A Hessian free method to prevent zero-point energy leakage in classical trajectory simulation

The problem associated with the zero-point energy (ZPE) leak in classical trajectory calculations is well known. Since ZPE is a manifestation of the quantum uncertainty principle, there are no restrictions on energy during the classical propagation of nuclei. This phenomenon can lead to unphysical results, such as forming products without the ZPE in the internal vibrational degrees of freedom (DOFs). The ZPE leakage also permits reactions below the quantum threshold for the reaction. We have developed a new Hessian-free method, inspired by the Lowe-Andersen thermostat model, to prevent energy dipping below a threshold in the local-pair (LP) vibrational DOFs. The idea is to pump the leaked energy to the corresponding local vibrational mode, taken from the other vibrational DOFs. We have applied the new correction protocol on the ab initio ground-state molecular dynamics simulation of the water dimer (H20)2, which dissociates due to unphysical ZPE spilling from the high-frequency OH modes. The LP-ZPE method has been able to prevent the ZPE spilling of the OH stretching modes by pumping back the leaked energy into the corresponding modes while this energy is taken from the other modes of the dimer itself, keeping the system as a microcanonical ensemble.

Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement Gravity versus SU(∞)-QGR

In a previous article we proposed a new model for quantum gravity (QGR) and cosmology, dubbed SU(∞)-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent the SU(∞) symmetry group. In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the SU(∞) representing Hilbert spaces. Using quantum uncertainty relations, it is shown that the parameter space—the spacetime—has a 3+1 dimensional Lorentzian geometry. Here, after a review of SU(∞)-QGR, including a demonstration that its classical limit is Einstein gravity, we compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by the holographic principle and quantum entanglement. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. The hope is that this exercise provides a better understanding of gravity as a universal quantum force and clarifies the physical nature of the spacetime. We identify several common features among the studied models: the importance of 2D structures; the algebraic decomposition to tensor products; the special role of the SU(2) group in their formulation; the necessity of a quantum time as a relational observable. We discuss how these features can be considered as analogous in different models. We also show that they arise in SU(∞)-QGR without fine-tuning, additional assumptions, or restrictions.

Quantum uncertainty relations of Tsallis relative $\alpha$ entropy coherence baed on MUBs

In this paper, we discuss quantum uncertainty relations of Tsallis relative $\alpha$ entropy coherence for a single qubit system based on three mutually unbiased bases. For $\alpha\in[\frac{1}{2},1)\cup(1,2]$, the upper and lower bounds of sums of coherence are obtained. However, the above results cannot be verified directly for any $\alpha\in(0,\frac{1}{2})$. Hence, we only consider the special case of $\alpha=\frac{1}{n+1}$, where $n$ is a positive integer, and we obtain the upper and lower bounds. By comparing the upper and lower bounds, we find that the upper bound is equal to the lower bound for the special $\alpha=\frac{1}{2}$, and the differences between the upper and the lower bounds will increase as $\alpha$ increases. Furthermore, we discuss the tendency of the sum of coherence, and find that it has the same tendency with respect to the different $\theta$ or $\varphi$, which is opposite to the uncertainty relations based on the R\'{e}nyi entropy and Tsallis entropy.

The Presheaf of Conditional Expectations, a Bridge Between Probability and Intuitionistic Truth Value

Research for a theory of quantum gravity has recently led to the use of presheaf topos. Quantum uncertainty is linked to the truth values of intuitionistic logic. This paper proposes transposing this model into a classic probability context, that of conditional mathematical expectations. A simulation of Brownian motion is offered for illustrative purposes.

Secondary and University Students’ Descriptions of Quantum Uncertainty and the Wave Nature of Quantum Particles

Teaching and learning of quantum physics at secondary level is an active field of research. One important challenge is finding ways to promote understanding of quantum concepts without the mathematical formalism that is embedded in quantum mechanics but unavailable on the secondary level. We investigated Norwegian secondary students’ (N = 291) descriptions of the wave nature of quantum particles and the uncertainty principle, as expressed during work with learning resources using a sociocultural approach emphasizing history, philosophy, and nature of science aspects. Responses from university students (N = 40) given after a formalism-based course in quantum physics were included for comparison. Themes were identified using thematic analysis and analyzed from the perspective of pedagogical link-making, seeing different themes as representing different levels of explanations of the concepts (phenomenological, qualitative, mathematical). The most dominant theme in descriptions of particle wave nature was that particles exhibit wave behavior in experiments, while referring to the mathematical description of particles by wave functions was a less prominent theme, even among university students. Two uncertainty principle themes were found: uncertainty as inability to measure pairs of variables precisely, and uncertainty as innate blurriness in nature. Largely missing from descriptions of both concepts were meaningful links between different levels of explanations. Based on the results, we discuss ways forward for teaching particle wave nature and uncertainty in secondary education.

Fisher and Skew Information Correlations of Two Coupled Trapped Ions: Intrinsic Decoherence and Lamb-Dicke Nonlinearity

It is well known that many quantum information processing methods in artificial atoms depend largely on their engineering properties and their ability to generate quantum correlations. In this paper, we investigate the non-classical correlation dynamics of two trapped ions by using local quantum Fisher information, local quantum uncertainty, as well as logarithmic negativity. The system engineering is designed such that the two-trapped-ions work as two diploe-coupled qubits in a Lamb-Dicke regime. The center-of-mass vibrational modes are initially in coherent/even coherent states. It is found that the two-trapped-ions correlations can be controlled by the Lamb-Dicke nonlinearity, the nonclassicality effect of the initial center-of-mass vibrational mode, as well as the trapped-ion coupling and the intrinsic decoherence. The sudden changes in the non-classical correlations and their stability are shown against Lamb-Dicke nonlinearity, the nonclassicality, the trapped-ion coupling, and the intrinsic decoherence.

The accelerated Gisin state: its non-locality, quantum correlations and efficiency to perform quantum masking

The local and non local behavior of the accelerated Gisin state are investigated either before or after filtering process. It is shown that, the possibility of predicting the non-local behavior is forseen at large values of the weight of the Gisin and acceleration parameters. Due to the filtering process, the non-locality behavior of the Gisin state is predicted at small values of the weight parameter. The amount of non classical correlations are quantified by means of the local quantum uncertainty (LQU)and the concurrence, where the LQU is more sensitive to the non-locality than the concurrence. The phenomenon of the sudden changes is displayed for both quantifiers. Our results show that, the accelerated Gisin state could be used to mask information, where all the possible partitions of the masked state satisfy the masking criteria. Moreover, there is a set of states, which satisfy the masking condition, that is generated between each qubit and its masker qubit. For this set, the amount of the non-classical correlations increases as the acceleration parameter increases . Further, the filtering process improves these correlations, where their maximum bounds are much larger than those depicted for non-filtered states.