We show that several classes of mixed quantum states in finite-dimensional Hilbert spaces which can be characterized as being, in some respect, 'most classical' can be described and analyzed in a unified way. Among the states we consider are separable states of distinguishable particles, uncorrelated states of indistinguishable fermions and bosons, as well as mixed spin states decomposable into probabilistic mixtures of pure coherent states. The latter were the subject of the recent paper by Giraud et. al., who showed that in the lowest-dimensional, nontrivial case of spin 1, each such state can be decomposed into a mixture of eight pure states. Using our method we prove that in fact four pure states always suffice.
We propose a protocol in which the faithful and deterministic teleportation of an arbitrary mixture of diagonal states is completed $via$ classical correlation and classical communication. Our scheme can be generalized straightforwardly to the case of $N$-qubits by using $N$ copies of classical correlated pairs and classical communication. Moreover, a varying scheme by using the generalized classical correlated state within a multiqubit space is also presented. In addition, the arbitrary mixed state whose set of eigenvectors is known are a direct application of our protocol.
Mixtures of coherent states are commonly regarded as classical. Here we show that there is a quantum advantage in discriminating between coherent states in a mixture, implying the presence of quantum properties in the mixture, which are however not captured by commonly used non-classicality measures. We identify a set of desired properties for any non-classicality measure that aims to capture these quantum features, and define the discord potential CD, which we show to satisfy all those properties. We compare the discord potential with recently proposed coherence monotones, and prove that the …
Weakly interacting fermionic Gibbs states are Gaussian mixtures and classically simulable
Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）；State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University（清华大学物理系低维量子物理国家重点实验室）
The density operators obtained by taking partial traces do not represent proper mixtures of the subsystems of a compound physical system, but improper mixtures, since the coefficients in the convex sums expressing them never bear the ignorance interpretation. As a consequence, assigning states to these subsystems is problematical in standard quantum mechanics (subentity problem). Basing on the proposal provided in the SR interpretation of quantum mechanics, where improper mixtures are considered as true nonpure states conceptually distinct from proper mixtures, we show here that proper and imp…
We introduce a Werner-like mixture [R. F. Werner, Phys. Rev. A {\bf 40}, 4277 (1989)] by considering two correlated but different degrees of freedom, one with discrete variables and the other with continuous variables. We evaluate the mixedness of this state, and its degree of entanglement establishing its usefulness for quantum information processing like quantum teleportation. Then, we provide its tomographic characterization. Finally, we show how such a mixture can be generated and measured in a trapped system like one electron in a Penning trap.
We propose a methodology to emulate quantum phenomena arising from any non-classical quantum state using only a finite set of mixtures of coherent states. This allows us to successfully reproduce well-known quantum effects using resources that can be much more feasibly generated in the laboratory. We present a simple procedure to experimentally carry out quantum-state emulation with coherent states, illustrate it emulating multi-photon NOON states with few phase-averaged coherent states, and demonstrate its capabilities in observing fundamental quantum-mechanical effects, such as the Hong-Ou-M…
The characterization of mixtures of non-interacting, spectroscopically similar quantum components has important applications in chemistry, biology, and materials science. We introduce an approach based on quantum tracking control that allows for determining the relative concentrations of constituents in a quantum mixture, using a single pulse which enhances the distinguishability of components of the mixture and has a length that scales linearly with the number of mixture constituents. To illustrate the method, we consider two very distinct model systems: mixtures of diatomic molecules in the …
According to Popescu's recent analysis [Phys. Rev. Lett. {\bf72}, 797 (1994)], {\it nonideal} measurements, rather than ideal ones, may be more sensitive to reveal nonlocal correlations between distant parts of composite quantum systems. The outcome statistics of joint nonideal measurements on local states should by definition admit local hidden variable models. We prove that the density operator of a local composite system must be convex mixture of the subsystems' density operators. This result depends essentially on a plausible consistency condition restricting the class of admissible local …
We use a recently proposed measure of quantum correlations (work deficit), to measure the strength of the nonlocality of an equal mixture of two bipartite, orthogonal, but locally indistinguishable separable states. This gives supporting evidence of nonzero value for a separable state, for this measure of nonlocality. We also show that this measure of quantum correlations places a different order on the set of states, than the good asymptotic measures of entanglement. And that such a different order imposed on two states by the work deficit and any entanglement measure, cannot be explained by …
In this article we extend results from our previous work [Bendersky, de la Torre, Senno, Figueira and Acín, Phys. Rev. Lett. 116, 230406 (2016)] by providing a protocol to distinguish in finite time and with arbitrarily high success probability any algorithmic mixture of pure states from the maximally mixed state. Moreover, we introduce a proof-of-concept experiment consisting in a situation where two different random sequences of pure states are prepared; these sequences are indistinguishable according to quantum mechanics, but they become distinguishable when randomness is replaced with pseu…
In this study, we show that the interaction energy plays an important role on the quantum decoherence: If we pay attention to the oscillation phase factor, $e^{-iE_{int}t/\hbar},$ we see that the time average of the macro-system's density matrix becomes nearly diagonal, where the states giving extrema of interaction energy are privileged to describe the quantum decoherence. This approach is compatible with the von Neumann's old work, which has been recently studied with renewed interest: The thermal mixture of states can be reached by the time average of a density of matrix due to the oscillat…
We consider a relaxation of a single mode of the quantized field in a presence of one- and two-photon absorption and emission processes. Exact stationary solutions of the master equation for the diagonal elements of the density matrix in the Fock basis are found in the case of completely saturated two-photon emission. If two-photon processes dominate over single-photon ones, the stationary state is a mixture of phase averaged even and odd coherent states.
We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections. Instead of it, we use the convex set of states in order to construct a new lattice whose atoms are all physical states: pure states and improper mixtures. This is done in order to overcome one of the problems which appear in the standard quantum logical f…
In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix $ρ(t)$ with only diagonal elements in a given basis $\{|n\rangle\}$, it may be treated as a classical mixture, i.e., a system which randomly occupies the basis states $|n\rangle$ with probabilities $ρ_{nn}(t)$. Fully equivalent to so-called smoothing in classical probability theory, subsequent probing of the occupation of the states $|n\rangle$ improves our…
The one-dimensional interacting Bose-Fermi mixtures, exhibiting quantum phase transitions at zero temperature, are particularly valuable for the study of quantum critical phenomena. In the present paper, we analytically study quantum phase diagram, equation of state and quantum criticality of the Bose-Fermi mixture using the thermodynamic Bethe ansatz equations. We show that thermodynamical properties display universal scaling behaviour at quantum criticality. Furthermore, quantum criticality of the Bose-Fermi mixture in an harmonic trap is also studied within the local density approximation. …
In this thesis, the properties of mixtures of Bose-Einstein condensates at $T = 0$ have been investigated using quantum Monte Carlo (QMC) methods and Density Functional Theory (DFT) with the aim of understanding physics beyond the mean-field theory in Bose-Bose mixtures.
We report on the first realization of heteronuclear dipolar quantum mixtures of highly magnetic erbium and dysprosium atoms. With a versatile experimental setup, we demonstrate binary Bose-Einstein condensation in five different Er-Dy isotope combinations, as well as one Er-Dy Bose-Fermi mixture. Finally, we present first studies of the interspecies interaction between the two species for one mixture.
We study cavity optomechanics of a mixture of ultracold atoms with tunable nonlinear collisions. We show that atomic collisions provide linear couplings between fictitious condensate oscillators, leading to possibilities of achieving a globally coupled quantum optomechanical network with an integrated atom chip. Potential applications range from simulating collective nonequilibrium dynamics in fields well past physics to probing unique properties of quantum mixtures.
It is argued that proper and improper quantum mixed states have no observable differences, and hence should not be distinguished. This has implications for subjective approaches to quantum mechanics, and invalidates one of the main motivations for relational interpretations of QM.
We demonstrate that the current laser technology used for field-free molecular alignment via a cascade of Raman rotational transitions allows for observing long-discussed non-linear quantum phenomena in the dynamics of the periodically kicked rotor. This includes the scaling of the absorbed energy near the conditions of quantum resonance and Anderson-like localisation in the angular momentum. Based on these findings, we suggest a novel approach to tunable selective rotational excitation and alignment in a molecular mixture, using trains of short laser pulses. We demonstrate the efficiency of t…
QMoE: A Quantum Mixture of Experts Framework for Scalable Quantum Neural Networks
Department of Electrical Engineering and Computer Science, University of Arkansas（电气工程与计算机科学系，阿肯色大学）；Department of Electrical and Computer Engineering, Kansas State University（电气与计算机工程系，堪萨斯州立大学）；Department of Computer and Information Sciences, University of Delaware（计算机与信息科学系，德克萨斯大学）
The existence of quantum droplets in binary Bose-Einstein condensate mixtures rely on beyondmean field effects, competing with mean-field effects. Interestingly, the beyond-mean field effect is changing from repulsive in 3D to attractive in 1D leading to drastically different behaviors. We study in detail the crossover between these two regimes in a quasi-1D regime where the radial wavefunction is frozen. Quantum droplets exist for all values and sign of the mean-field interaction. We find that approaching the crossover is experimentally appealing as it reduces the relative importance of three…
Quantum information platforms made great progress in the control of many-body entanglement and the implementation of quantum error correction, but it remains a challenge to realize both in the same setup. Here, we propose a mixture of two ultracold atomic species as a platform for universal quantum computation with long-range entangling gates, while providing a natural candidate for quantum error-correction. In this proposed setup, one atomic species realizes localized collective spins of tunable length, which form the fundamental unit of information. The second atomic species yields phononic …
With a recently developed time evolving block decimation (TEBD) algorithm, we numerically study the ground state quantum phase diagram of fermi mixtures with attractive inter-species interactions loaded in one-dimensional optical lattices. For our study, we adopt a general asymmetric Hubbard model (AHM) with species-dependent tunneling rates to incorporate the possibility of mass imbalance in the mixtures. We find clear signatures for the existence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in this model in the presence of population imbalance. Our simulation also reveals that in the p…
We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of hopping imbalance. Our analysis is based on dynamical mean-field theory (DMFT) and its real-space generalization at finite temperature. We study the temperature dependence of the transition into the ordered state as a function of the interaction strength and the imbalance parameter in two and three spatial dimensions. We show that below the critical temperature for Néel order mass-imbalanced mixtures also exhibit a charge-density wave, which provides a dir…
The capacity of classical channels is convex. This is not the case for the quantum capacity of a channel: the capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities and thus is non-convex. Here we show that this effect goes beyond the quantum capacity and holds for the private and classical environment-assisted capacities of quantum channels.
We report on the dynamical formation of self-bound quantum droplets in attractive mixtures of $^{39}$K atoms. Considering the experimental observations of Semeghini et al., Phys. Rev. Lett. 120, 235301 (2018), we perform numerical simulations to understand the relevant processes involved in the formation of a metastable droplet from an out-of-equilibrium mixture. We first analyze the so-called self-evaporation mechanism, where the droplet dissipates energy by releasing atoms, and then we consider the effects of losses due to three-body recombinations and to the balancing of populations in the …
We present a source engineering concept for a binary quantum mixture suitable as input for differential, precision atom interferometry with drift times of several seconds. To solve the non-linear dynamics of the mixture, we develop a set of scaling approach equations and verify their validity contrasting it to the one of a system of coupled Gross-Pitaevskii equations. This scaling approach is a generalization of the standard approach commonly used for single species. Its validity range is discussed with respect to intra- and inter-species interaction regimes. We propose a multi-stage, non-line…
We systematically investigate the ground-state properties of self-bound droplets of quasi-two-dimensional binary Bose gases by using the Gaussian state theory. We find that quantum droplets consists two macroscopic squeezed phases and a macroscopic coherent phase. We map out the phase diagram and determine all phase boundaries via both numerical and nearly analytical methods. In particular, we find three easily accessible signatures for the quantum phases and the stablization mechanism of the self-bound droplets by precisely measuring their radial size. Our studies indicate that binary droplet…
In this paper, we present a general framework to solve a fundamental problem in Random Matrix Theory (RMT), i.e., the problem of describing the joint distribution of eigenvalues of the sum $\bsA+\bsB$ of two independent random Hermitian matrices $\bsA$ and $\bsB$. Some considerations about the mixture of quantum states are basically subsumed into the above mathematical problem. Instead, we focus on deriving the spectral density of the mixture of adjoint orbits of quantum states in terms of Duistermaat-Heckman measure, originated from the theory of symplectic geometry. Based on this method, we …
The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: i) an interacting atomic Bose gas, and ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition (QPT) is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground-state is degenerate. For repulsive and small attractive interaction, the ground-state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transi…
Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is equally important, but the set of possibilities is far richer. The two basic ways in which a pair of time-ordered quantum systems may be causally related are by a cause-effect mechanism or by a common cause acting on both. Here, we show a coherent mixture of these two possibilities. We realize this nonclassical causal relation in a quantum optics experiment…
In Quantum Non Demolition measurements, the sequence of observations is distributed as a mixture of multinomial random variables. Parameters of the dynamics are naturally encoded into this family of distributions. We show the local asymptotic mixed normality of the underlying statistical model and the consistency of the maximum likelihood estimator. Furthermore, we prove the asymptotic optimality of this estimator as it saturates the usual Cramér Rao bound.
We extent the recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons (ML-MCTDHB) for simulating the correlated quantum dynamics of bosonic mixtures to the fermionic sector and establish a unifying approach for the investigation of the correlated quantum dynamics of mixture of indistinguishable particles, be it fermions or bosons. Relying on a multi-layer wave-function expansion, the resulting Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX) can be adapted to efficiently resolve system-specific intra- and inter-species c…
In a recent Letter, Bennett and coworkers [1] argue that proofs of exotic quantum effects using closed timelike curves (CTC's) based on the work of Deutsch [2], or other nonlinear quantum dynamics, suffer from a fallacy that they call the "linearity trap," by which one cannot assume that a classical mixture of input states will lead to the same mixture of corresponding output states. We show that this prescription is inconsistent with the assumption that one can verify the postulated nonlinear evolution. Specifically, if some agent can empirically verify the deterministic nonlinear action of a…
A quantum liquid in a heterogeneous mixture of $^{41}$K and $^{87}$Rb atoms is studied using the diffusion Monte Carlo method and Density Functional Theory. The perturbative Lee-Huang-Yang term for a heterogeneous mixture is verified and it is proved to be valid only near the gas-liquid transition. Based on the equations of state of the bulk mixture, calculated with diffusion Monte Carlo, extensions to Lee-Huang-Yang corrected mean-field energy functionals (MF+LHY) are presented. Using Density Functional Theory, a systematic comparison between different functionals is performed, focusing on th…
We study two-component atomic gas mixtures in one dimension involving both bosons and fermions. When the inter-species interaction is attractive, we report a rich variety of coherent ground-state phases that vary with the intrinsic and relative strength of the interactions. We avoid any artifacts of lattice discretization by developing a novel implementation of a continuous matrix product state ansatz for mixtures and priorly demonstrate the validity of our approach on the integrable point that exists for mixtures with equal masses and interactions (Lai-Yang model) where we find that the ansat…
We present a many-body description for two-component ultracold bosonic gases when one of the species is in the weakly interacting regime and the other is either weakly or strongly interacting. In the one-dimensional limit the latter case system is a hybrid in which a Tonks-Girardeau gas is immersed in a Bose-Einstein condensate, which is an example of a new class of quantum system involving a tunable, superfluid environment. We describe the process of phase separation microscopically and semiclassically in both situations and show that the quantum correlations are maintained in the separated p…
We consider strongly interacting boson-boson mixtures on one-dimensional lattices and, by adopting a qualitative mean-field approach, investigate their quantum phases as the interspecies repulsion is increased. In particular, we analyze the low-energy "quantum emulsion" metastable states occurring at large values of the interspecies interaction, which are expected to prevent the system from reaching its true ground state. We argue a significant decrease in the visibility of the time-of-flight images in the case of these spontaneously disordered states.
We propose a modified expectation-maximization algorithm by introducing the concept of quantum annealing, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. The expectation-maximization (EM) algorithm is an established algorithm to compute maximum likelihood estimates and applied to many practical applications. However, it is known that EM heavily depends on initial values and its estimates are sometimes trapped by local optima. To solve such a problem, quantum annealing (QA) was proposed as a novel optimization approach motivated by quantum mechanics…
The low energy dynamics of mesoscopic systems strongly depends on the presence of internal equilibration. For this reason, a better interpretation of ultracold atom experiments requires a more accurate understanding of how quantum chaos manifests itself in these systems. In this paper, we consider a simple but experimentally relevant one-dimensional system of a few ultracold fermions moving in a double-well potential. We analyze its many-body spectral properties, which are commonly used to trace quantum chaos. We observe some signatures of quantum chaos already in the system with three particl…
If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement…
The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It is also the algorithm of choice to fit mixture models: generative models that represent unlabelled points originating from $k$ different processes, as samples from $k$ multivariate distributions. In this work we define and use a quantum version of EM to fit a Gaussian Mixture Model. Given quantum access to a dataset of $n$ vectors of dimension $d$, our algori…
Self-bound quantum droplets are a newly discovered phase in the context of ultracold atoms. In this work we report their experimental realization following the original proposal by Petrov [Phys. Rev. Lett. 115, 155302 (2015)], using an attractive bosonic mixture. In this system spherical droplets form due to the balance of competing attractive and repulsive forces, provided by the mean-field energy close to the collapse threshold and the first-order correction due to quantum fluctuations. Thanks to an optical levitating potential with negligible residual confinement we observe self-bound dropl…
We developed a new quantum annealing (QA) algorithm for Dirichlet process mixture (DPM) models based on the Chinese restaurant process (CRP). QA is a parallelized extension of simulated annealing (SA), i.e., it is a parallel stochastic optimization technique. Existing approaches [Kurihara et al. UAI2009, Sato et al. UAI2009] and cannot be applied to the CRP because their QA framework is formulated using a fixed number of mixture components. The proposed QA algorithm can handle an unfixed number of classes in mixture models. We applied QA to a DPM model for clustering vertices in a network wher…
