Pure State Research Articles

Matrix product state approximations to quantum states of low energy variance

We show how to efficiently simulate pure quantum states in one dimensional systems that have both finite energy density and vanishingly small energy fluctuations. We do so by studying the performance of a tensor network algorithm that produces matrix product states whose energy variance decreases as the bond dimension increases. Our results imply that variances as small as ∝1/log⁡N can be achieved with polynomial bond dimension. With this, we prove that there exist states with a very narrow support in the bulk of the spectrum that still have moderate entanglement entropy, in contrast with typical eigenstates that display a volume law. Our main technical tool is the Berry-Esseen theorem for spin systems, a strengthening of the central limit theorem for the energy distribution of product states. We also give a simpler proof of that theorem, together with slight improvements in the error scaling, which should be of independent interest.

Quantum Tensor-Product Decomposition from Choi-State Tomography

The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt or tensor-product decomposition. While quantum technological implementations of the former are thoroughly studied, entangling properties on the operator level are harder to extract in the quantum computational framework because of the exponential nature of sample complexity. Here, we present an algorithm for unbalanced partitions into a small subsystem and a large one (the environment) to compute the tensor-product decomposition of a unitary the effect of which on the small subsystem is captured in classical memory, while the effect on the environment is accessible as a quantum resource. This quantum algorithm may be used to make predictions about operator nonlocality and effective open quantum dynamics on a subsystem, as well as for finding low-rank approximations and low-depth compilations of quantum circuit unitaries. We demonstrate the method and its applications on a time-evolution unitary of an isotropic Heisenberg model in two dimensions. Published by the American Physical Society 2024

Electroluminescence from pure resonant states in hBN-based vertical tunneling junctions

Defect centers in wide-band-gap crystals have garnered interest for their potential in applications among optoelectronic and sensor technologies. However, defects embedded in highly insulating crystals, like diamond, silicon carbide, or aluminum oxide, have been notoriously difficult to excite electrically due to their large internal resistance. To address this challenge, we realized a new paradigm of exciting defects in vertical tunneling junctions based on carbon centers in hexagonal boron nitride (hBN). The rational design of the devices via van der Waals technology enabled us to raise and control optical processes related to defect-to-band and intradefect electroluminescence. The fundamental understanding of the tunneling events was based on the transfer of the electronic wave function amplitude between resonant defect states in hBN to the metallic state in graphene, which leads to dramatic changes in the characteristics of electrons due to different band structures of constituent materials. In our devices, the decay of electrons via tunneling pathways competed with radiative recombination, resulting in an unprecedented degree of tuneability of carrier dynamics due to the significant sensitivity of the characteristic tunneling times on the thickness and structure of the barrier. This enabled us to achieve a high-efficiency electrical excitation of intradefect transitions, exceeding by several orders of magnitude the efficiency of optical excitation in the sub-band-gap regime. This work represents a significant advancement towards a universal and scalable platform for electrically driven devices utilizing defect centers in wide-band-gap crystals with properties modulated via activation of different tunneling mechanisms at a level of device engineering.

Brief theory of multiqubit measurement

Peculiarities of multiqubit measurement are for the most part similar to peculiarities of measurement for qudit — quantum object with finite-dimensional Hilbert space. Three different interpretations of measurement concept are analyzed. One of those is purely quantum and is in collection, for a given state of the object to be measured, of incompatible observable measurement results in amount enough for reconstruction of the state. Two others make evident the difference between the reduced density matrix and the density matrices of physical objects involved in the measurement. It is shown that the von Neumann projectors, in combination with the concept of qudit phase space, produce an idea of a phase portrait of qudit state as a set of mathematical expectations for projectors on the possible pure states. The phase portrait is not a probability distribution since the projectors on nonorthogonal states are incompatible observables. Along with that, the phase portrait includes probability distributions for all the resolutions of identity of the qudit observable algebra. Additional peculiarities of measurement of the qudit degenerated observables, caused by the possibility of independent measurement of the observables for the particles, make possible to distinguish the local reduction of the qudit particle states from the entanglement of the local measurement results. The phase portrait of a composite system comprised by a qudit pair generates local and conditional phase portraits of particles. The entanglement is represented by the dependence of the shape of conditional phase portrait on the properties of the observable used in the measurement for the other particle. Analysis of the properties of a conditional phase portrait of a multiqubit qubits shows that absence of the entanglement is possible only in the case of substantial restrictions imposed on the method of multiqubit decomposition into qubits. Such a special method for determination of particles exists for each multiqubit state.

Lorentz invariants of pure three-qubit states

Lorentz invariants of pure three-qubit states

Hamiltonian quantum generative adversarial networks

We propose Hamiltonian quantum generative adversarial networks (HQuGANs) to learn to generate unknown input quantum states using two competing quantum optimal controls. The game-theoretic framework of the algorithm is inspired by the success of classical generative adversarial networks in learning high-dimensional distributions. The quantum optimal control approach not only makes the algorithm naturally adaptable to the experimental constraints of near-term hardware, but also offers a more natural characterization of overparameterization compared to the circuit model. We numerically demonstrate the capabilities of the proposed framework to learn various highly entangled many-body quantum states, using simple two-body Hamiltonians and under experimentally relevant constraints such as low-bandwidth controls. We analyze the computational cost of implementing HQuGANs on quantum computers and show how the framework can be extended to learn quantum dynamics. Furthermore, we introduce a cost function that circumvents the problem of mode collapse that prevents convergence of HQuGANs and demonstrate how to accelerate the convergence of them when generating a pure state. Published by the American Physical Society 2024

Canonical Typicality for Other Ensembles than Micro-canonical

AbstractWe generalize Lévy’s lemma, a concentration-of-measure result for the uniform probability distribution on high-dimensional spheres, to a much more general class of measures, so-called GAP measures. For any given density matrix $$\rho $$ ρ on a separable Hilbert space $${\mathcal {H}}$$ H , $${\textrm{GAP}}(\rho )$$ GAP ( ρ ) is the most spread-out probability measure on the unit sphere of $${\mathcal {H}}$$ H that has density matrix $$\rho $$ ρ and thus forms the natural generalization of the uniform distribution. We prove concentration-of-measure whenever the largest eigenvalue $$\Vert \rho \Vert $$ ‖ ρ ‖ of $$\rho $$ ρ is small. We use this fact to generalize and improve well-known and important typicality results of quantum statistical mechanics to GAP measures, namely canonical typicality and dynamical typicality. Canonical typicality is the statement that for “most” pure states $$\psi $$ ψ of a given ensemble, the reduced density matrix of a sufficiently small subsystem is very close to a $$\psi $$ ψ -independent matrix. Dynamical typicality is the statement that for any observable and any unitary time evolution, for “most” pure states $$\psi $$ ψ from a given ensemble the (coarse-grained) Born distribution of that observable in the time-evolved state $$\psi _t$$ ψ t is very close to a $$\psi $$ ψ -independent distribution. So far, canonical typicality and dynamical typicality were known for the uniform distribution on finite-dimensional spheres, corresponding to the micro-canonical ensemble, and for rather special mean-value ensembles. Our result shows that these typicality results hold also for $${\textrm{GAP}}(\rho )$$ GAP ( ρ ) , provided the density matrix $$\rho $$ ρ has small eigenvalues. Since certain GAP measures are quantum analogs of the canonical ensemble of classical mechanics, our results can also be regarded as a version of equivalence of ensembles.

Entropy variances of pure coherent states in the diffusion channel

Abstract Using the operator correspondence of the real and fictious modes in the thermo entangled state representation, we solve the quantum master equation describing the diffusion channel and obtain the Kraus operator-sum representation of its analytical solution. we find that the pure coherent states evolve into the new mixed thermal superposed states in the diffusion channel. Also, we investigate the statistical properties of the initial coherent states and their entropy evolutions in the diffusion channel, and find that the entropy evolutions are only related to the decay time and without the amplitudes of the initial coherent states.

Limitations of Classically Simulable Measurements for Quantum State Discrimination.

In the realm of fault-tolerant quantum computing, stabilizer operations play a pivotal role, characterized by their remarkable efficiency in classical simulation. This efficiency sets them apart from nonstabilizer operations within the quantum computational theory. In this Letter, we investigate the limitations of classically simulable measurements in distinguishing quantum states. We demonstrate that any pure magic state and its orthogonal complement of odd prime dimensions cannot be unambiguously distinguished by stabilizer operations, regardless of how many copies of the states are supplied. We also reveal intrinsic similarities and distinctions between the quantum resource theories of magic states and entanglement in quantum state discrimination. The results emphasize the inherent limitations of classically simulable measurements and contribute to a deeper understanding of the quantum-classical boundary.

Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium.

A vibrational electronic-thermofield coupled cluster (VE-TFCC) approach is developed to calculate thermal properties of non-adiabatic vibronic coupling systems. The thermofield (TF) theory and a mixed linear exponential ansatz based on second-quantized Bosonic construction operators are introduced to propagate the thermal density operator as a "pure state" in the Bogoliubov representation. Through this compact representation of the thermal density operator, the approach is basis-set-free and scales classically (polynomial) as the number of degrees of freedoms (DoF) in the system increases. The VE-TFCC approach is benchmarked with small test models and a real molecular compound (CoF4- anion) against the conventional sum over states (SOS) method and applied to calculate thermochemistry properties of a gas-phase reaction: CoF3 + F- → CoF4-. Results shows that the VE-TFCC approach, in conjunction with vibronic models, provides an effective protocol for calculating thermodynamic properties of vibronic coupling systems.

The role of thermal and squeezed photons in the entanglement dynamics of the double Jaynes–Cummings model

The effects of squeezed photons and thermal photons on the entanglement dynamics of atom-atom, atom-field and field-field subsystems are studied for the double Jaynes–Cummings model. For this purpose, squeezed coherent states and Glauber-Lachs states of radiation are chosen as field states. For the atomic states, we choose one of the Bell state as pure state and a Werner-type state as mixed state. Werner-type state is used to understand the effects of mixedness on entanglement. To measure the entanglement between the two atoms, Wootters’ concurrence is used; whereas for the atom-field and field-field subsystems, negativity is chosen. The squeezed photons and thermal photons create, destroy and transfer entanglement within various subsystems. Also, the addition of squeezed photons and thermal photons either lengthens or shortens the duration of entanglement sudden deaths (ESD) associated with atom-atom, atom-field and field-field entanglement dynamics in a complementary way. The effects of Ising-type interaction, detuning and Kerr-nonlinearity on the entanglement dynamics are studied. Each of these interactions removes the ESDs associated with various subsystems. We show that new entanglements are created in this atom-field system by introducing Ising-type interaction between the two atoms. With proper choice of the parameters corresponding to Ising-type interaction, detuning and Kerr-nonliearity, entanglement can be transferred among various subsystems.

A highly sensitive spectrofluorimetric method for the determination of bilastine in human plasma: Application of content uniformity testing.

Bilastine, a new second generation antihistaminic drug, has been widely used for relieving symptoms of allergic rhinitis and urticaria without a sedative effect. A simple, cost-effective, and highly sensitive fluorimetric method was developed for the estimation of bilastine in human plasma, in addition to its pure state and tablets. The suggested method depended on binary complex formation of eosin with bilastine in a buffered medium at pH 4.2. The formed complex resulted in quantitative quenching of eosin emission at 538 nm after excitation at 335 nm. This method demonstrates a broad range of linearity, spanning from 200 to 1000 ng/mL, and exhibits exceptional sensitivity, with a limit of detection and quantitation of 30.85 and 93.48 ng/mL, respectively. In addition, this spectrofluorimetric method may be employed to determine the amount of bilastine in human plasma and tablets with satisfactory accuracy and excellent precision. Furthermore, the content uniformity of bilastine in commercially available tablets was successfully tested by this approach. Compared with the reference method, there were no significant variations in terms of precision or accuracy. In conclusion, the proposed protocol is highly recommended to quantitatively estimate bilastine in different quality control settings.

Quantum states generation and manipulation in a programmable silicon-photonic four-qubit system with high-fidelity and purity

We present a programmable silicon photonic four-qubit integrated circuit for the generation and manipulation of diverse quantum states. The silicon photonic chip integrates photon-pair sources, pump-reducing filters, wavelength-division-multiplexing filters, Mach–Zehnder interferometer switches, and single-qubit arbitrary gates, enabling versatile state preparation and tomography. We measure Hong–Ou–Mandel interference with an impressive 98% visibility using four-photon coincidence, laying the foundation for high-purity qubits. Our analysis involves estimating the fidelity and purity of distinct quantum states through maximum-likelihood estimation applied to tomographic measurements. In our experimental results, we showcase the following achievements: a heralded single qubit achieving 98.2% fidelity and 98.3% purity, a Bell state reaching 95.2% fidelity and 94.8% purity, and a four-qubit system with two simultaneous Bell states exhibiting 87.4% fidelity and 84.6% purity. Finally, a four-qubit Greenberger–Horne–Zeilinger (GHZ) state demonstrates 85.4% fidelity and 81.7% purity. In addition, we certify the entanglement of the four-photon GHZ state through Bell’s inequality violations and a negative entanglement witness.

Characterizing the geometry of the Kirkwood–Dirac-positive states

The Kirkwood–Dirac (KD) quasiprobability distribution can describe any quantum state with respect to the eigenbases of two observables A and B. KD distributions behave similarly to classical joint probability distributions but can assume negative and nonreal values. In recent years, KD distributions have proven instrumental in mapping out nonclassical phenomena and quantum advantages. These quantum features have been connected to nonpositive entries of KD distributions. Consequently, it is important to understand the geometry of the KD-positive and -nonpositive states. Until now, there has been no thorough analysis of the KD positivity of mixed states. Here, we investigate the dependence of the full convex set of states with positive KD distributions on the eigenbases of A and B and on the dimension d of the Hilbert space. In particular, we identify three regimes where convex combinations of the eigenprojectors of A and B constitute the only KD-positive states: (i) any system in dimension 2; (ii) an open and dense probability one set of bases in dimension d = 3; and (iii) the discrete-Fourier-transform bases in prime dimension. Finally, we show that, if for example d = 2m, there exist, for suitable choices of A and B, mixed KD-positive states that cannot be written as convex combinations of pure KD-positive states. We further explicitly construct such states for a spin-1 system.

Geometric flavours of quantum field theory on a Cauchy hypersurface. Part II: Methods of quantization and evolution

In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the point of differential geometry in infinite dimensions. In this second part we use the tools of Gaussian analysis in infinite dimensional spaces introduced in the first part to describe rigorously the procedures of geometric quantization in the space of Cauchy data of a scalar theory. This leads us to discuss and establish relations between different pictures of QFT. We also apply these tools to describe the geometrization of the space of pure states of quantum field theory as a Kähler manifold. We use this to derive an evolution equation that preserves the geometric structure and avoid norm losses in the evolution. This leads us to a modification of the Schrödinger equation via a quantum connection that we discuss and exemplify in a simple case.

Monogamy of quantum correlations shared in a cavity-freeoptomechanical system

In this work, we discuss the monogamy property of quantum correlations (entanglement and steering) distributed in a cavity-free optomechanical system. In a tripartite pure Gaussian state, we verify the hierarchy of the studied quantum correlations. We investigate in detail the CKW-type monogamy inequalities, based on Gaussian Rényi-2 entropy entanglement, as well as, Gaussian steering. We quantify genuine tripartite entanglement by using the minimum residual Gaussian entanglement. In addition, we consider the minimum residual Gaussian steering as a quantifier of genuine tripartite steering. Our results indicate that, in the one-mode versus two-mode Gaussian state, the correlations hierarchy was respected; in the considered pure state, the monogamy of entanglement and steering distribution was proven and the studied genuine tripartite correlations have similar time evolution under the same conditions.

Role of outer shell electron-nuclear distant of transition metal atoms (TMA) on band gap reduction and optical properties of TiO2 semiconductor

The reduction of the band gap of titanium dioxide (TiO2) via transition metal atoms (TMAs) is the focus of many research groups to increase its absorption to visible region of electromagnetic (EM) radiation. In this modeling it was shown that atoms having near outer electron shells affect strongly on the band gap of TiO2. The TiO2 has exceptional photoactivity, high stability, and cost-effectiveness. The results of the current study emphasized that adjustable TiO2 photocatalyst material can be produced through band gap reduction by Pt, Pd, and Ni dopants. The electronic configurations and optical properties of both undoped and (Ni, Pd and Pt)-doped TiO2 have been studied using first-principles calculations within the framework of Density Functional Theory (DFT) with the aid of the Vienna Ab initio Simulation Package (VASP). The role of electronegativity of TMAs on band gap drop was discussed for the first time. The band gap of clean TiO2 was found to be 3.2 eV using the band structure (BS) and Tauq model. The results indicate that Ni TMA with lowest electronegativity reduces the band gap of TiO2 to the lowest value (0.86 eV). The results of BS and density of state revealed the fact that small outer shell electron-nuclear distant TMA more affected the band gap of TiO2. The band gap determined from the imaginary part of the optical dielectric function closely aligns with those determined from the BS diagram. The increase in the refractive index (n) was observed with the increase of Ni, Pd, and Pt into the TiO2 structure, which indicates an increase in charge density within the TiO2 structure. The reflectance, absorbance, and transmittance results suggest that Pd and Pt-doped TiO2 are responsive to the visible region of electromagnetic radiation, whereas Ni-doped TiO2 exhibits responsiveness in the IR region. In its pure state; TiO2 was found almost transparent in the visible and IR regions of EM radiation.

The maximal violation of the Svetlichny inequality for “X” states and the extended GHZ states

For a quantum system, violation of a Svetlichny inequality indicates the existence of genuine nonlocality. Through the same mathematical analysis approach, we derive the analytical expressions of the maximal violation of the Svetlichny inequality for certain three-qubit pure states and mixed “X” states. These pure states represented in the five-parameter form belong to extended GHZ states. It is convenient to use the obtained expression to distinguish the genuine nonlocal states in these states. We also obtain the analytical expression of the maximal violation of Svetlichny inequality for a subclass of four-qubit “X” states. We show the application potentiality of these expressions by designing two schemes where quantum resources are converted from less qubits “X” states to more qubits “X” states.

Selective topological valley transport of elastic waves in a Bragg-type phononic crystal plate

Based on the quantum valley Hall effect analogy, this work proposes a phononic crystal plate with ligament-type beams to obtain the topological valley transmission of elastic waves. A pure Bragg degenerate state appears in the high-frequency region with a resonator introduced. By rotating the central scatterer and the beams, the mirror symmetry is broken to form a topological bandgap. Subsequently, this work finds that two selective edge states also appear beside the commonly non-trivial crossing edge states in the topological bandgap by calculating the projected band and eigenvalue spectrum of the supercell with different valley Hall phases phononic crystals. Their appearance is due to band separation of the topological edge states caused by an increase in the rotation angle. Both selective edge states can transmit topologically in specific paths. They will help further to broaden the width of the frequency band of topological transmission. Besides, an elastic wave splitter is designed and demonstrated numerically, which can form two channels and three channels in different frequency bands. With the topological selective edge state disappearing, a topological corner state exists in the edge bandgap. This work provides a theoretical reference for practical applications of broadband elastic wave topological transmission and elastic energy trapping.

Nonlocal fermions with local interactions and the SYK model

One of the most promising routes to non-fermi liquids and strange metals has been through SYK models (Sachdev 2010 Phys. Rev. Lett. 105 151602) which necessarily involve large flavor degrees of freedom and interactions with imposed disorder. We introduce an interacting model of nonlocal spinless fermions in which large flavor and effective disorder emerge spontaneously in the extreme nonlocal limit. This model may be thought of as an expansion in a dimensionless ‘locality scale,’ α, with the limit α→0 recovering a conventional local action. For finite α, the resulting interacting nonlocal action exhibits a large number of low-energy degrees of freedom—proportional to α—and the structure factor mediating the local interactions between these fermions is effectively random for large α. In one dimension, with finite α, we show that interactions are marginal to the one loop level (as they are in the conventional local case), preserving a gapless phase. At large α the interaction strength becomes comparable to the bandwidth and we analyze this large flavor limit in a manner similar to the diagrammatic approach to SYK. As α is increased we argue that the gapless phase established by conventional RG possibly crosses over to a gapless SYK phase, although the ‘melon’ diagrams are not exclusively dominant. We speculate on how this model might arise physically from an S-matrix connecting pure excited states—rather than the vacuum—to access finite temperature interacting fermions.