Quantum Reports

In this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering $\pi$ periodically pumped parameters (oscillator frequencies and coupling) and using suitable transformations, we show that the quantum dynamics can be determined by two classical Meissner oscillators. We then study analytically the stability of these differential equations and the dynamics of photon excitations and entanglement in the quantum system numerically. Our analysis shows two interesting results, which can be summarized as follows: (i) Classical instability of classical analog of quantum oscillators and photon excitation numbers (expectations $⟨N_j⟩$) are strongly correlated, and (ii) photon excitations and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts and provide a nice complement to the existing works studying the dynamics of coupled quantum oscillators. Full article

Starting from the geometric description of quantum systems, we propose a novel approach to time-independent dissipative quantum processes according to which energy is dissipated but the coherence of the states is preserved. Our proposal consists of extending the standard symplectic picture of quantum mechanics to a contact manifold and then obtaining dissipation by using appropriate contact Hamiltonian dynamics. We work out the case of finite-level systems for which it is shown, by means of the corresponding contact master equation, that the resulting dynamics constitute a viable alternative candidate for the description of this subclass of dissipative quantum systems. As a concrete application, motivated by recent experimental observations, we describe quantum decays in a 2-level system as coherent and continuous processes. Full article

Since the beginning of the 21st century, a new interdisciplinary research movement has started, which aims at developing quantum math-like (or simply quantum-like) models to provide an explanation for a variety of socio-economic processes and human behaviour. By making use of mainly the probabilistic aspects of quantum theory, this research movement has led to many important results in the areas of decision-making and finance. In this article, we introduce a novel and more exhaustive approach, to analyze the socio-economic processes and activities, than the pure quantum math-like modelling approach, by taking into account the physical foundations of quantum theory. We also provide a plausibility argument for its exhaustiveness in terms of what we can expect from such an approach, when it is applied to, for example, a generic socio-economic decision process. Full article

In 1933, Kolmogorov synthesized the basic concepts of probability that were in general use at the time into concepts and deductions from a simple set of axioms that said probability was a $\sigma$-additive function from a boolean algebra of events into [0, 1]. In 1932, von Neumann realized that the use of probability in quantum mechanics required a different concept that he formulated as a $\sigma$-additive function from the closed subspaces of a Hilbert space onto $[0,1]$. In 1935, Birkhoff & von Neumann replaced Hilbert space with an algebraic generalization. Today, a slight modification of the Birkhoff-von Neumann generalization is called “quantum logic”. A central problem in the philosophy of probability is the justification of the definition of probability used in a given application. This is usually done by arguing for the rationality of that approach to the situation under consideration. A version of the Dutch book argument given by de Finetti in 1972 is often used to justify the Kolmogorov theory, especially in scientific applications. As von Neumann in 1955 noted, and his criticisms still hold, there is no acceptable foundation for quantum logic. While it is not argued here that a rational approach has been carried out for quantum physics, it is argued that (1) for many important situations found in behavioral science that quantum probability theory is a reasonable choice, and (2) that it has an arguably rational foundation to certain areas of behavioral science, for example, the behavioral paradigm of Between Subjects experiments. Full article

Integration of chip-scale quantum technology was the main aim of this study. First, the recent progress on silicon-based photonic integrated circuits is surveyed, and then it is shown that silicon integrated quantum photonics can be considered a compelling platform for the future of quantum technologies. Among subsections of quantum technology, quantum emitters were selected as the object, and different quantum emitters such as quantum dots, 2D materials, and carbon nanotubes are introduced. Later on, the most recent progress is highlighted to provide an extensive overview of the development of chip-scale quantum emitters. It seems that the next step towards the practical application of quantum emitters is to generate position-controlled quantum light sources. Among developed processes, it can be recognized that droplet–epitaxial QD growth has a promising future for the preparation of chip-scale quantum emitters. Full article

Contextuality is often described as a unique feature of the quantum realm, which distinguishes it fundamentally from the classical realm. This is not strictly true, and stems from decades of the misapplication of Kolmogorov probability. Contextuality appears in Kolmogorov theory (observed in the inability to form joint distributions) and in non-Kolmogorov theory (observed in the violation of inequalities of correlations). Both forms of contextuality have been observed in psychological experiments, although the first form has been known for decades but mostly ignored. The complex dynamics of neural systems (neurobehavioural regulatory systems) and of collective intelligence systems (social insect colonies) are described. These systems are contextual in the first sense and possibly in the second as well. Process algebra, based on the Process Theory of Whitehead, describes systems that are generated, transient, open, interactive, and primarily information-driven, and seems ideally suited to modeling these systems. It is argued that these dynamical characteristics give rise to contextuality and non-Kolmogorov probability in spite of these being entirely classical systems. Full article

In this paper, we demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogolyubov transformations lead to pairs of the spin network’s edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere. Full article

The second quantum technological revolution started around 1980 with the control of single quantum particles and their interaction on an individual basis. These experimental achievements enabled physicists, engineers, and computer scientists to utilize long-known quantum features—especially superposition and entanglement of single quantum states—for a whole range of practical applications. We use a publication set of 54,598 papers from Web of Science, published between 1980 and 2018, to investigate the time development of four main subfields of quantum technology in terms of numbers and shares of publications, as well as the occurrence of topics and their relation to the 25 top contributing countries. Three successive time periods are distinguished in the analyses by their short doubling times in relation to the whole Web of Science. The periods can be characterized by the publication of pioneering works, the exploration of research topics, and the maturing of quantum technology, respectively. Compared to the USA, China’s contribution to the worldwide publication output is overproportionate, but not in the segment of highly cited papers. Full article

Indeterminacy associated with the probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here, we express it as an effective amount (measure) of distinct outcomes instead. The resulting μ-uncertainties are described by the effective number theory whose central result, the existence of a minimal amount, leads to a well-defined notion of intrinsic irremovable uncertainty. We derive $\mu$-uncertainty formulas for arbitrary set of commuting operators, including the cases with continuous spectra. The associated entropy-like characteristics, the $\mu$-entropies, convey how many degrees of freedom are effectively involved in a given measurement process. In order to construct quantum $\mu$-entropies, we are led to quantum effective numbers designed to count independent, mutually orthogonal states effectively comprising a density matrix. This concept is basis-independent and leads to a measure-based characterization of entanglement. Full article

It is well known that, using the conventional non-Hermitian but $\mathcal{PT}-$symmetric Bose–Hubbard Hamiltonian with real spectrum, one can realize the Bose–Einstein condensation (BEC) process in an exceptional-point limit of order N. Such an exactly solvable simulation of the BEC-type phase transition is, unfortunately, incomplete because the standard version of the model only offers an extreme form of the limit, characterized by a minimal geometric multiplicity $K = 1$. In our paper, we describe a rescaled and partitioned direct-sum modification of the linear version of the Bose–Hubbard model, which remains exactly solvable while admitting any value of $K\ge 1$. It offers a complete menu of benchmark models numbered by a specific combinatorial scheme. In this manner, an exhaustive classification of the general BEC patterns with any geometric multiplicity is obtained and realized in terms of an exactly solvable generalized Bose–Hubbard model. Full article

Photon subtraction is useful to produce nonclassical states of light addressed to applications in photonic quantum technologies. After a very accelerated development, this technique makes possible obtaining either single photons or optical cats on demand. However, it lacks theoretical formulation enabling precise predictions for the produced fields. Based on the representation generated by the two-mode $SU(2)$ coherent states, we introduce a model of entangled light beams leading to the subtraction of photons in one of the modes, conditioned to the detection of any photon in the other mode. We show that photon subtraction does not produce nonclassical fields from classical fields. It is also derived a compact expression for the output field from which the calculation of conditional probabilities is straightforward for any input state. Examples include the analysis of squeezed-vacuum and odd-squeezed states. We also show that injecting optical cats into a beam splitter gives rise to entangled states in the Bell representation. Full article

We analyze possible connections between quantum-inspired classifications and support vector machines. Quantum state discrimination and optimal quantum measurement are useful tools for classification problems. In order to use these tools, feature vectors have to be encoded in quantum states represented by density operators. Classification algorithms inspired by quantum state discrimination and implemented on classic computers have been recently proposed. We focus on the implementation of a known quantum-inspired classifier based on Helstrom state discrimination showing its connection with support vector machines and how to make the classification more efficient in terms of space and time acting on quantum encoding. In some cases, traditional methods provide better results. Moreover, we discuss the quantum-inspired nearest mean classification. Full article

It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, i.e., that its integral is one and that the marginal properties are satisfied. However, this is generally not true. We introduced a class of quantum states for which this property is satisfied; these states are dubbed “Feichtinger states” because they are defined in terms of a class of functional spaces (modulation spaces) introduced in the 1980s by H. Feichtinger. The properties of these states were studied, giving us the opportunity to prove an extension to the general case of a result due to Jaynes on the non-uniqueness of the statistical ensemble, generating a density operator. Full article

We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectra, and transit to the Hermitian configuration for the appropriate values of the involved parameters. We provide a concrete generalization of the Swanson oscillator that includes the Caldirola–Kanai model as a particular case. Explicit solutions are given in both the classical and quantum pictures. Full article

We present a simple proof of the fact that the minimum time $T_{AB}$ for quantum evolution between two arbitrary states $\left|A\right.⟩$ and $\left|B\right.⟩$ equals $T_{AB}=\hslash {cos}^{-1}\left[\left|⟨A|B⟩\right|\right]/\mathsf{\Delta }E$ with $\mathsf{\Delta }E$ being the constant energy uncertainty of the system. This proof is performed in the absence of any geometrical arguments. Then, being in the geometric framework of quantum evolutions based upon the geometry of the projective Hilbert space, we discuss the roles played by either minimum-time or maximum-energy uncertainty concepts in defining a geometric efficiency measure $\epsilon$ of quantum evolutions between two arbitrary quantum states. Finally, we provide a quantitative justification of the validity of the inequality $\epsilon \le 1$ even when the system only passes through nonorthogonal quantum states. Full article

The physical synthesis concept for quantum circuits, the interaction between synthesis and physical design processes, was first introduced in our previous work. This concept inspires us to propose some techniques that can minimize the number of extra inserted SWAP operations required to run a circuit on a nearest-neighbor architecture. Minimizing the number of SWAP operations potentially decreases the latency and error probability of a quantum circuit. Focusing on this concept, we present a physical synthesis technique based on transformation rules to decrease the number of SWAP operations in nearest-neighbor architectures. After the qubits of a circuit are mapped onto the physical qubits provided by the target architecture, our procedure is fed by this mapping information. Our method uses the obtained placement and scheduling information to apply some transformation rules to the original netlist to decrease the number of extra SWAP gates required for running the circuit on the architecture. We follow two policies in applying a transformation rule, greedy and simulated-annealing-based policies. Simulation results show that the proposed technique decreases the average number of extra SWAP operations by about 20.6% and 24.1% based on greedy and simulated-annealing-based policies, respectively, compared with the best in the literature. Full article

We propose a physical mechanism of conformation-induced proton pumping in mitochondrial Complex I. The structural conformations of this protein are modeled as the motion of a piston having positive charges on both sides. A negatively charged electron attracts the piston, moving the other end away from the proton site, thereby reducing its energy and allowing a proton to populate the site. When the electron escapes, elastic forces assist the return of the piston, increasing proton site energy and facilitating proton transfer. We derive the Heisenberg equations of motion for electron and proton operators and rewrite them in the form of rate equations coupled to the phenomenological Langevin equation describing piston dynamics. This set of coupled equations is solved numerically. We show that proton pumping can be achieved within this model for a reasonable set of parameters. The dependencies of proton current on geometry, temperature, and other parameters are examined. Full article

Bell’s inequality is investigated in parity-time ($\mathcal{PT}$) symmetric quantum mechanics, using a recently developed form of the inequality by Maccone, with two $\mathcal{PT}$-qubits in the unbroken phase with real energy spectrum. It is shown that the inequality produces a bound that is consistent with the standard quantum mechanics even after using Hilbert space equipped with $\mathcal{CPT}$ inner product and therefore, the entanglement has identical structure with standard quantum mechanics. Consequently, the no-signaling principle for a two-qubit system in $\mathcal{PT}$-symmetric quantum theory is preserved. Full article

We discuss different formal frameworks for the description of generalized probabilities in statistical theories. We analyze the particular cases of probabilities appearing in classical and quantum mechanics and the approach to generalized probabilities based on convex sets. We argue for considering quantum probabilities as the natural probabilistic assignments for rational agents dealing with contextual probabilistic models. In this way, the formal structure of quantum probabilities as a non-Boolean probabilistic calculus is endowed with a natural interpretation. Full article