arXiv subjects

Gregory D. Scholes

Publications and source records attributed to Gregory D. Scholes.

At least 19 recordsLinked to original sources

arXiv2026

Minimal representations of topology-preserving quantum-like states

We provide an equitable partition that gives an exact, minimal representation for the graph Cartesian product formed from quantum-like bits that preserves the relevant spectral and topological properties. We show that this result follows from the fact that the operations of taking the Cartesian product of graphs and constructing equitable partition of the graphs commute. Numerical simulations illustrate the preserved emergent eigenstates in the reduced structures. Additionally, we provide a construction of the minimal structure without passing through the Cartesian product. Finally, we frame quantum-like structures in the language of topology and fibrations.

quant-ph↗

arXiv2026

Measurements on the separated subsystems of an entangled state

The entangled states of composite quantum systems are well studied. The particle-like nature of these systems also means that, while entangled, they can be physically separated and measurements performed on the separated subsystems. Measurements on the separated subsystems A and B should pertain to vectors in the local Hilbert space of each subsystem, but to date it has not been clear how to elucidate the relevant states of the separated subsystems because it is not obvious how to resolve them from states given in the tensor product basis, except for the separable states. Here it is shown that the projections of any general entangled state that are detected by measurements on the separated subsystems can be obtained considering the corresponding (cosets of) states in the free vector space from which the tensor product space is defined. The result eliminates the need to invoke random collapse, and from this perspective nonlocality arises because of the way measurements on each separated subsystem projects possible measurement outcomes.

quant-ph↗

arXiv2026

Computational Methods of Wave Propagation for Semiclassical Models of High Harmonic Generation in Bulk Solids

We present a theoretical framework for self consistent treatment of nonlinear light-matter interactions in the ultra-fast strong-field regime based on numerical solution of Maxwell's equations and semiconductor Bloch equations. This framework is shown to describe high-order harmonic generation and propagation in bulk semiconductors, investigating differences in reflected and transmitted harmonic spectra due to propagation effects. We show that the propagation of the combined field of the driving laser pulse and generated harmonics in a bulk semiconductor significantly modifies the harmonic spectra, affecting interpretation of experimental results relating the transmitted harmonic spectra to the underlying electronic structure of the material. This model allows the self-consistent description of strong-field light-matter interactions in the non-perturbative regime, opening the way to explore the transition between fully classical and quantum regimes of interaction, tunneling and multiphoton regimes of material ionization, and perturbative and non-perturbative regimes of harmonic generation in bulk materials.

physics.optics↗

arXiv2026

Mechanism of wavefunction collapse in measurements of separated quantum subsystems

The specific advance of this work is to propose a mechanism by which superpositions collapse during measurement of the separated subsystems of entangled quantum states. It is shown how the phase that locks together entangled states plays a special role in the measurement of isolated subsystems. This `contextual' phase is installed randomly into the entangled state, and decides the measurement outcomes for the subsystems by directing the collapse of each superposition to a particular classical outcome when a subsystem is measured. The measuring apparatus thus obtains a classical read-out of the quantum correlations embedded in an entangled state. More broadly, these results solidify the theory of measurement of quantum superpositions.

quant-ph↗

arXiv2026

Quantum-like states from classical systems

This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space that comprises superpositions of states in a tensor product basis. The basis for constructing QL graphs and their properties is reviewed and extended. An optimization of the graph product is developed to produce a more compact graph with the essential properties required to produce states that mimic many of the properties of quantum states. This provides a concrete visualization of the correlation structure in a quantum state space. The question of whether and, if so, how, entanglement can be exhibited by these QL systems is discussed critically and contrasted to the concept of `classical entanglement' in optics.

quant-ph↗

arXiv2026

Existence, structure, and properties of quantum-like states

The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can closely emulate states of composite quantum systems, such as coupled two-level systems that display separable linear combinations of states. Examples of classical systems are suggested that show these states. These include multipole moments of waves or networks of phase oscillators. The work indicates that composite QL states can be manifest in complex network structures relevant to quantum biology or engineered into circuits, or even possibly soft matter.

quant-ph↗

arXiv2026

Operational bounds and diagnostics for coherence in energy transfer

Excitation energy transfer in light-harvesting aggregates is highly efficient, yet whether quantum coherence plays an operational role in transport remains debated. A central challenge is that coherence is usually inferred from spectroscopic signatures, whereas transport performance is assessed through specific observables and depends on both the open system dynamics and the initial state preparation. Here we develop a resource theoretic approach that quantifies the maximum change that initial site-basis coherence can induce in a chosen readout under fixed reduced dynamics. The central quantity is the resource impact functional, which yields state independent, readout specific bounds on coherence-induced changes in signals and transport figures of merit. We apply the framework to two models. For a donor-acceptor dimer, we analyse coherence sensitivity across coupling and bath-timescale regimes and bound trapping efficiency and average transfer time in terms of the impact functional. For a multi-site chain with terminal trapping, we derive rigorous criteria that distinguish population placement from sensitivity to initial state site-basis coherence. These include upper bounds on the largest advantage over incoherent preparations, necessary delocalization requirements for achieving a prescribed improvement, and a simple pairwise sufficient condition that can be checked from local information. For quasi-local reduced dynamics, we further obtain a Lieb-Robinson-type bound that constrains when coherence prepared in a distant region can influence a localized readout at finite times. Together, these results provide operational diagnostics and rigorous bounds for benchmarking coherence effects and for identifying regimes in which they are necessarily negligible or potentially relevant in excitonic transport models.

quant-ph↗

arXiv2026

Operational impact of quantum resources in chemical dynamics

Quantum coherence and other non-classical features are widely discussed in chemical dynamics, yet it remains difficult to quantify when such resources are operationally relevant for a given process and observable. While quantum resource theories provide a comprehensive framework for comparing free and resourceful settings, existing approaches typically rely on resource monotones or on performance bounds under free operations, and do not directly quantify the maximal influence a chosen resource can exert on a fixed chemical dynamics. Here, we introduce task specific, process level quantifiers that upper bound the largest change a quantum resource can induce in a target figure of merit. Central is a resource impact functional $\mathcal{C}_M(Λ)$, defined by comparing a state with its paired resource-free counterpart under the same quantum channel $Λ$, which admits an operational interpretation in binary hypothesis testing. We derive variation and time bounds that constrain how rapidly a resource can modify a target signal, providing resource-aware analogues of quantum speed limits. Moreover, we show that open system dynamics can be decomposed into free and resourceful components such that only the resourceful component contributes to $\mathcal{C}_M(Λ)$, thereby isolating the parts of a generator responsible for resource-induced changes in the observable. We illustrate the framework exemplary for energy transfer in a donor-acceptor dimer in two analytically solvable regimes. Our results provide a general toolbox for diagnosing and benchmarking quantum resource effects in molecular processes.

quant-ph↗

arXiv2025

Dynamics in an emergent quantum-like state space generated by a nonlinear classical network

This work exploits a framework whereby a graph (in the mathematical sense) serves to connect a classical system to a state space that we call `quantum-like' (QL). The QL states comprise arbitrary superpositions of states in a tensor product basis. The graph plays a special dual role by directing design of the classical system and defining the state space. We study a specific example of a large, dynamical classical system -- a system of coupled phase oscillators -- that maps, via a graph, to the QL state space. We investigate how mixedness of the state diminishes or increases as the underlying classical system synchronizes or de-synchronizes respectively. This shows the interplay between the nonlinear dynamics of the variables of the classical system and the QL state space. We prove that maps from one time point to another in the state space are linear maps. In the limit of a strongly phase-locked classical network -- that is, where couplings between phase oscillators are very large -- the state space evolves according to unitary dynamics, whereas in the cases of weaker synchronization, the classical variables act as a hidden environment that promotes decoherence of superpositions. We examine how similar the properties of QL states are to quantum states. We find that during decoherence of the QL states, the off-diagonal density matrix elements decay and that this decay can be observed in any basis we choose for measurement. More surprisingly, we show that a no-cloning theorem (that is, a state of a QL bit cannot be copied) applies not only to the QL states, but also to the underlying classical system.

quant-ph↗

arXiv2025

Quantum information with quantum-like bits

In previous work we have proposed a construction of quantum-like bits that could endow a large synchronizing classical system, for example of oscillators, with quantum-like function that is not compromised by decoherence. In the present paper we investigate further this platform of quantum-like states. Firstly, we discuss a general protocol on how to construct classical synchronizing networks that allow for emergent states. We then study how gates can be implemented on those states. This suggests the possibility of quantum-like information processing on a special class of many-body classical systems. Finally, we show that our approach allows for non-Kolmogorov interference, a feature that separates our model from a classical probabilistic system. This paper aims to explore the mathematical structure of quantum-like resources distilled from classical synchronizing systems, and shows how arbitrary gates can be implemented by manipulating many-body correlations.

quant-ph↗

arXiv2025

Encoding quantum-like information in classical synchronizing dynamics

In previous work, we introduced a formalism that maps classical networks of nonlinear oscillators onto a quantum-like Hilbert space. We demonstrated that specific network transformations correspond to quantum gates, underscoring the potential of classical many-body systems as platforms for quantum-inspired information processing. In this paper, we extend this framework by systematically identifying the classical dynamics best suited for this purpose. Specifically, we address the question: Can the collective steady state of a classical network encode signatures of quantum information? We prove that the answer is affirmative for a special class of synchronizing many-body systems, namely, a complex-field extension of the Kuramoto model of nonlinearly coupled classical oscillators. Through this approach, we investigate how quantum-like entangled states can emerge from classical synchronization dynamics.

quant-ph↗

arXiv2025

Graphs that predict exciton delocalization

The field of molecular excitons and related supramolecular systems has largely focused on aggregates where nearest-neighbour couplings dominate. We propose that radically different states can be produced by moving beyond that paradigm. In practice, how to accomplish this task remains an open challenge because it requires development of ways to couple networks molecules more densely. In the present work we motivate why it would be worthwhile. We describe a merger of work developed in the field of discrete mathematics with concepts and needs for the field of molecular excitons. We discuss the reasons for exciton localization and posit how systems where the spectrum contains a gap can be robust to disorder, and thus maintain coherence, or delocalization. We propose that certain kinds of structures (expander graphs) specifying how molecules are coupled to each other, show such a gap and thus resilience to decoherence. We review relevant background known from graph theory. This perspective suggests a fascinating scope of new properties possible by demonstrating expander graph inspired excitonics.

physics.chem-ph↗

arXiv2025

Quantum-like product states constructed from classical networks

Can complex classical systems be designed to exhibit superpositions of tensor products of basis states, thereby mimicking quantum states? We exhibit a one-to one map between the product basis of quantum states comprising an arbitrary number of qubits and the eigenstates of a construction comprising classical oscillator networks. Specifically, we prove the existence of this map based on Cartesian products of graphs, where the graphs depict the layout of oscillator networks. We show how quantum-like gates can act on the classical networks to allow quantum-like operations in the state space.

quant-ph↗

arXiv2024

Disorder enhanced exciton transport and quantum information spreading with the assistance of cavity QED

Molecular materials have been studied as a potential platform for highly efficient transport such as exciton transport and quantum information spreading. However, one detrimental factor to transport efficiency is the inherent disorder of the molecular system, where site-to-site hopping is suppressed by Anderson localization. Here we theoretically report a novel approach to eliminate the negative impact of disorder by strongly coupling the system to a cavity, where the cavity photon bridges spatially separated sites and builds an additional transport channel, cavity-mediated jumping. Our analysis of the open quantum system dynamics shows in terms of long-range transport, the two channels hold a competitive relation. When disorder suppresses site-to-site hopping, transport occurs mainly through cavity-mediated jumping in disguise. Therefore, with the assistance of the cavity, disorder in certain ranges can enhance transport and certain disordered systems can even be more efficient for transport than the homogeneous system. These results provide insight into the design of next-generation materials for exciton transport and quantum information spreading by leveraging hybrid light-matter states.

quant-ph↗

arXiv2024

Molecular Entanglement Witness by Absorption Spectroscopy in Cavity QED

Producing and maintaining molecular entanglement at room temperature and detecting multipartite entanglement features of macroscopic molecular systems remain key challenges for understanding inter-molecular quantum effects in chemistry. Here, we study the quantum Fisher information, a central concept in quantum metrology, as a multipartite entanglement witness. We generalize the entanglement witness functional related to quantum Fisher information regarding non-identical local response operators. We show that it is a good inter-molecular entanglement witness for ultrastrong light-matter coupling in cavity quantum electrodynamics, including near the superradiant phase transition. We further connect quantum Fisher information to the dipole correlator, which suggests that this entanglement could be detected by absorption spectroscopy. Our work proposes a general protocol to detect inter-molecular entanglement in chemical systems at room temperature.

quant-ph↗

arXiv2024

Quantum-like states on complex synchronized networks

Recent work has exposed the idea that interesting quantum-like probability laws, including interference effects, can be manifest in classical systems. Here we propose a model for quantum-like (QL) states and QL bits. We suggest a way that huge, complex systems can host robust states that can process information in a QL fashion. Axioms that such states should satisfy are proposed. Specifically, it is shown that building blocks suited for QL states are networks, possibly very complex, that we defined based on $k$-regular random graphs. These networks can dynamically encode a lot of information that is distilled into the emergent states we can use for QL like processing. Although the emergent states are classical, they have properties analogous to quantum states. Concrete examples of how QL functions are possible are given. The possibility of a `QL advantage' for computing-type operations and the potential relevance for new kinds of function in the brain are discussed and left as open questions.

physics.soc-ph↗

arXiv2023

Foundations of Quantum Information for Physical Chemistry

Quantum information, a field in which great advances have been made in the past decades, now presents opportunities for chemistry. One roadblock to progress, especially for experimental chemical science, is that new concepts and technical definitions need to be learned. In this paper, we review some basic, but sometimes misunderstood, concepts of quantum information based on the mathematical formulation of quantum mechanics that will be useful for chemists interested in discovering ways that chemistry can contribute to the quantum information field. We cover topics including qubits and their density matrix formalism, quantum measurement as a quantum operation, information theory, and entanglement. We focus on the difference between the concepts in the quantum context and the classic context. We also discuss the relation and distinction among entanglement, correlation, and coherence. We aim to clarify the rigorous definition of these concepts, and then indicate some examples in physical chemistry.

quant-ph↗

arXiv2023

Manipulation of Charge Delocalization in a Bulk Heterojunction Material Using a Mid-Infrared Push Pulse

In organic bulk heterojunction materials, charge delocalization has been proposed to play a vital role in the generation of free carriers by reducing the Coulomb attraction via an interfacial charge transfer exciton (CTX). Pump-push-probe (PPP) experiments produced evidence that the excess energy given by a push pulse enhances delocalization, thereby increasing photocurrent. However, previous studies have employed near-IR push pulses in the range 0.4-0.6 eV which is larger than the binding energy of a typical CTX. This raises the doubt that the push pulse may directly promote dissociation without involving delocalized states. Here, we perform PPP experiments with mid-IR push pulses at energies that are well below the binding energy of a CTX state (0.12-0.25 eV). We identify three types of CTX: delocalized, localized, and trapped. The excitation resides over multiple polymer chains in delocalized CTXs, while is restricted to a single chain (albeit maintaining a degree of intrachain delocalization) in localized CTXs. Trapped CTXs are instead completely localized. The pump pulse generates a hot delocalized CTX, which relaxes to a localized CTX, and eventually to trapped states. We find that photo-exciting localized CTXs with push pulses resonant to the mid-IR charge transfer absorption can promote delocalization and contribute to the formation of long-lived charge separated states. On the other hand, we found that trapped CTX are non-responsive to the push pulses. We hypothesize that delocalized states identified in prior studies are only accessible in systems where there is significant interchain electronic coupling or regioregularity that supports either interchain or intrachain polaron delocalization. This emphasizes the importance of engineering the micromorphology and energetics of the donor-acceptor interface to exploit a full potential of a material for photovoltaic applications.

physics.chem-ph↗