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We study a notion analogous to the $p$-Approximation Property ($p$-AP) for Banach spaces, within the noncommutative context of operator spaces. Referred to as the $p$-Operator Approximation Property ($p$-OAP), this concept is linked to the ideal of operator $p$-compact mappings. We present several equivalent characterizations based on the density of finite-rank mappings within specific spaces for different topologies, and also one in terms of a slice mapping property. Additionally, we investigate how this property transfers from the dual or bidual to the original space. As an application, the $p$-OAP for the reduced $C^*$-algebra of a discrete group implies that operator $p$-compact Herz-Schur multipliers can be approximated in $\cb$-norm by finitely supported multipliers.

Recent results have shown that the secret-key rate of coherent-one-way (COW) quantum key distribution (QKD) scales quadratically with the system's transmittance, thus rendering this protocol unsuitable for long-distance transmission. This was proven by using a so-called zero-error attack, which relies on an unambiguous state discrimination (USD) measurement. This type of attack allows the eavesdropper to learn the whole secret key without introducing any error. Here, we investigate the feasibility and effectiveness of zero-error attacks against COW QKD with present-day technology. For this, we introduce two practical USD receivers that can be realized with linear passive optical elements, phase-space displacement operations and threshold single-photon detectors. The first receiver is optimal with respect to its success probability, while the second one can impose stronger restrictions on the protocol's performance with faulty eavesdropping equipment. Our findings suggest that zero-error attacks could break the security of COW QKD even assuming realistic experimental conditions.

We continue our study of the mapping ideal of operator $p$-compact maps, previously introduced by the authors. Our approach embraces a more geometric perspective, delving into the interplay between operator $p$-compact mappings and matrix sets, specifically we provide a quantitative notion of operator $p$-compactness for the latter. In particular, we consider operator $p$-compactness in the bidual and its relation with this property in the original space. Also, we deepen our understanding of the connections between these mapping ideals and other significant ones (e.g., completely $p$-summing, completely $p$-nuclear).

We introduce a notion of completely bounded holomorphic functions defined on the open unit ball of an operator space. We endow the set of these functions with an operator space structure, and in the scalar-valued case we identify an operator space predual for it which is a noncommutative version of Mujica's predual for the space of bounded holomorphic functions and satisfies similar properties. In particular, our predual is a free holomorphic operator space in the sense that it satisfies a linearization property for vector-valued completely bounded holomorphic functions. Additionally, several different operator space approximation properties transfer between the predual and the domain., Comment: 26 pages

We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be $\mathbb R$-linear. We obtain a generalization of the aforementioned result to completely coarse maps defined on the unit ball of an operator space. By relaxing the condition to a small scale one, we prove that there are many non-linear examples of maps which are completely Lipshitz in small scale. We define a geometric parameter for homogeneous Hilbertian operator spaces which imposes restrictions on the existence of such maps.

The classical Mazur map is a uniform homeomorphism between the unit spheres of $L_p$ spaces, and the version for noncommutative $L_p$ spaces has the same property. Odell and Schlumprecht used two types of generalized Mazur maps to prove that the unit sphere of a Banach space $X$ with an unconditional basis is uniformly homeomorphic to the unit sphere of a Hilbert space if and only if $X$ does not contain $\ell_\infty^n$'s uniformly. We prove a noncommutative version of this result, yielding uniform homeomorphisms between spheres of unitarily invariant ideals, and along the way we study noncommutative versions of the aforementioned generalized Mazur maps: one based on the $p$-convexification procedure, and one based on the minimization of quantum relative entropy. The main result provides new examples of Banach spaces whose unit spheres are uniformly homeomorphic to the unit sphere of a Hilbert space (in fact, spaces with the property (H) of Kasparov and Yu).

Current experimental data guarantees the presence of physics beyond the Standard Model in the neutrino sector. The responsible physical description might show itself through virtual effects on low-energy observables. In particular, massive neutrinos are able to produce contributions to the triple gauge coupling $WW\gamma$. The present paper deals with the calculation, estimation and analysis of one-loop contributions from Majorana neutrinos to the Lorentz-covariant $WW\gamma$ parametrization. Our calculations show that CP-odd effects vanish exactly, whereas CP-even contributions, $\Delta\kappa$ and $\Delta Q$, remain. According to our estimations, the effects from heavy neutrinos with masses in the range of hundreds of GeVs dominate over those from light neutrinos. This investigation shows that contributions from heavy Majorana neutrinos to the anomaly $\Delta\kappa$ could be as large as $\sim{\cal O}(10^{-3})$, one order of magnitude below the Standard-Model contribution. We find that the International Linear Collider, sensitive to triple gauge couplings participating in $WW$ production, might measure these effects in electron-positron collisions at a center-of-mass energy of $800\,{\rm GeV}$, as long as heavy-neutrino masses are $\gtrsim300\,{\rm GeV}$ and below $\sim1500\,{\rm GeV}$., Comment: Accepted by Physical Review D for publication, 16 pages, 4 figures

Lorentz-violating Yukawa couplings lying within the renormalizable part of the SME generate Lorentz-invariant one-loop contributions to electromagnetic moments of fermions. These proceedings provide a discussion on such contributions and present bounds on SME coefficients from experimental data on electromagnetic moments. Constraints as restrictive as $\sim10^{-14}$ are found., Comment: Presented at the Ninth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, May 17-26, 2022

As AI-enabled software systems become more prevalent in smart manufacturing, their role shifts from a reactive to a proactive one that provides context-specific support to machine operators. In the context of an international research project, we develop an AI-based software platform that shall facilitate the collaboration between human operators and manufacturing machines. We conducted 14 structured interviews with stakeholders of the prospective software platform in order to determine the individual relevance of selected quality characteristics for human-AI teaming in smart manufacturing. These characteristics include the ISO 25010:2011 standard for software quality and AI-specific quality characteristics such as trustworthiness, explicability, and auditability. The interviewees rated trustworthiness, functional suitability, reliability, and security as the most important quality characteristics for this context, and portability, compatibility, and maintainability as the least important. Also, we observed agreement regarding the relevance of the quality characteristics among interviewees having the same role. On the other hand, the relevance of each quality characteristics varied depending on the concrete use case of the prospective software platform. The interviewees also were asked about the key success factors related to human-AI teaming in smart manufacturing. They identified improving the production cycle, increasing operator efficiency, reducing scrap, and reducing ergonomic risks as key success criteria. In this paper, we also discuss metrics for measuring the fulfillment of these quality characteristics, which we intend to operationalize and monitor during operation of the prospective software platform., Comment: Preprint: to appear in QUATIC'22 International Conference on the Quality of Information and Communications Technology