Andrei Klimov

Andrei Klimov
University of Guadalajara | UDG · Departamento de Física (CUCEI)

PhD

About

269
Publications
20,644
Reads
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4,408
Citations
Citations since 2017
49 Research Items
1587 Citations
20172018201920202021202220230100200300
20172018201920202021202220230100200300
20172018201920202021202220230100200300
20172018201920202021202220230100200300
Introduction
Continuos and discrete phase-space methods. Discrete quantum systems. Quantum optical models.

Publications

Publications (269)
Preprint
Full-text available
Despite the indisputable merits of the Wigner phase-space formulation, it has not been widely explored for systems with SU(1,1) symmetry, as a simple operational definition of the Wigner function has proved elusive in this case. We capitalize on the unique properties of the parity operator, to derive in a consistent way a \emph{bona fide} SU(1,1) W...
Article
Full-text available
We analyze the dynamics of N-qubit systems in the measurement space under the action of symmetric Hamiltonians. We show that the evolution of the discrete distribution function, representing the global properties of multipartite states, becomes quasicontinuous in the macroscopic limit N ≫ 1. The shorttime dynamics can be approximately described as...
Article
We demonstrate that the multipoles associated with the density matrix are truly observable quantities that can be unambiguously determined from intensity moments. Given their correct transformation properties, these multipoles are the natural variables to deal with a number of problems in the quantum domain. In the case of polarization, the moments...
Preprint
Full-text available
Even the most classical states are still governed by quantum theory. A fantastic array of physical systems can be described by their Majorana constellations of points on the surface of a sphere, where concentrated constellations and highly symmetric distributions correspond to the least and most quantum states, respectively. If these points are cho...
Article
Full-text available
In quantum optics, nonclassicality of quantum states is commonly associated with negativities of phase-space quasiprobability distributions.We argue that the impossibility of any classical simulations with phase-space functions is a necessary and sufficient condition of nonclassicality. The problem of such phase-space classical simulations for part...
Preprint
We demonstrate that the multipoles associated with the density matrix are truly observable quantities that can be unambiguously determined from intensity moments. Given their correct transformation properties, these multipoles are the natural variables to deal with a number of problems in the quantum domain. In the case of polarization, the moments...
Preprint
Full-text available
We apply the semi-classical limit of the generalized $SO(3)$ map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on $T^{\ast }\mathcal{S}_{2}$. Using the asymptotic form of the star-product, we manage to "quantize" one of the classical dynami...
Preprint
Full-text available
We construct an informationally complete set of mutually unbiased - like bases for N ququarts. These bases are used in an explicit tomographic protocol which performance is analyzed by estimating quadratic errors and compared to other reconstruction schemes.
Preprint
Full-text available
We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the classically evolved Wigner function corresponds to a non-positive operator $\hat{R}(t)$, which does not describe a physical state. The rate of appeara...
Preprint
Full-text available
We analyse periodically modulated quantum systems with $SU(2)$ and $SU(1,1)$ symmetries. Transforming the Hamiltonian into the Floquet representation we apply the Lie transformation method, which allows us to classify all effective resonant transitions emerging in time-dependent systems. In the case of a single periodically perturbed system, we pro...
Preprint
We introduce a discrete Q-function of N qubit system projected into the space of symmetric measurements as a tool for analyzing general properties of quantum systems in the macroscopic limit. For known states the projected Q-function helps to visualize the results of collective measurements, and for unknown states it can be approximately reconstruc...
Article
Full-text available
We apply the semi-classical limit of the generalized SO(3) map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on T*S2. Using the asymptotic form of the star-product, we manage to “quantize” one of the classical dynamic variables and introduc...
Article
We prove that all macroscopic properties of the N -qubit cluster state are asymptotically invariant under local transformations in the limit N ≫ 1, and can be described by a distribution function similar to that of the completely mixed state.
Article
Full-text available
Conventional classical sensors are approaching their maximum sensitivity levels in many areas. Yet these levels are still far from the ultimate limits dictated by quantum mechanics. Quantum sensors promise a substantial step ahead by taking advantage of the salient sensitivity of quantum states to the environment. Here, we focus on sensing rotation...
Article
Full-text available
We analyze periodically modulated quantum systems with SU(2) and SU(1,1) symmetries. Transforming the Hamiltonian into the Floquet representation we apply the Lie transformation method, which allows us to classify all effective resonant transitions emerging in time-dependent systems. In the case of a single periodically perturbed system, we propose...
Article
Full-text available
We show that a polynomial Hˆ(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice leads to a re-ordering of the associated energy eigenfunctions of Hˆ such that the number of their nodes doe...
Article
We propose a practical recipe to compute the s -parametrized maps for systems with SU(1, 1) symmetry using a connection between the Q- and P- symbols through the action of an operator invariant under the group. This establishes equivalence relations between s -parametrized SU(1, 1)-covariant maps. The particular case of the self-dual (Wigner) phase...
Article
We propose an approach to the analysis of the semiclassical evolution of spinlike systems. We show that an appropriate discretization of distributions in classical phase space (in this case the two-dimensional sphere S2) allows us to describe long-time dynamics (including the Schrödinger cat times) in terms of classical trajectories, both in stable...
Preprint
Full-text available
We propose a practical recipe to compute the ${s}$-parametrized maps for systems with $SU(1,1)$ symmetry using a connection between the ${Q}$ and ${P} $ symbols through the action of an operator invariant under the group. The particular case of the self-dual (Wigner) phase-space functions, defined on the upper sheet of the two-sheet hyperboloid (or...
Preprint
Full-text available
Conventional classical sensors are approaching their maximum sensitivity levels in many areas. Yet these levels still are far from the ultimate limits dictated by quantum mechanics. Quantum sensors promise a substantial step ahead by taking advantage of the salient sensitivity of quantum states to the environment. Here, we focus on sensing rotation...
Article
The striking differences between quantum and classical systems predicate disruptive quantum technologies. We peruse quantumness from a variety of viewpoints, concentrating on phase-space formulations because they can be applied beyond particular symmetry groups. The symmetry-transcending properties of the Husimi Q function make it our basic tool. I...
Article
We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincaré sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now...
Preprint
Full-text available
We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincar\'e sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: n...
Preprint
The striking differences between quantum and classical systems predicate disruptive quantum technologies. We peruse quantumness from a variety of viewpoints, concentrating on phase-space formulations because they can be applied beyond particular symmetry groups. The symmetry-transcending properties of the Husimi $Q$ function make it our basic tool....
Preprint
We show that nonclassicality of phase-space quasi-probability distributions is tied to violations of principles of physical reality in device-dependent scenarios. In this context, the nonclassicality problem has its dual form expressed as a device-dependent analog of Bell inequalities. This approach is applicable even to systems with only one spati...
Article
Full-text available
In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive...
Article
Full-text available
We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the classically evolved Wigner function corresponds to a non-positive operator $\hat{R}(t)$ , which does not describe a physical state. The rate of appear...
Article
Full-text available
We present analytic expressions for the s-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents for quadratic Hamiltonians. The results are applied for the study of the quantum dissipative dynamics of the time-honored Kerr and Lipkin models, explo...
Preprint
Full-text available
We develop a general scheme for an analysis of macroscopic qudit systems: a) introduce a set of collective observables, which characterizes the macroscopic properties of qudits in an optimal way; b) construct projected $\tilde{Q}$-functions for $N$ qudit systems, containing full macroscopic information; c) propose a collective tomographic protocol...
Preprint
Full-text available
We present analytic expressions for the $s$-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents for quadratic Hamiltonians. The results are applied for the study of the quantum dissipative dynamics of the time-honored Kerr and Lipkin models, exp...
Preprint
Full-text available
In spite of their potential usefulness, Wigner functions for systems with SU(1,1) dynamical symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom,...
Article
We propose a scheme for a deterministic extraction of entanglement by means of a reduction process involving local von Neumann measurements. In an example of a tripartite system, we show that by choosing appropriate measurement bases for a given qubit, one can map an initial three-qubit state into outcome pure bipartite states with the same amount...
Preprint
Full-text available
We present results on the * product for SU(3) Wigner functions over SU(3)/U(2). In particular, we present a form of the so-called correspondence rules, which provide a differential form of the * product A*B and A*B when A is an su(3) generator. For the su(3) Wigner map, these rules must contain second order derivatives and thus substantially differ...
Article
Full-text available
We derive a continuity equation for the evolution of the SU(2) Wigner function under nonlinear Kerr evolution. We give explicit expressions for the resulting quantum Wigner current, and discuss the appearance of the classical limit. We show that the global structure of the quantum current significantly differs from the classical one, which is clear...
Preprint
Full-text available
We derive a continuity equation for the evolution of the SU(2) Wigner function under nonlinear Kerr evolution. We give explicit expressions for the resulting quantum Wigner current, and discuss the appearance of the classical limit. We show that the global structure of the quantum current significantly differs from the classical one, which is clear...
Article
We discuss the quantum phase transitions (QPT) in N-spin chains from the point of view of collective observables. We show that the measurement space representation is a convenient tool for the analysis of phase transitions, allowing the determination of an appropriate set of macroscopic order parameters (for a given Hamiltonian). Quantum correlatio...
Article
Full-text available
We discuss the tomography of N-qubit states using collective measurements. The method is exact for symmetric states, whereas for not completely symmetric states the information accessible can be arranged as a mixture of irreducible SU(2) blocks. For the fully symmetric sector, the reconstruction protocol can be reduced to projections onto a canonic...
Preprint
Full-text available
We discuss the tomography of $N$-qubit states using collective measurements. The method is exact for symmetric states, whereas for not completely symmetric states the information accessible can be arranged as a mixture of irreducible SU(2) blocks. For the fully symmetric sector, the reconstruction protocol can be reduced to projections onto a canon...
Article
We discuss equilibration and thermalization processes in N-spin systems from the point of view of collective observables. We show that the measurement space approach is a convenient tool for the analysis of these effects, allowing one to observe the emergence of irreversibility even for a relatively small numbers of particles. Equilibrating dynamic...
Article
We propose a method for accounting the simplest type of systematic errors in the mutually unbiased bases (MUB) tomography, emerging due to an imperfect (non-orthogonal) preparation of measurement bases. The present approach allows to analyze analytically the performance of MUB tomography in finite systems of an arbitrary (prime) dimension. We compa...
Article
We survey some applications of SU(2) covariant maps to the phase space quantum mechanics of systems with fixed or variable spin. A generalization to SU(3) symmetry is also briefly discussed in framework of the axiomatic Stratonovich–Weyl formulation.
Article
Full-text available
We analyse the phase space representation of the optimal measurement of a phase shift in an interferometer with equal photon loss in both its arms. In the local phase estimation scenario with a fixed number of photons, we identify features of the spin Wigner function that warrant sub-shot noise precision, and discuss their sensitivity to losses. We...
Article
We analyze the stable and unstable evolution of spin-like systems in the framework of the Truncated Wigner and Unitary Approximations, and test the dependence of the time scale where the classical evolution determines the dynamics of a quantum system on the semiclassical parameter.
Article
Full-text available
We further elaborate on a phase-space picture for a system of N qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and different entanglement properties. We discuss the construction of discrete covariant Wigner functions for these bundles...
Article
We formulate the construction of cyclic and non-cyclic complete sets of mutually unbiased bases, corresponding to the underlyining field and semifield structures, in the framework of the symplectic approach.
Article
We have developed a general method for constructing a set of non-orthogonal bases with equal separations between all different basis' states for N-qubit systems. Using these bases we derive an explicit expression for the optimal tomography in non-orthogonal bases and discuss the amount of non-classical resources required for the bases preparation a...
Article
Full-text available
Quantum metrology allows for a tremendous boost in the accuracy of measurement of diverse physical parameters. The estimation of a rotation constitutes a remarkable example of this quantum-enhanced precision, and it has been demonstrated in, e.g., magnetometry and polarimetry. When the rotation axis is known, NOON states are optimal for this task,...
Article
We show that reformulating the Direct State Tomography (DST) protocol in terms of projections into a set of non-orthogonal bases one can perform an accuracy analysis of DST in a similar way as in the standard projection-based reconstruction schemes. i.e. in terms of the Hilbert-Schmidt distance between estimated and true states. This allows us to d...
Article
We analyze collective properties of N-qubit states. In particular, we exhaustively discuss the localization aspect of distributions in the measurement space and introduce the concept of Gaussian states in the macroscopic limit. The effect of local shifts on the localization and Gaussianity is analyzed.
Article
It is shown that transient spin-spin correlations in one-dimensional spin S>>1 chain can be enhanced for initially factorized and individually squeezed spin states. Such correlation transfer form "internal" to "external" degrees of freedom can be well described by using a semiclassical phase-space approach.
Article
We investigate polarization squeezing in squeezed coherent states with varying coherent amplitudes. In contrast to the traditional characterization based on the full Stokes parameters, we experimentally determine the Stokes vector of each excitation subspace separately. Only for states with a fixed photon number do the methods coincide; when the ph...
Article
We analyze different families of discrete maps\ in the N-qubit systems in the context of the permutation invariance. We prove that the tomographic condition imposed on the self-dual (Wigner) map is incompatible with the requirement of the invariance under particle permutations, which makes it impossible to project the Wootters-like Wigner function...
Article
Full-text available
We investigate polarization squeezing in squeezed coherent states with varying coherent amplitudes. In contrast to the traditional characterization based on the full Stokes parameters, we experimentally determine the Stokes vector of each excitation manifold separately. Only for states with a fixed photon number do the methods coincide; when the ph...
Article
Full-text available
The characterization of quantum polarization of light requires knowledge of all the moments of the Stokes variables, which are appropriately encoded in the multipole expansion of the density matrix. We look into the cumulative distribution of those multipoles and work out the corresponding extremal pure states. We find that SU(2) coherent states ar...
Article
Full-text available
Using a relation between a biorthogonal set of equiseparable bases and the weak values of the density matrix we derive an explicit formula for its tomographic reconstruction completely analogous to the standard mutually unbiased bases expansion.
Article
Full-text available
We study semiclassical dynamics of the resonant Dicke model under the rotation wave approximation (RWA) for initial vacuum field state and all excited atoms in the asymptotic limit of a large number of atoms. We develop a new approach for description of the evolution of such unstable states by combining semiclassical and quantum approaches.
Article
Full-text available
We discuss the polarization of paraxial and nonparaxial classical light fields by resorting to a multipole expansion of the corresponding polarization matrix. It turns out that only a dipolar term contributes when one considers SU(2) (paraxial) or SU(3) (nonparaxial) as fundamental symmetries. In this latter case, one can alternatively expand in SU...
Article
Full-text available
The semiclassical evolution of the generalized SU(2) Wigner function for quantum systems with a variable number of excitations is discussed in detail. It is shown that in the framework of the Liouvillian approach quantum dynamics can be approximately described in terms of classical trajectories on an appropriate four-dimensional symplectic manifold...
Article
Full-text available
A semi-classical analysis of the quantum rigid-rotor motion based on a phase-space description of the rotation in terms of a SO(3) covariant Wigner-like distribution is presented. The results are applied to the description of the intense-field alignment of an anisotropically polarizable molecule with high rotational excitation.
Article
Full-text available
The full characterization of quantum polarization of light requires the knowledge of all the moments of the Stokes variables, which are appropriately encoded in the multipole expansion of the density matrix. We look into the cumulative distribution of those multipoles and work out the corresponding extremal states. We find that SU(2) coherent state...
Article
We propose a measure to quantify correlations in a bipartite quantum system of two quibits by assessing the minimum difference between outcome states of a subsystem by performing a local measurement on the other subsystem. This maximum similarity measure is a monotone function of the concurrence for pure states of two qubits; for mixed states it ac...
Article
The standard construction of complete sets of mutually unbiased bases (MUBs) in prime power dimensions is based on the quadratic Gauss sums. We introduce complete MUB sets for three, four, and five qubits that are unitarily inequivalent to all existing MUB sets. These sets are constructed by using certain exponential sums, where the degree of the p...
Article
Full-text available
Systems of four nonbinary particles, each having three or more internal states, exhibit maximally entangled states that are inaccessible to four qubits. This breaks the pattern of two- and three-particle systems, in which the existing graph states are equally accessible to binary and nonbinary systems alike. We compare the entanglement properties o...
Article
Full-text available
We capitalize on a multipolar expansion of the polarisation density matrix, in which multipoles appear as successive moments of the Stokes variables. When all the multipoles up to a given order $K$ vanish, we can properly say that the state is $K$th-order unpolarized, as it lacks of polarization information to that order. First-order unpolarized st...
Article
Full-text available
We show there is a natural connection between Latin squares and commutative sets of monomials defining geometric structures in finite phase-space of prime power dimensions. A complete set of such monomials defines a mutually unbiased basis (MUB) and may be associated with a complete set of mutually orthogonal Latin squares (MOLS). We translate some...
Article
Full-text available
We put forward an operational degree of polarization that can be extended in a natural way to fields whose wave fronts are not necessarily planar. This measure appears as a distance from a state to the set of all its polarization-transformed counterparts. By using the Hilbert-Schmidt metric, the resulting degree is a sum of two terms: one is the pu...
Article
We introduce a discrete $Q$ function of an $N$-qubit system projected into the space of symmetric measurements as a tool for analyzing general properties of quantum systems in the macroscopic limit. For known states the projected $Q$ function helps to visualize the results of collective measurements, and for unknown states it can be approximately r...
Article
Full-text available
An explicit construction of all the possible sets of n commuting monomials for an n-qudit system as well as an algorithm for the determination of their factorization are given here. The results are applied for the generation of locally non-isomorphic mutually unbiased complete sets and their classification according to the separability properties....
Article
We analyze the creation of quantum correlations in a two-qubit system, initially prepared in a classical state, when only one qubit is locally coupled to a bath through a Hamiltonian interaction. We argue that a substantial part of the generated correlations is related to the presence of virtual excitations in the qubit-bath subsystem. The appearan...
Article
The probabilistic scheme for making two copies of two nonorthogonal pure states requires two auxiliary systems, one for copying and one for attempting to project onto the suitable subspace. The process is performed by means of a unitary-reduction scheme which allows having a success probability of cloning different from zero. The scheme becomes opt...
Article
We present a new parametrization of families of complex Hadamard matrices stemming from the Fourier matrices in every prime power dimension. We connect continuous Abelian groups with families of complex Hadamard matrices and conjecture that the constructed families are maximal. Also, we derive new relations for complex Hadamard matrices in every pr...
Article
A scheme for quantum-state tomography is presented that can be performed for polarized light with an arbitrary photon-number distribution. The proposed method fills the gap between existing polarization-tomography schemes for single-photon states and for optical fields with very large photon numbers. It consists of an optical homodyne setup trigger...
Article
Full-text available
We advocate a simple multipole expansion of the polarisation density matrix. The resulting multipoles appear as successive moments of the Stokes variables and can be obtained from feasible measurements. In terms of these multipoles, we construct a whole hierarchy of measures that accurately assess higher-order polarization fluctuations.
Article
We analyze the appearance of quantum correlations of two qubits prepared in a classical state. One qubit is locally coupled to a bath through a Hamiltonian interaction. We find that the generated correlations is related to the presence of virtual excitations of qubit-bath interaction.
Conference Paper
The concepts of macroscopicity and localization for large quantum systems is discussed and analyzed in relation with the asymptotic evolution in the measurement space under action of random and chaotic Hamiltonians.
Article
We set forth a method to analyze the orbital angular momentum of a light field. Instead of using the canonical formalism for the conjugate pair angle-angular momentum, we model this latter variable by the superposition of two independent harmonic oscillators along two orthogonal axes. By describing each oscillator by a standard Wigner function, we...
Article
Full-text available
An efficient method for assessing the quality of quantum state tomography is developed. Special attention is paid to the tomography of multipartite systems in terms of unbiased measurements. Although the overall reconstruction errors of different sets of mutually unbiased bases are the same, differences appear when particular aspects of the measure...
Article
We propose a scheme for preparing a set of bases constituted by equidistant states of a quantum system in prime dimension starting with a single entangled system-ancilla state. The required quantum correlations between the involved systems as a function of the separability constant are analyzed. A comparative analysis of errors in tomographic recon...