the properties of these Noether charges and the structure of the laws of interaction among particles. Full article

Quantum batteries are quantum systems designed to store energy and release it on demand. The optimization of their performance is an intensively studied topic within the realm of quantum technologies. Such optimization forces the question: how do quantum many-body systems work as quantum batteries? To address this issue, we rely on symmetry and symmetry breaking via quantum phase transitions. Specifically, we analyze a dimerized quantum XY chain in a transverse field as a prototype of an energy storage device. This model, which is characterized by ground states with different symmetries depending on the Hamiltonian parameters, can be mapped onto a spinless fermionic chain with superconducting correlations, displaying a rich quantum phase diagram. We show that the stored energy strongly depends on the quantum phase diagram of the model when large charging times are considered. Full article

Marcolli, Chomsky, and Berwick described the minimalist program, proposed by Chomsky in generative linguistics, as an algebra of binary trees in an analogy of quantum physics on Feynman diagrams. In this paper, we proposed another model of the minimalist program based on simplicial Hodge theory by taking the relevant brain neural network into account. We focused on a long directed pathway connecting distant areas in the brain, and took the (abstract) simplex spanning the locations on the terminal area, which the signals going through the pathway can reach. The identity of each signal is represented by the symmetry of the corresponding face, consisting of locations receiving the signal simultaneously. Then, we showed that this model fits the minimalist program. Further, we calculated the spectrum and eigenspaces of the Hodge Laplacian in important cases and found their surprising rationality. According to this rationality, we could draw pictures of syntactic relations based only on the calculation without using linguistic knowledge. In addition, though word order depends on what language is used, and thus has nothing to do with the minimalist program, planar word arrangements are still possible and within the scope of our model. Full article

Recently there have been several studies devoted to the investigation of the fate of fundamental relativistic symmetries at the foreseen unification of gravity and quantum regime, that is the Planck scale. In order to preserve covariance of the formulation even if in an amended formulation, new mathematical tools are required. In this work, we consider DSR theories that modify covariance by introducing a non-trivial structure in momentum space. Additionally, we explore the possibility of investigating both universal quantum gravity corrections and scenarios where different particle species are corrected differently within the framework of these models. Several astroparticle phenomena are then analyzed to test the phenomenological predictions of DSR models. Full article

The class imbalance problem presents a critical challenge in real-world applications, particularly in high-stakes domains such as healthcare, finance, disaster management, and fault diagnosis, where accurate anomaly detection is paramount. Class imbalance often disrupts the inherent symmetry of data distributions, resulting in suboptimal performance of traditional machine learning models. Conventional approaches such as undersampling and oversampling are commonly employed to address this issue; however, these methods can introduce additional asymmetries, including information loss and overfitting, which ultimately compromise model efficacy. This study introduces an innovative approach leveraging quantum machine learning (QML), specifically the Variational Quantum Classifier (VQC), to restore and capitalize on the symmetrical properties of data distributions without relying on resampling techniques. By employing quantum circuits optimized to mitigate the asymmetries inherent in imbalanced datasets, the proposed method demonstrates consistently superior performance across diverse datasets, with notable improvements in Recall for minority classes. These findings underscore the potential of quantum machine learning as a robust alternative to classical methods, offering a symmetry-aware solution to class imbalance and advancing QML-driven technologies in fields where equitable representation and symmetry are of critical importance. Full article

Nuclear physics provides a natural laboratory for studying two kinds of fermions: protons and neutrons. These particles share similarities in mass and strong nuclear interactions, which are often described by isospin symmetry. However, isospin is not a good quantum number due to the differences between protons and neutrons in charge and quark mass. These differences become more pronounced as we approach or move beyond the dripline, affecting the structures and decay properties of mirror nuclei. To explore these intriguing phenomena, researchers have developed novel theoretical frameworks. In this article, we review the results from the Gamow shell model and Gamow coupled-channel, which account for the mirror symmetry breaking influenced by nuclear forces and continuum effects. Specifically, we discuss the recently observed mirror asymmetries in nuclei at the boundaries of the nuclide landscape and their theoretical explanations. We examine the breaking of mirror symmetry in the spectra of $N=8$ isotones versus $Z=8$ isotopes, as well as the decay properties of the ²²Al-²²F mirror pair. Such studies enhance our understanding of strong interactions and the behavior of open quantum systems. Full article

Hopf–Galois extensions extend the idea of principal bundles to noncommutative geometry, using Hopf algebras as symmetries. We show that the matrix embeddings in Bratteli diagrams are iterated direct sums of Hopf–Galois extensions (quantum principal bundles) for certain finite abelian groups. The corresponding strong universal connections are computed. We show that $M_n\left(\mathbb{C}\right)$ is a trivial quantum principle bundle for the Hopf algebra $\mathbb{C}[{\mathbb{Z}}_n\times {\mathbb{Z}}_n]$. We conclude with an application relating calculi on groups to calculi on matrices. Full article

We propose a distinct mechanism to explain the matter–antimatter imbalance observed in the universe, rooted in quantum entanglement asymmetry (QEA). Our concept of QEA differs from its usage in the recent literature, where it typically measures how much symmetry is broken within a subsystem of a larger quantum system. Here, we define QEA as an intrinsic asymmetry in the entanglement properties of particle–antiparticle pairs in the early universe, leading to a preferential survival of matter over antimatter. We develop a theoretical framework incorporating QEA into the standard cosmological model, providing clear justification for the asymmetry in entangled states and corresponding modifications to the Hamiltonian. Numerical simulations using lattice Quantum Chromodynamics (QCD) demonstrate that QEA can produce a net baryon asymmetry consistent with observations. We also predict specific signatures in Cosmic Microwave Background (CMB) anisotropies and large-scale structure formation, offering potential avenues for empirical verification. This work aims to deepen the understanding of cosmological asymmetries and highlight the significance of quantum entanglement in the universe’s evolution. Full article

The inseparability criterion provides a straightforward and efficient method for identifying and quantifying two-mode Gaussian quantum entanglement, making it a crucial tool in quantum optics experiments. However, it is crucial to recognize that the inseparability criterion serves only as a sufficient condition for entanglement assessment, thereby posing a risk of missed detection during evaluation. This paper investigates the use of the inseparability criterion in assessing two-mode squeezed states, with a particular focus on examining missed entanglement detection due to entanglement asymmetry. The results show that when decoherence symmetrically affects both modes, the inseparability criterion effectively detects entanglement. In contrast, when this symmetry is broken, the criterion may fail to identify entanglement, with the likelihood of missed detection increasing with increasing asymmetry. By comparing these results with the positive partial transpose criterion, which serves as a necessary and sufficient condition, the occurrence of missed detections by the inseparability criterion is confirmed. Our research not only provides valuable insights into the application of the inseparability criterion in quantum information tasks but also deepens the understanding of its operational principles and limitations. Full article

The present work deals with the computational study of HC₃N$··$HCN$··$H₂C₂-, (HC₃N)₂$··$H₂C₂-, and HC₃N$··$(H₂C₂)₂-mixed trimers. The different equilibrium structures of the different low-lying minima on the corresponding potential energy surface (PES) were accurately determined, and the relative stabilities were computed by extrapolation procedures to the complete basis set limit. For each mixed trimer, the non-covalent interactions ruling the structure of the most stable isomer were analyzed using the QTAIM (Quantum Theory of Atoms in Molecules) approach. Additional insights into these interactions were provided by the Natural Bond Orbital (NBO) and Symmetry-Adapted Perturbation Theory (SAPT) methods. These results can be used to assist further theoretical investigations and experimental studies on the formation of larger molecules potentially relevant in astrochemistry. Full article

Continuous-variable quantum key distribution (CV-QKD) has been increasingly studied, which offers the advantage of compatibility with modern coherent optical communication systems. In contrast to CV-QKD with a transmitting local oscillator, the local local oscillator CV-QKD avoids the security vulnerabilities of a local oscillator by generating a local oscillator at the receiver. In practice, the frequency offset of the two lasers introduces extra phase noise, which is generally suppressed by various carrier phase recovery algorithms. However, the accuracy of carrier phase recovery can be influenced by the power of the pilot tone, particularly as the transmission distance increases. To further improve accuracy, we propose a method based on the unscented particle filter algorithm, to increase the accuracy of phase estimation, effectively restore the quantum signal and reduce excess noise. In our work, we demonstrated a local local oscillator CV-QKD experiment with a finite-size block of $1\times {10}^8$ under a transmission distance of 50 km. Through our method, we achieved a secret key rate of 525 kbps, which represents a 28% improvement. These results confirm that our proposed method not only improves the accuracy of carrier phase recovery, but also provides a new approach for future research on algorithms for long-distance CV-QKD. Furthermore, our study improves the phase compensation performance, enabling the orthogonal components of the quantum signal to exhibit enhanced symmetry in phase space. Full article

This paper explores fundamental issues in the correct contraction and expansion of operators, with a primary focus on the concept of symmetry within operator theory. Special attention is given to how symmetry influences the behavior of operators, particularly regarding their approximation and convergence properties. In the domains of quantum mechanics and condensed matter physics, such operators are essential for modeling phenomena like superconductivity, excitons, and surface states. The symmetric properties of operators have a profound impact on the physical interpretations and predictions these models generate. A rigorous analysis is provided regarding the existence of correct contractions and expansions for a specific class of nonlinear operators, demonstrating how symmetry affects the structural integrity of operators under natural conditions. The study presents a comprehensive description of the set of all correct contractions, expansions, and regular expansions, with an application to a third-order nonlinear differential expression. Additionally, a condition for the unique solvability of a Bitsadze–Samarskii-type problem is derived, showcasing how symmetry plays a crucial role in guiding the solution of complex physical models. Furthermore, the paper emphasizes the importance of preserving symmetry in the construction of operators, ensuring the consistency and accuracy of mathematical models. This has significant implications for both theoretical research and practical applications in various fields, including nuclear physics and quantum theory. Full article

The gauge covariance of the quark gap equation is compared for the case of three different quark–gluon vertices: the bare vertex, a Ball–Chiu-like vertex constrained by the corresponding Slavnov–Taylor identity, and a full vertex including the transverse components derived from transverse Slavnov–Taylor identities. The covariance properties are verified with the chiral quark condensate and the pion decay constant in the chiral limit. Full article

We propose a temperature-dependent optimization procedure for the second-nearest neighbor (2NN) sp³s* tight-binding (TB) theory parameters to calculate the effects of strain, structure dimensions, and alloy composition on the band structure of heterostructure spherical core/shell quantum dots (QDs). We integrate the thermoelastic theory of solids with the 2NN sp³s* TB theory to calculate the strain, core and shell dimensions, and composition effects on the band structure of binary/ternary CdSe/Cd(Zn)S and ZnSe/Zn(Cd)S QDs at any temperature. We show that the 2NN sp³s* TB theory with optimized parameters greatly improves the prediction of the energy dispersion curve at and in the vicinity of L and X symmetry points. We further used the optimized 2NN sp³s* TB parameters to calculate the strain, core and shell dimensions, and composition effects on the nanocrystal bandgaps of binary/ternary CdSe/Cd(Zn)S and ZnSe/Zn(Cd)S core/shell QDs. We conclude that the 2NN sp³s* TB theory provides remarkable agreement with the measured nanocrystal bandgaps of CdSe/Cd(Zn)S and ZnSe/Zn(Cd)S QDs and accurately reproduces the energy dispersion curves of the electronic band structure at any temperature. We believe that the proposed optimization procedure makes the 2NN sp³s* TB theory reliable and accurate in the modeling of core/shell QDs for nanoscale devices. Full article