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arXiv:2402.14109 · The European Physical Journal C

Effects of underlying topology on quantum state discrimination

Aatif Kaisar Khan, Yasir Hassan Dar, Elias C. Vagenas, Salman Sajad Wani, Saif M. Al-Kuwari, Mir Faizal

Published Mar 8, 2024• 1 citation
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Abstract

Abstract In this work, we show that quantum state discrimination can be modified due to a change in the underlying topology of a system. In particular, we explicitly demonstrate that the quantum state discrimination of systems with underlying discrete topology differs from that of systems with underlying continuous topology. Such changes in the topology of a spacetime can occur in certain quantum gravity approaches. In fact, all approaches to quantum gravity can be classified into two types: those with underlying continuous topology (such as string theory) and those with an underlying discrete topology (such as loop quantum gravity). We demonstrate that the topology of these two types of quantum gravity approaches has different effects on the quantum state discrimination of low-energy quantum systems. We also show that any modification of quantum mechanics, which does not change the underlying topology, does not modify quantum state discrimination.

DOI
10.1140/epjc/s10052-024-12598-9

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Abstract In this work, we show that quantum state discrimination can be modified due to a change in the underlying topology of a system. In particular, we explicitly demonstrate that the quantum state discrimination of systems with underlying discrete topology differs from that of systems with underlying continuous topology. Such changes in the topology of a spacetime can occur in certain quantum gravity approaches. In fact, all approaches to quantum gravity can be classified into two types: those with underlying continuous topology (such as string theory) and those with an underlying discrete topology (such as loop quantum gravity). We demonstrate that the topology of these two types of quantum gravity approaches has different effects on the quantum state discrimination of low-energy quantum systems. We also show that any modification of quantum mechanics, which does not change the underlying topology, does not modify quantum state discrimination.
We show that a recent proposal for the quantization of gravity based on discrete spacetime implies a modification of standard quantum mechanics that naturally leads to a loss of coherence in quantum states of the type discussed by Milburn. The proposal overcomes the energy conservation problem of previously proposed decoherence mechanisms stemming from quantum gravity. Mesoscopic quantum systems (as Bose–Einstein condensates) appear as the most promising testing grounds for an experimental verification of the mechanism.
This paper investigates the influence of dynamic topology systems on quantum computing, focusing on the development of a framework for simulation and prediction of quantum computation performance. The core claim is that the inherent properties of dynamic topology can be leveraged to design and optimize quantum algorithms through detailed simulations. We propose a model that constructs a quantum environment by simulating the dynamic evolution of a topological system, allowing for the prediction and refinement of quantum algorithms' effectiveness. This research addresses a relatively unexplored area within quantum computing, aiming to provide a novel approach to algorithm optimization.
This research aims to study the behavior of quantum tunneling within the framework of polymer quantization, where spacetime has a discrete structure with a fundamental length μ0\mu_0μ0​. From the Hamiltonian difference equation, we obtained analytical wave functions in each region of the potential barrier and numerically calculated the transmission coefficient and Wigner time delay τw\tau_wτw​ for comparison with standard quantum mechanics. The calculation results show that when the particle energy is lower than the potential barrier E<W0E < W_0E<W0​, the tunneling time τw(n)\tau_w(n)τw​(n) increases rapidly within the narrow barrier and saturates when the width is sufficiently large, confirming that the Hartman effect phenomenon persists even when the spacetime structure is discontinuous. The value of μ0\mu_0μ0​ affects the saturation time but does not change the qualitative nature of this behavior. In the case of E>W0E > W_0E>W0​, the time increases continuously with width, which is consistent with standard quantum mechanics. This result suggests that the semi-classical properties of potential barrier penetration, particularly the Hartman effect, are stable against modifications to spacetime structure and provide important insights into understanding the behavior of quantum systems within a framework inspired by Loop Quantum Gravity (LQG).
The state of two or more particle systems in quantum mechanics is generally expressed as linear superpositions of tensor products of discrete states; and entanglement is connected to the superpositions that cannot be expressed by a single tensor product. On the other hand a discussion of nonlocality is always present in quantum entanglement and furthermore this nonlocality may be revealed via entanglement in the cases of the topological effects in quantum mechanics. In this work, aiming a more systematic and a complementary framework we focus on a comparison of the topological effects of Aharonov-Bohm type whose roots seem to be common. In this context, we will discuss the roles of three topological effects on an entangled quantum mechanical system.
Quantum topology, a field of theoretical physics, explores the properties of spacetime that are inherently quantum mechanical. The concept of quantum topology offers a potential framework for understanding and manipulating the geometry of spacetime at the fundamental level. This paper investigates the application of adaptive geometry topology transformations to quantum systems, aiming to enhance the accuracy and efficiency of simulations and calculations. We propose a novel algorithm that dynamically adjusts the underlying topology of a quantum system based on its internal geometric structure, enabling automated optimization and improved simulation results. The core claim centers on the ability of this algorithm to self-correct and refine the topological structure during the simulation process, addressing limitations of traditional topological transformation methods.
Several phenomenological approaches to quantum gravity predict the existence of a minimal measurable length and/or a maximum measurable momentum near the Planck scale. When embedded into the framework of quantum mechanics, such constraints induce a modification of the canonical commutation relations and thus a generalization of the Heisenberg uncertainty relations, commonly referred to as generalized uncertainty principle (GUP). Different models of quantum gravity imply different forms of the GUP. For instance, in the framework of string theory the GUP is quadratic in the momentum operator, while in the context of doubly special relativity it includes an additional linear dependence. Among the possible physical consequences, it was recently shown that the quadratic GUP induces a universal decoherence mechanism, provided one assumes a foamy structure of quantum spacetime close to the Planck length. Along this line, in the present work we investigate the gravitational decoherence associated to the linear-quadratic GUP and we compare it with the one associated to the quadratic GUP. We find that, despite their similarities, the two generalizations of the Heisenberg uncertainty principle yield decoherence times that are completely uncorrelated and significantly distinct. Motivated by this result, we introduce a theoretical and experimental scheme based on cavity optomechanics to measure the different time evolution of nonlocal quantum correlations corresponding to the two aforementioned decoherence mechanisms. We find that the deviation between the two predictions occurs on time scales that are macroscopic and thus potentially amenable to experimental verification. This scenario provides a possible setting to discriminate between different forms of the GUP and therefore different models of quantum gravity.