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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Uniaxial Strain Control of Bulk Ferromagnetism in Rare-Earth Titanates

The perovskite rare-earth titanates are model Mott insulators with magnetic ground states that are very sensitive to structural distortions. These distortions couple strongly to the orbital degrees of freedom and, in principle, it should be possible to tune the superexchange and the magnetic transition with strain. We investigate the representative system (Y,La,Ca)TiO 3 , which exhibits low crystallographic symmetry and no structural instabilities. From magnetic susceptibility measurements of the Curie temperature, we demonstrate direct, reversible, and continuous control of ferromagnetism by influencing the TiO 6 octahedral tilts and rotations with uniaxial strain. The relative change in T C as a function of strain is well described by ab initio calculations, which provides detailed understanding of the complex interactions among structural, orbital, and magnetic properties in rare-earth titanates. The demonstrated manipulation of octahedral distortions opens up far-reaching possibilities for investigations of electron-lattice coupling, competing ground states, and magnetic quantum phase transitions in a wide range of quantum materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Classical combinatorial optimization scaling for random Ising models on 2D heavy-hex graphs

Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum algorithms such as the quantum approximate optimization algorithm. In this study, a specific class of near term quantum computing hardware defined combinatorial optimization problems, Ising models on heavy-hex graphs both with and without geometrically local cubic terms, are examined for their classical computational hardness via empirical computation time scaling quantification. Specifically the time-to-solution (TTS) metric using the classical heuristic simulated annealing is measured for finding optimal variable assignments (ground states), as well as the time required for the optimization software Gurobi to find an optimal variable assignment. Because of the sparsity of these Ising models, the classical algorithms are able to find optimal solutions efficiently even for large instances (i.e. 100 000 spin variables). The Ising models both with and without geometrically local cubic terms exhibit average-case linear-time or weakly quadratic scaling when solved exactly using Gurobi, and the Ising models with no cubic terms show evidence of exponential-time TTS scaling when sampled using simulated annealing. These findings point to the necessity of developing and testing more complex, namely more densely connected, optimization problems in order for quantum computing to ever have a practical advantage over classical computing. Our results are another illustration that different classical algorithms can indeed have exponentially different running times, thus making the identification of the best practical classical technique important in any quantum computing vs. classical computing comparison.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Fluctuating Ru trimer precursor to a two-stage electronic transition in RuP

Superconductivity in binary ruthenium pnictides occurs proximal to and upon suppression of a non-magnetic ground state, preceded by a pseudogap phase associated with Fermi surface instability, and its critical temperature, T c , is maximized around the pseudogap quantum critical point. By analogy with isoelectronic iron based counterparts, antiferromagnetic fluctuations became ''usual suspects" as putative mediators of superconducting pairing. Here we report on a high temperature local symmetry breaking in RuP, nonsuperconducting parent of the maximum- T c branch of these novel superconductors, revealed by combined nanostructure-sensitive powder and single crystal X-ray total scattering analyses. Large local distortions of Ru chains associated with orbital-charge trimerization, further assembled into hexamers, exist above the two-stage electronic transition in RuP. In the pseudogap regime the precursors order with distortions retaining their strength, whereas they acquire spin-singlet characteristics which dramatically enhances the distortion as the nonmagnetic ground state establishes. The precursors enable the nonmagnetic ground state and presumed complex oligomerization, and the relevance of pseudogap fluctuations for superconductivity emerges as a distinct prospect. As a transition metal system in which partial d-manifold filling combined with high crystal symmetry promotes electronic instabilities, this represents a further example of local electronic precursors underpinning the macroscopic collective behavior of quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Nematicity and nematic fluctuations in iron-based superconductors

The reduction of rotational symmetry in a crystalline solid driven by an electronic mechanism is referred to as electronic nematicity. This phenomenon – initially thought to be rare – has by now been observed in an increasing number of systems. Here, the iron-based superconductors present an ideal material platform to study nematicity in crystalline solids. Their nematic transition is pronounced, it can be studied with a wide range of experimental techniques; it is easily tunable; and high-quality samples are widely available. As research on nematicity in iron-based materials is now in its second decade, it builds on tremendous progress in theoretical concepts and experimental techniques. Thus, a stage has been reached at which the nematic phase can be addressed with confidence in its full complexity, including momentum-, time- and material- dependence of the order parameter. Important open questions concern the mechanism by which nematicity affects superconducting pairing and normal-state properties, with a central role for the challenging issue of nematic quantum criticality.

Electronic properties and materials↗
DOE OSTI2025

Lie-algebraic classical simulations for quantum computing

The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for Clifford circuits, tensor networks for low entanglement-generating circuits, or Wick's theorem for fermionic Gaussian states have become central tools in quantum computing. In this work, we contribute to this body of knowledge by presenting a framework for classical simulations, dubbed “𝔤-sim”, which is based on the underlying Lie algebraic structure of the dynamical process. When the dimension of the algebra grows at most polynomially in the system size, there exist observables for which the simulation is efficient. Indeed, we show that 𝔤-sim enables new regimes for classical simulations, is able to deal with certain forms of noise in the evolution, as well as can be used to tackle several paradigmatic variational and nonvariational quantum computing tasks. For the former, we perform Lie-algebraic simulations to train and optimize parametrized quantum circuits (thus effectively showing that some variational models can be dequantized), design enhanced parameter initialization strategies, solve tasks of quantum circuit synthesis, and train a quantum-phase classifier. For the latter, we report large-scale noiseless and noisy simulations on benchmark problems. By comparing the limitations of 𝔤-sim and certain Wick's theorem-based simulations, we find that the two methods become inefficient for different types of states or observables, hinting at the existence of distinct, nonequivalent resources for classical simulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Krylov complexity in mixed phase space

We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans two-dimensional random matrix models featuring (I) GOE-Poisson and (II) GUE-Poisson transitions and extends to higher-dimensional cases, including a stringy matrix model (GOE-Poisson) and the mass-deformed SYK model (GUE-Poisson). Krylov complexity consistently emerges as a reliable marker of quantum chaos, displaying a characteristic peak in the chaotic regime that gradually diminishes as the Brody parameter approaches zero, signaling a shift toward integrability. These results establish Krylov complexity as a powerful diagnostic of quantum chaos and highlight its interplay with eigenvalue statistics in mixed phase systems.

chaos & nonlinear dynamics↗
DOE OSTI2020

Photophysics of graphene quantum dot assemblies with axially coordinated cobaloxime catalysts

We report a study of chromophore-catalyst assemblies composed of light harvesting hexabenzocoronene (HBC) chromophores axially coordinated to two cobaloxime complexes. The chromophore-catalyst assemblies were prepared using bottom-up synthetic methodology and characterized using solid-state NMR, IR, and x-ray absorption spectroscopy. Detailed steady-state and time-resolved laser spectroscopy was utilized to identify the photophysical properties of the assemblies, coupled with time-dependent DFT calculations to characterize the relevant excited states. The HBC chromophores tend to assemble into aggregates that exhibit high exciton diffusion length (D = 18.5 molecule 2 /ps), indicating that over 50 chromophores can be sampled within their excited state lifetime. We find that the axial coordination of cobaloximes leads to a significant reduction in the excited state lifetime of the HBC moiety, and this finding was discussed in terms of possible electron and energy transfer pathways. By comparing the experimental quenching rate constant (1.0 × 10 9 s -1 ) with the rate constant estimates for Marcus electron transfer (5.7 × 10 8 s -1 ) and Förster/Dexter energy transfers (8.1 × 10 6 s -1 and 1.0 × 10 10 s -1 ), we conclude that both Dexter energy and Marcus electron transfer process are possible deactivation pathways in CoQD-A. No charge transfer or energy transfer intermediate was detected in transient absorption spectroscopy, indicating fast, subpicosecond return to the ground state. Finally, these results provide important insights into the factors that control the photophysical properties of photocatalytic chromophore-catalyst assemblies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Reductive Dynamic and Static Excited State Quenching of a Homoleptic Ruthenium Complex Bearing Aldehyde Groups

A new homoleptic Ru polypyridyl complex bearing two aldehyde groups on each bipyridine ligand, [Ru(dab) 3 ](PF 6 ) 2 , where dab is 4,4′-dicarbaldehyde-2,2′-bipyridine, was synthesized, characterized, and utilized for iodide photo-oxidation studies. In acetonitrile (CH 3 CN) solution, the complex displayed an intense metal-to-ligand charge transfer (MLCT) absorbance maximum at 475 nm (ε = 22,000 M –1 cm –1 ) and an infrared (IR) band at 1712 cm –1 assigned to the pendent aldehyde groups. Visible light excitation in air-saturated solution resulted in room temperature photoluminescence (PL) with a maximum at 675 nm, a quantum yield, ϕ PL = 0.048, and an excited state lifetime, τ ο = 440 ns, from which radiative and nonradiative relaxation rate constants were extracted, k r = 9.1 × 10 4 s –1 and knr = 1.8 × 10 6 s –1 . Pulsed visible light excitation yielded transient UV–vis and IR absorption spectra consistent with an MLCT excited state; relaxation occurred with the maintenance of two isosbestic points in the visible region, and a lifetime that agreed with that measured by time-resolved PL. Cyclic voltammetry studies in a CH 3 CN solution with 0.1 M TBAPF 6 electrolyte revealed a quasi-reversible oxidation, E°(Ru III/II ) = +1.25 V vs. Fc +/0 , and three sequential one-electron reductions at −1.10, −1.25, and −1.54 V vs. Fc +/0 . Here, an excited state reduction potential of E°(Ru *2+/+ ) = +0.89 V vs. Fc +/0 was estimated with the Rehm–Weller expression. Titration of tetrabutylammonium iodide, TBAI, into a CD 3 CN solution of [Ru(dab) 3 ](PF 6 ) 2 resulted in significant shifts in the aldehyde H atom and 3,3′-biypridyl resonances that were analyzed with a 1:1 equilibrium model, from which K eq = 460 M –1 was extracted, increasing to 5800 M –1 when the solvent was changed to acetone-d 6 . Iodide titrations resulted in a significant quenching of the [Ru(dab) 3 ] *2+ lifetime and quantum yield in both CH 3 CN and acetone solvents. In CH 3 CN, the quenching was mainly dynamic and well described by the Stern–Volmer model, from which a quenching rate constant, k q , of 4.5 × 10 10 M –1 s –1 and an equilibrium constant, K eq , of 8.3 × 10 3 M –1 were obtained. In acetone, the static quenching pathway by iodide was greatly enhanced, with a K eq of 1.2 × 10 4 M –1 and a higher k q of 9.2 × 10 10 M –1 s –1 .

Aldehydes↗
DOE OSTI2026

Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems

Here, we present a perspective on recent progress in machine-learning (ML) force-field approaches for large-scale Landau–Lifshitz–Gilbert (LLG) simulations of metallic spin systems. Building on a generalization of the Behler–Parrinello (BP) architecture originally developed for quantum molecular dynamics, we develop scalable and transferable ML models that faithfully capture the complex, environment-dependent electron-mediated exchange fields characteristic of itinerant magnets. A central ingredient of this framework is the implementation of symmetry-aware magnetic descriptors based on group-theoretical bispectrum formalisms. Leveraging these ML force fields, LLG simulations faithfully reproduce hallmark non-collinear magnetic orders—such as the 120° and tetrahedral states—on the triangular lattice, and successfully capture the complex spin textures emerging in the mixed-phase states of a square-lattice double-exchange model under thermal quench. We further discuss a generalized potential theory that extends the BP formalism to incorporate both conservative and nonconservative electronic torques, thereby enabling ML models to learn nonequilibrium exchange fields from computationally demanding microscopic approaches such as nonequilibrium Green’s-function techniques. This extension yields quantitatively accurate predictions of voltage-driven domain-wall motion and establishes a foundation for quantum-accurate, multiscale modeling of nonequilibrium spin dynamics and spintronic functionalities.

Descriptors↗
DOE OSTI2024

Structural and quantum chemical basis for OCP-mediated quenching of phycobilisomes

Cyanobacteria use large antenna complexes called phycobilisomes (PBSs) for light harvesting. However, intense light triggers non-photochemical quenching, where the orange carotenoid protein (OCP) binds to PBS, dissipating excess energy as heat. The mechanism of efficiently transferring energy from phycocyanobilins in PBS to canthaxanthin in OCP remains insufficiently understood. Using cryo–electron microscopy, we unveiled the OCP-PBS complex structure at 1.6- to 2.1-angstrom resolution, showcasing its inherent flexibility. Using multiscale quantum chemistry, we disclosed the quenching mechanism. Identifying key protein residues, we clarified how canthaxanthin’s transition dipole moment in its lowest-energy dark state becomes large enough for efficient energy transfer from phycocyanobilins. Our energy transfer model offers a detailed understanding of the atomic determinants of light harvesting regulation and antenna architecture in cyanobacteria.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Quantum guidelines for solid-state spin defects

Defects with associated electron and nuclear spins in solid-state materials have a long history relevant to quantum information science going back to the first spin echo experiments with silicon dopants in the 1950s. Since the turn of the century, the field has rapidly spread to a vast array of defects and host crystals applicable to quantum communication, sensing, and computing. From simple spin resonance to long-distance remote entanglement, the complexity of working with spin defects is fast advancing, and requires an in-depth understanding of their spin, optical, charge, and material properties in this modern context. This is especially critical for discovering new relevant systems dedicated to specific quantum applications. In this review, we therefore expand upon all the key components with an emphasis on the properties of defects and the host material,on engineering opportunities and other pathways for improvement. Finally, this review aims to be as defect and material agnostic as possible, with some emphasis on optical emitters,providing a broad guideline for the field of solid-state spin defects for quantum information.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Low-temperature trapping of N 2 reduction reaction intermediates in nitrogenase MoFe protein–CdS quantum dot complexes

The biological reduction of N 2 to ammonia requires the ATP-dependent, sequential delivery of electrons from the Fe protein to the MoFe protein of nitrogenase. It has been demonstrated that CdS nanocrystals can replace the Fe protein to deliver photoexcited electrons to the MoFe protein. Herein, light-activated electron delivery within the CdS:MoFe protein complex was achieved in the frozen state, revealing that all the electron paramagnetic resonance (EPR) active E-state intermediates in the catalytic cycle can be trapped and characterized by EPR spectroscopy. Prior to illumination, the CdS:MoFe protein complex EPR spectrum was composed of a S = 3/2 rhombic signal (g = 4.33, 3.63, and 2.01) consistent with the FeMo-cofactor in the resting state, E 0 . Illumination for sequential 1-h periods at 233 K under 1 atm of N 2 led to a cumulative attenuation of E 0 by 75%. This coincided with the appearance of S = 3/2 and S = 1/2 signals assigned to two-electron (E 2 ) and four-electron (E 4 ) reduced states of the FeMo-cofactor, together with additional S = 1/2 signals consistent with the formation of E 6 and E 8 states. Simulations of EPR spectra allowed quantification of the different E-state populations, along with mapping of these populations onto the Lowe–Thorneley kinetic scheme. The outcome of this work demonstrates that the photochemical delivery of electrons to the MoFe protein can be used to populate all of the EPR active E-state intermediates of the nitrogenase MoFe protein cycle.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath

Highlights: • System–environment quantum correlation: a main solid state NMR decoherence channel. • Non-separable system–environment model yields realistic spin decoherence rates. • New open quantum system approach explains irreversible decay of refocused NMR echoes. • Adiabatic quantum decoherence is inherently irreversible and eigen-selective. This work addresses adiabatic quantum decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system–environment interaction Hamiltonian that represents a partition of non-interacting subsystems and highlights the collective correlation that appears exclusively due to the coupling with a common environment. Remarkably, this simple, exactly solvable model encompasses relevant aspects of a many-body open quantum system and features the subtle quantum effects that arise when the size scales up to a macroscopic level. We derive an analytical expression for the time dependence of the density matrix elements (in the preferred basis) without assuming coarse-graining. The resulting decoherence function is eigen-selective and is a complex exponential whose exponent has a real part that introduces a decay similar to that in the spin-boson model. On the contrary, the imaginary part depends on the quantum numbers and geometry of the whole partition and does not reflect the system temperature. Motivated by decoherence in solid-state NMR, and in search of realistic numerical estimations, we apply the theoretical results to a partition of dipole-coupled spin pairs in contact with a common phonon bath, using typical parameters of hydrated salts. The proposal allows estimating the decoherence time scale in terms of the system physical constants: sound velocity and eigenvalue distribution width. As a significant novelty, the decoherence function phase depends on the eigenvalue distribution throughout the sample. It plays the leading role, overshadowing the mechanism associated with the bath thermal state. Finally, we apply the formalism to describe decoherence in the “magic echo” NMR reversal experiment. We find that the system–environment correlation explains the origin of irreversibility, and both the decoherence rate value and its dependence on the dipolar frequency, are remarkably similar to the experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantum quenches of an SO(5) pseudospin reveal Higgs bosons

A controlled dynamical probe measurement of complex order parameter fluctuations of a system may reveal its massive collective excitations. Here, we design dynamical quench protocols to excite independently all ten midgap Higgs bosons in the isotropic Balian-Werthamer state of a spinful p -wave superfluid or superconductor. The analysis is based on microscopic equations of motion of an SO(5) pseudospin, an extension of the usual Bloch equation to a five-dimensional space. Key to these protocols is the realization of quenches that break the rotational symmetry of the kinetic energy and exploit the irreducible representation of the angular momentum J = 2. For perturbative quenches, we find ( nondecaying ) periodic oscillations in time of these Higgs modes. Finally, we present experimental protocols for superconductors (superfluids), with the intention of unveiling the nature of their order parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Quantum optical classifier with superexponential speedup

Abstract Classification is a central task in deep learning algorithms. Usually, images are first captured and then processed by a sequence of operations, of which the artificial neuron represents one of the fundamental units. This paradigm requires significant resources that scale (at least) linearly in the image resolution, both in terms of photons and computational operations. Here, we present a quantum optical pattern recognition method for binary classification tasks. It classifies objects without reconstructing their images, using the rate of two-photon coincidences at the output of a Hong-Ou-Mandel interferometer, where both the input and the classifier parameters are encoded into single-photon states. Our method exhibits the behaviour of a classical neuron of unit depth. Once trained, it shows a constant $${{\mathcal{O}}}(1)$$ O ( 1 ) complexity in the number of computational operations and photons required by a single classification. This is a superexponential advantage over a classical artificial neuron.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Fractional Statistics

The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter θ. θ = 0, π correspond to bosons and fermions, respectively; at intermediate values, we say that we have fractional statistics. In two dimensions, θ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve nonabelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of nonabelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern–Simons terms. The crossings of one-dimensional anyons on a ring are unidirectional, such that a fractional phase θ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently, the anyon behavior predicted for quasiparticles in the ν = 1/3 fractional quantum Hall state has been observed in both scattering and interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.

Physics↗
DOE OSTI2020

ChIMES: A Machine-Learned Interatomic Model Targeting Improved Description of Condensed Phase Chemistry in Energetic Materials

In this report we detail completion of a Physics and Engineering Model Level Two Milestone targeting improved reactive interatomic potentials (IAPs) for energetic materials (EM) through machine learning. The specific goals of this milestone were to develop, validate, and document a new reactive molecular dynamics method for EM, based on machine learning by (1) generating databases of first-principles-derived forces, stresses, and energies for HN3 and 3,4-bis(3-nitrofurazan- 4-yl)furoxan (DNTF) (2) generate atomistic force fields from these databases via ML, and (3) benchmark model performance against first principles calculations. These goals were achieved by (1) further developing a machine learned reactive IAP and generation approach (i.e. the Chebyshev Interaction Model for Efficient Simulation or “ChIMES”), for which resulting IAPs can approach the predictive power of quantum-mechanical approaches at a fraction of the computational expense, and (2) applying the ChIMES framework to develop models for HN3 and DNTF. We find that for simple energetic materials like HN3, high accuracy ChIMES models can be obtained through application of a fitting approach that does not use active machine learning. We demonstrate the suitability of ChIMES models for simulations involving EM by using the HN3 model in multiscale shock technique simulations to predict the HN3 Chapman-Jouguet detonation state and investigate chemical evolution out to 1 ns following shock compression. This model is then used in larger direct shock (DS) simulations for a preliminary investigation of how bubbles (i.e. voids) influence material response under shock compression. We find that more complex EM (i.e. DNTF) necessitate a more sophisticated fitting approach, and develop a new active learning method and python tool to meet this challenge. We demonstrate that this fitting approach yields ChIMES models that out-perform commonly used standard reactive IAPs as well as semi-empirical quantum methods, and discuss the systematic improvability of these actively learned ChIMES models. We also describe challenges related to model development for EM such as DNTF, for which few experimental or previous simulation data are available (e.g. which could otherwise inform generation of training data). To overcome this issue, we establish a semi-empirical quantum ChIMES capability which can be used to efficiently map out relevant thermodynamic and configurational space, and generate ChIMES-IAP training data in a multiscale manner. We also show that these semi-empirical quantum ChIMES models can be used to generate predictions for the shock Hugoniot (the Hugoniot is the locus of thermodynamic states found in a shocked material) equation of state, investigate related thermochemistry, and explore carbon condensation following shock compression. This work represents a substantial advance in our atomistic modeling capability for EM that will provide much needed information on the chemistry of detonation for continued development of continuum models based on the Cheetah thermochemical code.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Analyzing the Free States of one Quantum Resource Theory as Resource States of Another

In the context of quantum resource theories (QRTs), free states are defined as those that can be obtained at no cost under a certain restricted set of conditions. However, when taking a free state from one QRT and evaluating it through the optics of another QRT, it might well turn out that the state is now extremely resourceful. Such realization has recently prompted numerous works characterizing states across several QRTs. Here, in this work, we contribute to this body of knowledge by analyzing the resourcefulness in free states for—and across witnesses of—the QRTs of multipartite entanglement, fermionic non-Gaussianity, imaginarity, realness, spin coherence, Clifford non-stabilizerness, $S_n$-equivariance, and non-uniform entanglement. We provide rigorous theoretical results as well as present numerical studies that showcase the rich and complex behavior that arises in this type of cross-examination.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗