Understanding the human brain is one of the most significant challenges of the 21st century. As theoretical studies continue to improve the description of the complex mechanisms that regulate biological processes, in parallel numerous experiments are conducted to enrich or verify these theoretical predictions also with the aim of extrapolating more accurate models. In the fields of magnetometry and thermometry, among the various sensors proposed for biological application, nitrogen‐vacancy (NV) centers are emerging as a promising solution due to their perfect biocompatibility and the possibility of being positioned in close proximity to the cell membrane, thus allowing a nanometric spatial resolution down to the nano‐scale. Still many issues must be overcome to obtain either a sensitivity capable of revealing the very weak electromagnetic fields generated by neurons (or other excitable cells) during their firing activity or a spatial resolution sufficient to measure intracellular thermal gradient due to biological processes. However, over the last few years, significant improvements have been achieved in this direction, thanks to the use of innovative techniques. In this review, the new results regarding the application of NV centers will be analyzed and the main challenges that must be afforded for leading to practical applications will be discussed.

Since, in general, nonorthogonal states cannot be cloned, any eavesdropping attempt in a quantum-communication scheme using nonorthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in quantum-cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman [Phys. Rev. Lett. 75, 1239 (1995)] proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal states are superpositions of two localized wave packets traveling along separate channels. Here we present an experiment realizing this scheme.

The codification in higher dimensional Hilbert Spaces (whose logical basis states are dubbed qudits in analogy with bidimensional qubits) presents various advantages both for Quantum Information applications and for studies on Foundations of Quantum Mechanics. Purpose of this review is to introduce qudits, to summarize their application to Quantum Communication and researches on Local Realism and, finally, to describe some recent experiment for realizing them. A Little more in details: after a short introduction, we will consider the advantages of testing local realism with qudits, discussing both the 3–4 dimensional case (both for maximally and non-maximally entanglement) and then the extension to an arbitrary dimension. Afterwards, we will discuss the theoretical results on using qudits for quantum communication, epitomizing the outcomes on a larger security in Quantum Key Distribution protocols (again considering separately qutrits, ququats and generalization to arbitrary dimension). Finally, we will present the experiments performed up to now for producing quantum optical qudits and their applications. In particular, we will mention schemes based on interferometric set-ups, orbital angular momentum entanglement and biphoton polarization. Finally, we will summarize what hyperentanglement is and its applications.

Nitrogen Vacancy centers in diamond interact with local magnetic and electric fields, temperature, strain, and pressure. Their ease of operation and exceptional performance has led to the emergence of a first generation of commercial NV-based quantum sensors, as scanning-probe systems, giving them wide recognition as the quantum technology with the most imminent market potential. In recent years, there is an effort to advance the TRL of those quantum technologies through several European initiatives.