Pure State Research Articles

Single-Molecule Magnet Behavior of Confined Dy(III) in a Mixed Heteroatom-Substituted Polyoxotungstate.

Two heteroatom-templated Dy(III)-confined polyoxotungstates [H2N(CH3)2]7Na7[Dy2(H2O)7(W4O9)(HPSeW15O54)(α-SeW9O33)2]·31H2O (1) and [H2N(CH3)2]14K2Na18{[Dy2(H2O)13W14O40]2[α-SeW9O33]4[HPSeW15O54]2}·44H2O (2) were synthesized by a one-pot aqueous reaction and structurally characterized. The most distinctive structural feature of complexes 1 & 2 is the simultaneous presence of both trivacant Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building blocks containing P(III)-Se(IV) heteroatoms. The trimeric polyanion of 1 can be represented as a fusion of two trivacant Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building units encapsulating the [Dy2(H2O)7(W4O9)]12+ cluster. On the other hand, hexameric polyoxoanions of 2 are described as four trivacant Keggin [α-SeW9O33]8- and two Dawson [HPSeW15O54]10-, building units anchoring a [Dy4(H2O)26W28O80]20+ cluster. The magnetic investigation revealed the presence of significant magnetic anisotropy and slow relaxation of magnetization behavior for complex 1 with a phenomenological energy barrier, Ueff = 13.58 K in the absence of an external magnetic field, and Ueff = 24.57 K in the presence of a 500 Oe external dc magnetic field. On the other hand, complex 2 favors the QTM relaxation process in the absence of an external magnetic field and shows field-induced slow relaxation of magnetization with Ueff = 11.11 K at 1500 Oe applied dc field. The in-depth analysis of magnetic relaxation dynamics shows that the relaxation process follows the Orbach as well as Raman relaxation pathways. Further, the ab initio calculation of the studied complexes confirms that the highly axial ground and first excited energy states (containing pure highest mJ states) are responsible for the observed single-molecule magnet (SMM) behavior. Remarkably, this is the first example of a mixed heteroatom-based Dy(III)-substituted polyoxotungstate with both trimeric Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building units showing SMM behavior.

Investigating entangled photons to quantify quantum correlations in dual optomechanical cavities.

Quantum correlations that go beyond quantum entanglement have a significant role in the fields of quantum information processing and quantum computation. In essence, when we describe a quantum system using pure states, quantum entanglement and quantum correlation are essentially indistinguishable. However, this equivalence breaks down when dealing with general mixed states. To contribute to understanding this distinction, we have considered a straightforward model for both generating and measuring these quantum correlations. We focus on two macroscopic mechanical resonators situated in separate Fabry–Perot cavities and coupled through the photon hopping process. Our model allows us to conduct a comprehensive examination and quantification of quantum correlations that extend beyond entanglement between these mechanical modes. Our approach begins with the determination of the global covariance matrix, serving as the foundation for calculating two key metrics: the Entropy of Formation and the Gaussian quantum Discord. These metrics enable us to quantify the extent of quantum entanglement and quantum correlations, respectively. Our analysis, based on these quantifiers, reveals that quantum discord serves as a more appropriate metric for characterizing the quantum correlations between the mechanical modes in an optomechanical quantum system, especially in the presence of robust photon hopping.

Sodium-rich solid state reaction synthesis of sodium tri-titanate for AMTEC application

Alkali-Metal-Thermal-Electric-Converter systems (AMTEC-systems) pose a promising approach for energy conversion, e.g. from waste heat. Central components are a gas-tight ion-conductive solid membrane and an enclosed porous electrode. The presented study covers an adapted synthesis routine for single-phase sodium-tritanate (Na2Ti3O7) and its assessment as an alternative AMTEC-membrane-material. In contrast to the conventional stoichiometric solid state reaction between sodium carbonate and titania, the adapted synthesis reaction was performed with sodium excess. Up to 900 °C, the as-synthesised material evinced both, a constant thermal expansion behaviour over various thermal cycles and an expected electric conductivity. More important, phase stability either in pure state as well as in contact with a potential electrode material (La0.8Sr0.2)0.98MnO3 was demonstrated by long term exposure at 900 °C over 240 h. According to those findings the synthesised Na2Ti3O7 is considered to be an alternative membrane-material for AMTEC-application.

Ensemble Ground State of a Many-Electron System with Fractional Electron Number and Spin: Piecewise-Linearity and Flat-Plane Condition Generalized.

Description of many-electron systems with a fractional electron number (Ntot) and fractional spin (Mtot) is of great importance in physical chemistry, solid-state physics, and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system and characterize the dependence of the energy and the spin-densities on both Ntot and Mtot, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at a constant Ntot, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods.

Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models

The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a toolset of Chebyshev polynomial-based iterative methods that provides a unified framework to study the thermodynamical properties, critical behavior and dynamics of frustrated quantum spin models with controlled accuracy. Similar to previous applications of the Chebyshev spectral methods to condensed matter systems, the algorithmic complexity scales linearly with the Hilbert space dimension and the Chebyshev truncation order. Using this approach, we study two paradigmatic quantum spin models on the honeycomb lattice: the Kitaev-Heisenberg (K-H) and the Kitaev-Ising (K-I) models. We start by applying the Chebyshev toolset to compute nearest-neighbor spin correlations, specific heat and entropy of the K-H model on a 24-spin cluster. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum states. The transitions between a variety of magnetic phases, namely ferromagnetic, Néel, zigzag and stripy antiferromagnetic and quantum spin liquid phases are obtained accurately and efficiently. We also determine the temperature dependence of the spin correlations, over more than three decades in temperature, by means of a finite temperature Chebyshev polynomial method introduced here. Finally, we report novel dynamical signatures of the quantum phase transitions in the K-I model. Our findings suggest that the efficiency, versatility and low-temperature stability of the Chebyshev framework developed here could pave the way for previously unattainable studies of quantum spin models in two dimensions.

Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation. Essentially, for quantum systems prepared in pure states, it is difficult to differentiate between quantum entanglement and quantum correlation. Nonetheless, this indistinguishability is no longer holds for mixed states. To contribute to a better understanding of this differentiation, we have explored a simple model for both generating and measuring these quantum correlations. Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities, coupled through the photon hopping process. this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes. The key ingredient in analyzing quantum correlation in this system is the global covariance matrix. It forms the basis for computing two essential metrics: the logarithmic negativity ( ENm ) and the Gaussian interferometric power ( PGm ). These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations, respectively. Our study reveals that the Gaussian interferometric power ( PGm ) proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system, particularly in scenarios featuring resilient photon hopping.

Engineered Chimera Protein Constructs to Facilitate the Production of Heterologous Transmembrane Proteins in E. coli.

To delve into the structure-function relationship of transmembrane proteins (TMPs), robust protocols are needed to produce them in a pure, stable, and functional state. Among all hosts that express heterologous TMPs, E. coli has the lowest cost and fastest turnover. However, many of the TMPs expressed in E. coli are misfolded. Several strategies have been developed to either direct the foreign TMPs to E. coli's membrane or retain them in a cytosolic soluble form to overcome this deficiency. Here, we summarize protein engineering methods to produce chimera constructs of the desired TMPs fused to either a signal peptide or precursor maltose binding protein (pMBP) to direct the entire construct to the periplasm, therefore depositing the fused TMP in the plasma membrane. We further describe strategies to produce TMPs in soluble form by utilizing N-terminally fused MBP without a signal peptide. Depending on its N- or C-terminus location, a fusion to apolipoprotein AI can either direct the TMP to the membrane or shield the hydrophobic regions of the TMP, maintaining the soluble form. Strategies to produce G-protein-coupled receptors, TMPs of Mycobacterium tuberculosis, HIV-1 Vpu, and other TMPs are discussed. This knowledge could increase the scope of TMPs' expression in E. coli.

A computable quantification of multi-mode Gaussian coherence and complete monogamy relation

We propose a quantification CνGn of n-mode Gaussian coherence. The value of CνGn only depends on the covariance matrices and displacement vectors of continuous-variable states without any optimization procedures, and thus is easily calculated. For n=1, CνG1 is a proper Gaussian coherence measure of single-mode CV system. For n≥2, CνGn is invariant under any permutation of submodes, nonincreasing under any n-mode local incoherent Gaussian channels, vanishes at incoherent Gaussian states, and, satisfies the unification condition and the hierarchy condition that a multi-partite quantum correlation measure should obey. Thus CνGn is a multi-partite Gaussian correlation measure, which reveals, though the quantum coherence lives in single-partite systems, that the multi-mode coherence for continuous-variable systems can be regarded as a multipartite Gaussian correlation between modes, and such multi-partite Gaussian correlation is also a quantum resource. Moreover, we show that CνGn is completely monogamous as a multipartite Gaussian correlation measure. This means that the n-mode Gaussian coherence subjects to the principles of resource allocation. In addition, CνGn is an upper bound of the geometric-based single-mode Gaussian coherence measure CBu by the Bures distance at pure Gaussian states of mode ≤2 and can be used to detect coherence in any n-mode Gaussian states more efficiently.

Sharing Bell nonlocality of bipartite high-dimensional pure states using only projective measurements

Sharing Bell nonlocality of bipartite high-dimensional pure states using only projective measurements

Steady state engineering of a two-level system by the mixed-state inverse engineering scheme

The mixed-state inverse engineering scheme is a control scheme used for engineering the quantum state of a driven open quantum system from an initial steady state to a final steady state. In this paper, we present an analytical study of this scheme applied to the driven two-level model coupled to a heat reservoir. Typically, when the purity of the quantum state varies, incoherent control techniques are required for mixed-state engineering. However, we show that for both Markovian and non-Markovian dynamics, coherent control protocols can transfer the quantum state into the target state. This simplification comes at a cost, as the evolution of the quantum state must be limited to restricted conditions, resulting in special trajectories in its Hilbert space that connect the initial and target states.

Revealing incommensurability between device-independent randomness, nonlocality, and entanglement using Hardy and Hardy-type relations

A comprehensive treatment of the quantification of randomness certified device-independently by using the Hardy and Cabello-Liang-Li (CLL) nonlocality relations is provided in the two parties-two measurements per party-two outcomes per measurement (2-2-2) scenario. For the Hardy nonlocality, it is revealed that for a given amount of nonlocality signified by a particular non-zero value of the Hardy parameter, the amount of Hardy-certifiable randomness is not unique, unlike the way the amount of certifiable randomness is related to the CHSH nonlocality. This is because any specified non-maximal value of Hardy nonlocality parameter characterises a set of quantum extremal distributions. Then this leads to a range of certifiable amounts of randomness corresponding to a given Hardy parameter. On the other hand, for a given amount of CLL-nonlocality, the certifiable randomness is unique, similar to that for the CHSH nonlocality. Furthermore, the tightness of our analytical treatment evaluating the respective guaranteed bounds for the Hardy and CLL relations is demonstrated by their exact agreement with the Semi-Definite-Programming based computed bounds. Interestingly, the analytically evaluated maximum achievable bounds of both Hardy and CLL-certified randomness have been found to be realisable for non-maximal values of the Hardy and CLL nonlocality parameters. In particular, we have shown that even close to the maximum 2 bits of CLL-certified randomness can be realised from non-maximally entangled pure two-qubit states corresponding to small values of the CLL nonlocal parameter. This, therefore, clearly illustrates the quantitative incommensurability between randomness, nonlocality and entanglement.

Weak second-order quantum state diffusion unraveling of the Lindblad master equation

Simulating mixed-state evolution in open quantum systems is crucial for various chemical physics, quantum optics, and computer science applications. These simulations typically follow the Lindblad master equation dynamics. An alternative approach known as quantum state diffusion unraveling is based on the trajectories of pure states generated by random wave functions, which evolve according to a nonlinear Itô–Schrödinger equation (ISE). This study introduces weak first-order and second-order solvers for the ISE based on directly applying the Itô–Taylor expansion with exact derivatives in the interaction picture. We tested the method on free and driven Morse oscillators coupled to a thermal environment and found that both orders allowed practical estimation with a few dozen iterations. The variance was relatively small compared to the linear unraveling and did not grow with time. The second-order solver delivers a much higher accuracy and stability with bigger time steps than the first-order scheme, with a small additional workload. However, the second-order algorithm has quadratic complexity with the number of Lindblad operators as opposed to the linear complexity of the first-order algorithm.

Entanglement and entropy in multipartite systems: a useful approach

Quantum entanglement and quantum entropy are crucial concepts in the study of multipartite quantum systems. In this work, we show how the notion of concurrence vector, re-expressed in a particularly useful form, provides new insights and computational tools for the analysis of both. In particular, using this approach for a general multipartite pure state, one can easily prove known relations in an easy way and to build up new relations between the concurrences associated with the different bipartitions. The approach is also useful to derive sufficient conditions for genuine entanglement in generic multipartite systems that are computable in polynomial time. From an entropy-of-entanglement perspective, the approach is powerful to prove properties of the Tsallis-2 entropy, such as the subadditivity, and to derive new ones, e.g., a modified version of the strong subadditivity which is always fulfilled; thanks to the purification theorem these results hold for any multipartite state, whether pure or mixed.

Limit Theorems for the Cubic Mean-Field Ising Model

AbstractWe study a mean-field spin model with three- and two-body interactions. The equilibrium measure for large volumes is shown to have three pure states, the phases of the model. They include the two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point. We prove that the central limit theorem holds for a suitably rescaled magnetization, while its violation with the typical quartic behavior appears at the critical point.

Minimal orthonormal bases for pure quantum state estimation

We present an analytical method to estimate pure quantum states using a minimum of three measurement bases in any finite-dimensional Hilbert space. This is optimal as two bases are insufficient to construct an informationally complete positive operator-valued measurement (IC-POVM) for pure states. We demonstrate our method using a binary tree structure, providing an algorithmic path for implementation. The performance of the method is evaluated through numerical simulations, showcasing its effectiveness for quantum state estimation.

Phase Diffusion Mitigation in the Truncated Mach–Zehnder Interferometer

The presence of phase diffusion noise may lead to the loss of quantum measurement advantages, resulting in measurement results that cannot beat the standard quantum limit (SQL). Squeezing is considered an effective method for reducing the detrimental effect of phase diffusion on a measurement. Reasonable use of squeezing can make a measurement exceed the SQL. The Mach–Zehnder (MZ) interferometer has been exploited as a generic tool for precise phase measurement. Describing the reduction in quantum advantage caused by phase diffusion in an MZ interferometer that can be mitigated by squeezing is not easy to handle analytically because the input state changes from a pure state to a mixed state after experiencing the diffusion noise in the MZ interferometer. We introduce a truncated MZ interferometer, a symmetrical structure that can achieve the same potential phase sensitivity as the conventional MZ interferometer. This scheme can theoretically explain how phase diffusion reduces phase estimation and why squeezing counteracts the presence of phase diffusion. Using the Gaussian property of the input state and the characteristic of Gaussian operation in the squeezing, the two orthogonal field quantities of the quantum state are squeezed and anti-squeezed to different degrees, and the analytic results are obtained. This result can beat the SQL and provide reliable theoretical guidance for the experiment. The truncated MZ interferometer is more straightforward to build and operate than the conventional MZ interferometer. Moreover, it mitigates the phase diffusion noise via the squeezing operation, thus making it useful for applications in quantum metrology.

Virtual Quantum Resource Distillation.

Distillation, or purification, is central to the practical use of quantum resources in noisy settings often encountered in quantum communication and computation. Conventionally, distillation requires using some restricted "free" operations to convert a noisy state into one that approximates a desired pure state. Here, we propose to relax this setting by only requiring the approximation of the measurement statistics of a target pure state, which allows for additional classical postprocessing of the measurement outcomes. We show that this extended scenario, which we call "virtual resource distillation," provides considerable advantages over standard notions of distillation, allowing for the purification of noisy states from which no resources can be distilled conventionally. We show that general states can be virtually distilled with a cost (measurement overhead) that is inversely proportional to the amount of existing resource, and we develop methods to efficiently estimate such cost via convex and semidefinite programming, giving several computable bounds. We consider applications to coherence, entanglement, and magic distillation, and an explicit example in quantum teleportation (distributed quantum computing). This work opens a new avenue for investigating generalized ways to manipulate quantum resources.

Generalization of Gisin’s theorem to quantum fields

We generalize Gisin’s theorem on the relation between the entanglement of pure states and Bell non-classicality to the case of mode entanglement of separated groups of modes of quantum fields extending the theorem to cover also states with undefined particle number. We show that any pure state of the field which contains entanglement between two groups of separated modes violates some Clauser–Horne (CH) inequality. In order to construct the observables leading to a violation in the first step, we show an isomorphism between the Fock space built from a single-particle space involving two separated groups of modes and a tensor product of two abstract separable Hilbert spaces spanned by formal monomials of creation operators. In the second step, we perform a Schmidt decomposition of a given entangled state mapped to this tensor product space and then we map back the obtained Schmidt decomposition to the original Fock space of the system under consideration. Such obtained Schmidt decomposition in Fock space allows for construction of observables leading to a violation of the CH inequality. We also show that our generalization of Gisin’s theorem holds for the case of states on non-separable Hilbert spaces, which physically represent states with actually infinite number of particles. Such states emerge, for example, in the discussion of quantum phase transitions. Finally, we discuss the experimental feasibility of constructed Bell test and provide a necessary condition for realizability of this test within the realm of passive linear optics.

Microscopic contributions to the entropy production at all times: from nonequilibrium steady states to global thermalization

Based on exact integration of the Schrödinger equation, we numerically study microscopic contributions to the entropy production for the single electron transistor, a paradigmatic model describing a single Fermi level tunnel coupled to two baths of free fermions. To this end, we decompose the entropy production into a sum of information theoretic terms and study them across all relevant time scales, including the nonequilibrium steady state regime and the final stage of global thermalization. We find that the entropy production is dominated for most times by microscopic deviations from thermality in the baths and the correlation between (but not inside) the baths. Despite these microscopic deviations from thermality, the temperatures and chemical potentials of the baths thermalize as expected, even though our model is integrable. Importantly, this observation is confirmed for both initially mixed and pure states. We further observe that the bath-bath correlations are quite insensitive to the system-bath coupling strength contrary to intuition. Finally, the system-bath correlation, small in an absolute sense, dominates in a relative sense and displays pure quantum correlations for all studied parameter regimes.

Activation of metrologically useful genuine multipartite entanglement

We consider quantum metrology with several copies of bipartite and multipartite quantum states. We characterize the metrological usefulness by determining how much the state outperforms separable states. We identify a large class of entangled states that become maximally useful for metrology in the limit of large number of copies, even if the state is weakly entangled and not even more useful than separable states. This way we activate metrologically useful genuine multipartite entanglement. Remarkably, not only that the maximally achievable metrological usefulness is attained exponentially fast in the number of copies, but it can be achieved by the measurement of few simple correlation observables. We also make general statements about the usefulness of a single copy of pure entangled states. We surprisingly find that the multiqubit states presented in Hyllus et al (2010 Phys. Rev. A 82 012337), which are not useful, become useful if we embed the qubits locally in qutrits. We discuss the relation of our scheme to error correction, and its possible use for quantum metrology in a noisy environment.