Quantum Rep., Volume 2, Issue 1 (March 2020) – 14 articles

Over the last few years, we have witnessed an impressive growth of data traffic and a progressive Digital Transformation of Industry and Society: the deployment of the ultra-broadband and low latency network infrastructures (e.g., 5G) are leading to a global digitalization of several domains. These techno-economic trends are expected to continue and even accelerate in the next decade, at end of which, 6G and smart networks and services will be exploited. Innovation will continue to drive the global economy into the next decade. This paper draws some technology trends and applications scenarios for this horizon, where Quantum Optical Communications are likely to disrupt Information and Communications Technology (ICT) and Telecommunications. Among the enabling technologies and solutions moving in this direction, this paper briefly addresses: quantum optical switching and computing, THz-to-optical conversions and advanced metamaterials for smart radio-optical programmable environments and Artificial Intelligence. The paper concludes with the description of a future application scenario, called Quantum Optical Twin, where the above Quantum Optical Communications technologies are exploited to provide services such as: ultra-massive scale communications for connected spaces and ambient intelligence, holographic telepresence, tactile Internet, new paradigms of brain computer interactions, innovative forms of communications. Full article

We provide a recipe for the digitalization of linear and nonlinear quantum optics in networks of superconducting qubits. By combining digital techniques with boson-qubit mappings, we address relevant problems that are typically considered in analog simulators, such as the dynamical Casimir effect or molecular force fields, including nonlinearities. In this way, the benefits of digitalization are extended in principle to a new realm of physical problems. We present preliminary examples launched in IBM Q 5 Tenerife. Full article

Shannon entropy in position ( $S_{\mathbf{r}}$ ) and momentum ( $S_{\mathbf{p}}$ ) spaces, along with their sum ( $S_t$ ) are presented for unit-normalized densities of He, Li ${}^{+}$ and Be ${}^{2+}$ ions, spatially confined at the center of an impenetrable spherical enclosure defined by a radius $r_c$ . Both ground, as well as some selected low-lying singly excited states, viz., 1sns (n = 2–4) ³S, 1snp (n = 2–3) ³P, 1s3d ³D, are considered within a density functional methodology that makes use of a work function-based exchange potential along with two correlation potentials (local Wigner-type parametrized functional, as well as the more involved non-linear gradient- and Laplacian-dependent Lee-Yang-Parr functional). The radial Kohn-Sham (KS) equation is solved using an optimal spatial discretization scheme via the generalized pseudospectral (GPS) method. A detailed systematic analysis of the confined system (relative to the corresponding free system) is performed for these quantities with respect to $r_c$ in tabular and graphical forms, with and without electron correlation. Due to compression, the pattern of entropy in the aforementioned states becomes characterized by various crossovers at intermediate and lower $r_c$ regions. The impact of electron correlation is more pronounced in the weaker confinement limit and appears to decay with the rise in confinement strength. The exchange-only results are quite good to provide a decent qualitative discussion. The lower bounds provided by the entropic uncertainty relation hold well in all cases. Several other new interesting features are observed. Full article

We present an information geometric analysis of off-resonance effects on classes of exactly solvable generalized semi-classical Rabi systems. Specifically, we consider population transfer performed by four distinct off-resonant driving schemes specified by $\mathrm{su}\left(2;ℂ\right)$ time-dependent Hamiltonian models. For each scheme, we study the consequences of a departure from the on-resonance condition in terms of both geodesic paths and geodesic speeds on the corresponding manifold of transition probability vectors. In particular, we analyze the robustness of each driving scheme against off-resonance effects. Moreover, we report on a possible tradeoff between speed and robustness in the driving schemes being investigated. Finally, we discuss the emergence of a different relative ranking in terms of performance among the various driving schemes when transitioning from on-resonant to off-resonant scenarios. Full article

Quantum optics is regarded as the acknowledged method to provide network quantum keys distribution and in the future secure distributed quantum computing, but it should also provide cryptography protection for mobile robots and the Internet of Things (IoT). This task requires the design of new secret coding schemes, which can be also based on multiple-valued logic (MVL). However, this very specific logic model reveals new possibilities for the hierarchical data clustering of arbitrary data sets. The minimization of multiple-valued logic functions is proposed for the analysis of aggregated objects, which is possible for an arbitrary number of variables. In order to use all the useful properties of the multiple-valued logic, the heterogeneous network architecture is proposed, which includes three allocated levels of artificial intelligence (AI) logic modeling for discrete multiple-valued logic, Boolean logic, and fuzzy logic. Multiple-valued logic is regarded as the possible platform for additional secret coding, data aggregation, and communications, which are provided by the united high dimensional space for network addressing and the targeted control of robotic devices. Models of Boolean and fuzzy logic are regarded as separate logic levels in order to simplify the integration of various algorithms and provide control of additional data protection means for robotic agents. Full article

We describe two mixed-integer linear programming formulations, one a faster version of a previous proposal, the other a slower but better performing new model, for the design of Quantum Key Distribution (QKD) sub-networks dimensioned to secure existing core fiber plants. We exploit existing technologies, including non-quantum repeater nodes and multiple disjoint QKD paths to overcome reach limitations while maintaining security guarantees. We examine the models’ performance using simulations on both synthetic and real topologies, quantifying their time and resulting QKD network cost compared to our previous proposal. Full article

Dimensionless conductance through a disorderless lattice is studied using an alternative approach. Usually, the conductance of an ordered lattice is studied at a fixed size, either finite or infinite if the crystalline limit is reached. Here, we propose one to consider the set of systems of all sizes from zero to infinite. As a consequence, we find that the conductance presents fluctuations, with respect to system size, at a fixed energy. At the band edge, these fluctuations are described by a statistical distribution satisfied by an ensemble of chaotic cavities with reflection symmetry, which also satisfies a maximum-entropy, or minimum-information, criterion. Full article

We provide a broad overview of current quantum communication by analyzing the recent discoveries on the topic and by identifying the potential bottlenecks requiring further investigation. The analysis follows an industrial perspective, first identifying the state or the art in terms of protocols, systems, and devices for quantum communication. Next, we classify the applicative fields where short- and medium-term impact is expected by emphasizing the potential and challenges of different approaches. The direction and the methodology with which the scientific community is proceeding are discussed. Finally, with reference to the European guidelines within the Quantum Flagship initiative, we suggest a roadmap to match the effort community-wise, with the objective of maximizing the impact that quantum communication may have on our society. Full article

The probability representation of quantum mechanics where the system states are identified with fair probability distributions is reviewed for systems with continuous variables (the example of the oscillator) and discrete variables (the example of the qubit). The relation for the evolution of the probability distributions which determine quantum states with the Feynman path integral is found. The time-dependent phase of the wave function is related to the time-dependent probability distribution which determines the density matrix. The formal classical-like random variables associated with quantum observables for qubit systems are considered, and the connection of the statistics of the quantum observables with the classical statistics of the random variables is discussed. Full article

Magnesium ions have many cellular actions including the suppression of the excitability of neurons; however, the depolarization effect of magnesium ions seems to be contradictory. Thus several hypotheses have aimed to explain this effect. In this study, a quantum mechanical approach is used to explain the depolarization action of magnesium. The model of quantum tunneling of magnesium ions through the closed sodium voltage-gated channels was adopted to calculate the quantum conductance of magnesium ions, and a modified version of Goldman–Hodgkin–Katz equation was used to determine whether this quantum conductance was significant in affecting the resting membrane potential of neurons. Accordingly, it was found that extracellular magnesium ions can exhibit a depolarization effect on membrane potential, and the degree of this depolarization depends on the tunneling probability, the channels’ selectivity to magnesium ions, the channels’ density in the neuronal membrane, and the extracellular magnesium concentration. In addition, extracellular magnesium ions achieve a quantum conductance much higher than intracellular ones because they have a higher kinetic energy. This study aims to identify the mechanism of the depolarization action of magnesium because this may help in offering better therapeutic solutions for fetal neuroprotection and in stabilizing the mood of bipolar patients. Full article

We discuss the use of the Gilbert algorithm to tailor entanglement witnesses for unextendible product basis bound entangled states (UPB BE states). The method relies on the fact that an optimal entanglement witness is given by a plane perpendicular to a line between the reference state, entanglement of which is to be witnessed, and its closest separable state (CSS). The Gilbert algorithm finds an approximation of CSS. In this article, we investigate if this approximation can be good enough to yield a valid entanglement witness. We compare witnesses found with Gilbert algorithm and those given by Bandyopadhyay–Ghosh–Roychowdhury (BGR) construction. This comparison allows us to learn about the amount of entanglement and we find a relationship between it and a feature of the construction of UPBBE states, namely the size of their central tile. We show that in most studied cases, witnesses found with the Gilbert algorithm in this work are more optimal than ones obtained by Bandyopadhyay, Ghosh, and Roychowdhury. This result implies the increased tolerance to experimental imperfections in a realization of the state. Full article

The quantum Pusey–Barrett–Rudolph (PBR) theorem addresses the question of whether the quantum state corresponds to a ψ-ontic model (system’s physical state) or to a ψ-epistemic model (observer’s knowledge about the system). We reformulate the PBR theorem as a Monty Hall game and show that winning probabilities, for switching doors in the game, depend on whether it is a ψ-ontic or ψ-epistemic game. For certain cases of the latter, switching doors provides no advantage. We also apply the concepts involved in quantum teleportation, in particular for improving reliability. Full article

In this paper, we show that the standard techniques that are utilized to study the classical-like properties of the pure states for Hermitian systems can be adjusted to investigate the classicality of pure states for non-Hermitian systems. The method is applied to the states of complex-valued potentials that are generated by Darboux transformations and can model both non- $PT$ -symmetric and $PT$ -symmetric oscillators exhibiting real spectra. Full article

We study the Quantum Cheshire Cat effect in an open system coupled to a finite environment. We consider a very special type of coupling—pure dephasing—and show that there is a scattering-like mechanism which can be utilized to construct an open-loop control strategy for the weak values of the Cat and its grin. Full article