Quantum Reports

This paper examines no-hidden-variables theorems in quantum mechanics from the point of view of statistical mechanics. It presents a general analysis of the measurement process in the Boltzmannian framework that leads to a characterization of (in)compatible measurements and reproduces several features of quantum probabilities often described as “non-classical”. The analysis is applied to versions of the Kochen–Specker and Bell theorems to shed more light on their implications. It is shown how, once the measurement device and the active role of the measurement process are taken into account, contextuality appears as a natural feature of random variables. This corroborates Bell’s criticism that no-go results of the Kochen–Specker type are based on gratuitous assumptions. In contrast, Bell-type theorems are much more profound, but should be understood as nonlocality theorems rather than no-hidden-variables theorems. Finally, the paper addresses misunderstandings and misleading terminology that have confused the debate about hidden variables in quantum mechanics. Full article

Quantum annealers conventionally use forward annealing to generate heuristic solutions. Reverse annealing can potentially generate better solutions but necessitates an appropriate initial state. Ways to find such states are generally unknown or highly problem dependent, offer limited success, and severely restrict the scope of reverse annealing. We use a general method that improves the overall solution quality and quantity by feeding reverse annealing with low-quality solutions obtained from forward annealing. An experimental demonstration of solving the graph coloring problem using the D-Wave quantum annealers shows that our method is able to convert invalid solutions obtained from forward annealing to at least one valid solution obtained after assisted reverse annealing for $57\%$ of 459 random Erdos–Rényi graphs. Our method significantly outperforms random initial states, obtains more unique solutions on average, and widens the applicability of reverse annealing. Although the average number of valid solutions obtained drops exponentially with the problem size, a scaling analysis for the graph coloring problem shows that our method effectively extends the computational reach of conventional forward annealing using reverse annealing. Full article

Qubit systems based on trapped ultracold ions win one of the leading positions in the quantum computing field, demonstrating quantum algorithms with the highest complexity to date. Surface Paul traps for ion confinement open the opportunity to scale quantum processors to hundreds of qubits and enable high-connectivity manipulations on ions. To fabricate such a system with certain characteristics, the special design of a surface electrode structure is required. The depth of the trapping potential, the stability parameter, the secular frequency and the distance between an ion and the trap surface should be optimized for better performance. Here, we present the optimized design of a relatively simple surface trap that allows several important high-fidelity primitives: tight ion confinement, laser cooling, and wide optical access. The suggested trap design also allows us to perform an important basic operation, namely, splitting an ion chain into two parts. Full article

Under the quaternion group, $Q_8$, spin helicity emerges as a crucial element of the reality of spin and is complementary to its polarization. We show that the correlation in EPR coincidence experiments is conserved upon separation from a singlet state and distributed between its polarization and coherence. Including helicity accounts for the violation of Bell’s Inequalities without non-locality, and disproves Bell’s Theorem by a counterexample. Full article

Quantum Key Distribution (QKD) offers a revolutionary approach to secure communication, leveraging the principles of quantum mechanics to generate and distribute cryptographic keys that are immune to eavesdropping. As QKD systems become more widely adopted, the need for robust monitoring and management solutions has become increasingly crucial. The Cerberis3 QKD system from ID Quantique addresses this challenge by providing a comprehensive monitoring and visualization platform. The system’s advanced features, including central configuration, SNMP integration, and the graphical visualization of key performance metrics, enable network administrators to ensure their QKD infrastructure’s reliable and secure operation. Monitoring critical parameters such as Quantum Bit Error Rate (QBER), secret key rate, and link visibility is essential for maintaining the integrity of the quantum channel and optimizing the system’s performance. The Cerberis3 system’s ability to interface with encryption vendors and support complex network topologies further enhances its versatility and integration capabilities. By addressing the unique challenges of quantum monitoring, the Cerberis3 system empowers organizations to leverage the power of QKD technology, ensuring the security of their data in the face of emerging quantum computing threats. This article explores the Cerberus3 system’s features and its role in overcoming the monitoring challenges inherent to QKD deployments. Full article

We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic moments, each with a spin of $\frac{1}{2}$—these moments couple in free flight to create a spin-1 boson. Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of $\frac{1}{2}$, or it remains a boson and precedes without decoupling. The only variable in this study is the angle that orients a spin on the Bloch sphere, first identified in the 1920s. There are no hidden variables. The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, Q₈, which complexifies the Dirac field. The transition from a free-flight boson to a measured fermion causes the observed violation of Bell’s Inequalities and resolves the EPR paradox. Full article

The measurement problem of quantum mechanics concerns the question as to under which circumstances coherent wave evolution becomes disrupted to produce eigenstates of observables, instead of evolving superpositions of eigenstates. The problem already needs to be addressed within wave mechanics, before second quantization, because low-energy interactions can be dominated by particle-preserving potential interactions. We discuss a scattering array of harmonic oscillators, which can detect particles penetrating the array through interaction with a short-range potential. Evolution of the wave function of scattered particles, combined with Heisenberg’s assertion that quantum jumps persist in wave mechanics, indicates that the wave function will collapse around single oscillator sites if the scattering is inelastic, while it will not collapse around single sites for elastic scattering. The Born rule for position observation is then equivalent to the statement that the wave function for inelastic scattering amounts to an epistemic superposition of possible scattering states, in the sense that it describes a sum of probability amplitudes for inelastic scattering off different scattering centers, whereas, at most, one inelastic scattering event can happen at any moment in time. Within this epistemic interpretation of the wave function, the actual underlying inelastic scattering event corresponds to a quantum jump, whereas the continuously evolving wave function only describes the continuous evolution of probability amplitudes for scattering off different sites. Quantum jumps then yield definite position observations, as defined by the spatial resolution of the oscillator array. Full article

Motivated by the revitalized interest in the digital simulation of medium- and high-energy physics phenomena, we investigate the dynamics following a Yukawa interaction quench on IBM Q. Adopting the zero-dimensional version of the scalar Yukawa coupling model as our point of departure, we design low-depth quantum circuits, emulating its dynamics with up to three bosons. In the one-boson case, we demonstrate circuit compression, i.e., a constant-depth circuit containing only two controlled-NOT (CNOT) gates. In the more complex three-boson case, we design a circuit in which one Trotter step entails eight CNOTs. Using an analogy with the traveling salesman problem, we also provide a CNOT cost estimate for higher boson number truncations. Based on these circuits, we quantify the system dynamics by evaluating the expected boson number at an arbitrary time after the quench and the survival probability of the initial vacuum state (the Loschmidt echo). We also utilize these circuits to drive adiabatic transitions and compute the energies of the ground- and first-excited states of the considered model. Finally, through error mitigation, i.e., zero-noise extrapolation, we demonstrate the good agreement of our results with a numerically exact classical benchmark. Full article

Some time ago, Kobayashi et al. experimentally studied the so-called Lee–Naughton–Lebed’s (LNL) angular effect in strong electric fields [Kobayashi, K.; Saito, M.; Omichi E.; Osada, T. Phys. Rev. Lett. 2006, 96, 126601]. They found that strong electric fields split the LNL conductivity maxima in an $\alpha$-(ET)₂-based organic conductor and hypothetically introduced the corresponding equation for conductivity. In this paper, for the first time, we suggest the quantum mechanical theory of the LNL angular oscillations in moderately strong electric fields. In particular, we demonstrate that the approximate theoretical formula obtained by us well describes the above mentioned experiments. Full article

We report the results of an ab initio study of the linear and ring structures of cadmium telluride clusters [CdTe]_n (Cd_nTe_n) n ≤ 10 within the generalized gradient approximation (GGA) and Purdue–Burke–Ernzerhof (PBE) parameterization with Hubbard corrections (GGA+U). We optimized the linear and ring isomers for each size to obtain the lowest-energy structures and to understand their growth behavior. The cases of n < 8 for ring-type structures and n = 6 and 9 for linear-type structures were found to be the most favorable. All observed clusters with a linear structure were found to have a small highest-occupied–lowest-unoccupied molecular orbital (HOMO–LUMO) gap. The CdTe clusters with ring structure showed larger values of the HOMO–LUMO gaps than the band gap value for the bulk crystal. Structural and electronic properties like bond length, the HOMO–LUMO gap, binding energy, and electronegativity were analyzed. Full article

A strategy is developed for writing the time-dependent Schrödinger Equation (TDSE), and more generally the Dyson Series, as a convolution equation using recursive Fourier transforms, thereby decoupling the second-order integral from the first without using the time ordering operator. The energy distribution is calculated for a number of standard perturbation theory examples at first- and second-order. Possible applications include characterization of photonic spectra for bosonic sampling and four-wave mixing in quantum computation and Bardeen tunneling amplitude in quantum mechanics. Full article

The simulation analogy presented in this work enhances the accessibility of abstract quantum theories, specifically the stochastic hydrodynamic model (SQHM), by relating them to our daily experiences. The SQHM incorporates the influence of fluctuating gravitational background, a form of dark energy, into quantum equations. This model successfully addresses key aspects of objective-collapse theories, including resolving the ‘tails’ problem through the definition of quantum potential length of interaction in addition to the De Broglie length, beyond which coherent Schrödinger quantum behavior and wavefunction tails cannot be maintained. The SQHM emphasizes that an external environment is unnecessary, asserting that the quantum stochastic behavior leading to wavefunction collapse can be an inherent property of physics in a spacetime with fluctuating metrics. Embedded in relativistic quantum mechanics, the theory establishes a coherent link between the uncertainty principle and the constancy of light speed, aligning seamlessly with finite information transmission speed. Within quantum mechanics submitted to fluctuations, the SQHM derives the indeterminacy relation between energy and time, offering insights into measurement processes impossible within a finite time interval in a truly quantum global system. Experimental validation is found in confirming the Lindemann constant for solid lattice melting points and the ⁴He transition from fluid to superfluid states. The SQHM’s self-consistency lies in its ability to describe the dynamics of wavefunction decay (collapse) and the measure process. Additionally, the theory resolves the pre-existing reality problem by showing that large-scale systems naturally decay into decoherent states stable in time. Continuing, the paper demonstrates that the physical dynamics of SQHM can be analogized to a computer simulation employing optimization procedures for realization. This perspective elucidates the concept of time in contemporary reality and enriches our comprehension of free will. The overall framework introduces an irreversible process impacting the manifestation of macroscopic reality at the present time, asserting that the multiverse exists solely in future states, with the past comprising the formed universe after the current moment. Locally uncorrelated projective decays of wavefunction, at the present time, function as a reduction of the multiverse to a single universe. Macroscopic reality, characterized by a foam-like consistency where microscopic domains with quantum properties coexist, offers insights into how our consciousness perceives dynamic reality. It also sheds light on the spontaneous emergence of gravity in discrete quantum spacetime evolution, and the achievement of the classical general relativity limit in quantum loop gravity and causal dynamical triangulation. The simulation analogy highlights a strategy focused on minimizing information processing, facilitating the universal simulation in solving its predetermined problem. From within, reality becomes the manifestation of specific physical laws emerging from the inherent structure of the simulation devised to address its particular issue. In this context, the reality simulation appears to employ an optimization strategy, minimizing information loss and data management in line with the simulation’s intended purpose. Full article

The distinct spin, optical, and coherence characteristics of solid-state spin defects in semiconductors have positioned them as potential qubits for quantum technologies. Both bulk and two-dimensional materials, with varying structural properties, can serve as crystalline hosts for color centers. In this study, we conduct a comparative analysis of the spin–optical, electron–nuclear, and relaxation properties of nitrogen-bound vacancy defects using electron paramagnetic resonance (EPR) and electron–nuclear double resonance (ENDOR) techniques. We examine key parameters of the spin Hamiltonian for the nitrogen vacancy (${NV}^{-}$) center in 4H-SiC: D = 1.3 GHz, A_zz = 1.1 MHz, and C_Q = 2.53 MHz, as well as for the boron vacancy ($V_B^{-}$) in hBN: D = 3.6 GHz, A_zz = 85 MHz, and C_Q = 2.11 MHz, and their dependence on the material matrix. The spin–spin relaxation times T₂ (${NV}^{-}$ center: 50 µs and $V_B^{-}$: 15 µs) are influenced by the local nuclear environment and spin diffusion while Rabi oscillation damping times depend on crystal size and the spatial distribution of microwave excitation. The ENDOR absorption width varies significantly among color centers due to differences in crystal structures. These findings underscore the importance of selecting an appropriate material platform for developing quantum registers based on high-spin color centers in quantum information systems. Full article

The optimization of investment portfolios represents a pivotal task within the field of financial economics. Its objective is to identify asset combinations that meet specified criteria for return and risk. Traditionally, the maximization of the Sharpe Ratio, often achieved through quadratic programming, has constituted a popular approach for this purpose. However, real-world scenarios frequently necessitate more complex considerations, particularly in relation to portfolio diversification with a view to mitigating sector-specific risks and enhancing stability. The incorporation of diversification alongside the Sharpe Ratio into the optimization model creates a joint optimization task, which can be formulated as Quadratic Unconstrained Binary Optimization (QUBO) and addressed using quantum annealing or hybrid computing techniques. These techniques offer promising solutions. We present a novel QUBO formulation for this optimization, detailing its mathematical formulation and demonstrating its advantages over classical methods, particularly in handling diversification objectives. By leveraging available QUBO solvers and hybrid approaches, we explore the feasibility of handling large-scale problems while highlighting the importance of diversification in achieving robust portfolio performance. We finally elaborate on the results showing the trade-off between the observed values of the portfolio’s Sharpe Ratio and diversification, as a natural consequence of solving a multi-objective optimization problem. Full article

Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to the wave equation. The information related to the amplitude measures the strength of the potential coupling of the particle (which is itself aspatial) with each volume of its configuration space, i.e., its tendency to participate in an interaction localized in a region of ordinary physical space corresponding to that volume. The information connected to the phase is that required to obtain the time evolution of the particle as a persistent entity starting from a random succession of bits. It can be considered as the information provided by conservation principles. The meaning of the so-called “quantum potential” in this context is briefly discussed. Full article

We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate $\Gamma$ of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every time t. Due to invariance by unitary transformations, the dynamics of the eigenvalues ${\left\{{\lambda }_{\alpha }\right\}}_{\alpha =1}^n$ of the density matrix decouples from that of the eigenvectors, and is exactly described by stochastic equations that we derive. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large size $n\to \infty$ it matches with the inverse-Marchenko–Pastur distribution. In the case of perfect measurements, instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of $\lambda$’s at each time t and for each size n. Two relevant regimes emerge: at short times $t\Gamma =O\left(1\right)$, the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the $n\to \infty$ limit. In that case, all moments of the density matrix become self-averaging and it is possible to exactly characterize the entanglement spectrum. In the limit of large times $t\Gamma =O\left(n\right)$, one enters instead a regime in which the eigenvalues are exponentially separated $\log ({\lambda }_{\alpha }/{\lambda }_{\beta })=O(\Gamma t/n)$, but fluctuations $\sim O\left(\sqrt{\Gamma t/n}\right)$ play an essential role. We are still able to characterize the asymptotic behaviors of the entanglement entropy in this regime. Full article

The solutions to the radial Schrödinger equation for a pseudoharmonic potential and Kratzer potential have been studied separately in the past. Despite different reports on the Kratzer potential, the fundamental theoretical quantities such as Fisher information have not been reported. In this study, we obtain the solution to the radial Schrödinger equation for the combination of the pseudoharmonic and Kratzer potentials in the presence of a constant-dependent potential, utilizing the concepts and formalism of the supersymmetric and shape invariance approach. The position expectation value and momentum expectation value are calculated employing the Hellmann–Feynman Theory. These expectation values are then used to calculate the Fisher information for both position and momentum spaces in both the absence and presence of the constant-dependent potential. The results obtained revealed that the presence of the constant-dependent potential leads to an increase in the energy eigenvalue, as well as in the position and momentum expectation values. Additionally, the constant-dependent potential increases the Fisher information for both position and momentum spaces. Furthermore, the product of the position expectation value and the momentum expectation value, along with the product of the Fisher information, satisfies both Fisher’s inequality and Cramer–Rao’s inequality. Full article

The Schrödinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and non-quadratic potentials, in both one-dimensional and three-dimensional scenarios. Numerical computation of the energy spectrum of bound eigenfunctions in both cases reveals intriguing structures, including bound states with degeneracy matching the site number $N_w$, reminiscent of a finite harmonic oscillator spectrum. In contrast to electronic energy bands, the proton system displays a greater number of possible bound states due to the significant mass of protons. Extending previous research, this study rigorously determines the constraints on the energy gap and oscillation amplitude of the previously identified coherent states. The deviations in energy level spacing identified in the computed spectrum, leading to the minor splitting of electromagnetic modes, are analyzed and found not to hinder the onset of coherence. Finally, a more precise value of the energy gap is determined for the proton coherent states, ensuring their stability against thermal decoherence up to the melting temperature of the hosting metal. Full article

Inspired by the principles of quantum mechanics, we constructed a model of students’ misconceptions about heat and temperature, conceptualized as a quantum system represented by a density matrix. Within this framework, the presence or absence of misconceptions is delineated as pure states, while the probability of mixed states is also considered, providing valuable insights into students’ cognition based on the mental models they employ when holding misconceptions. Using the analysis model previously employed by Lei Bao and Edward Redish, we represented these results in a density matrix. In our research, we utilized the Zeo and Zadnik Thermal Concept Evaluation among 282 students from a private university in Northeast Mexico. Our objective was to extract information from the analysis of multiple-choice questions designed to explore preconceptions, offering valuable educational insights beyond the typical Correct–Incorrect binary analysis of classical systems. Our findings reveal a probability of 0.72 for the appearance of misconceptions, 0.28 for their absence, and 0.43 for mixed states, while no significant disparities were observed based on gender or scholarship status, a notable difference was observed among programs (p < 0.05). These results are consistent with the previous literature, confirming a prevalence of misconceptions within the student population. Full article