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Andrei B. Klimov

Publications and source records attributed to Andrei B. Klimov.

At least 19 recordsLinked to original sources
arXiv2026

Spin-coherent quantum designs

Coherent states bridge the gap between quantum and classical physics, but their overcomplete and nonorthogonal nature makes it difficult to identify the minimal discrete set needed to reconstruct quantum information. Finite spin-coherent tomography and discrete coherent-state operator bases are known, but here we address the more specific rank-resolved problem of preserving the canonical contravariant-symbol representation. We show that the canonical finite coherent-state formula reconstructs every operator in the rank-$S$ sector exactly if and only if the sampling points form a spherical $(2J+S)$-design. We call the associated configurations spin-coherent quantum designs. We further give a fully explicit positive-weight Gauss-Legendre construction that avoids the need for an equal-weight spherical design. Together, these results establish a unified framework for reading out physical observables from a handful of measurement samples, playing for spin systems the role that the so-called von Neumann lattice plays for canonical coherent states. Finally, we derive practical protocols for estimating moments of spin operators from these constructions, with direct applications to polarimetry, magnetometry, and quantum state tomography.

quant-ph↗
arXiv2021

From polarization multipoles to higher-order coherences

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 are measured after the light has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific values of the angles of the waveplates. For more general two-mode problems, equivalent measurements can be performed.

quant-ph↗
arXiv2021

Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

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 dynamic variables and introduce a discretized version of the Truncated Wigner Approximation (TWA). Two emblematic examples of quantum dynamics (rotor in an external field and two coupled spins) are analyzed, and the results of exact, continuous, and discretized versions of TWA are compared.

quant-ph↗
arXiv2021

Effective and efficient resonant transitions in periodically modulated quantum systems

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 propose an explicit iterative procedure for the determination of the effective interaction constants corresponding to every resonance both for weak and strong modulation. For coupled quantum systems we determine the efficient resonant transitions appearing as a result of time modulation and intrinsic non-linearities.

quant-ph↗
arXiv2021

Macroscopic features of quantum fluctuations in large N qubit system

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 reconstructed by measuring lowest moments of the of collective variables.

quant-ph↗
arXiv2020

$SU(1,1)$ covariant $s$-parametrized maps

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, equivalently, inside the Poincaré disc) are analyzed.

quant-ph↗
arXiv2020

Extremal quantum states

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. In terms of the latter, we examine quantities such as the Wehrl entropy, inverse participation ratio, cumulative multipolar distribution, and metrological power, which are linked to intrinsic properties of any quantum state. We use these quantities to formulate extremal principles and determine in this way which states are the most and least "quantum;" the corresponding properties and potential usefulness of each extremal principle are explored in detail. While the extrema largely coincide for continuous-variable systems, our analysis of spin systems shows that care must be taken when applying an extremal principle to new contexts.

quant-ph↗
arXiv2020

Rotation sensing at the ultimate limit

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 rotations, a topic of broad application. By resorting to the basic tools of estimation theory, we derive states that achieve the ultimate sensitivities in estimating both the orientation of an unknown rotation axis and the angle rotated about it. The critical enhancement obtained with these optimal states should make of them an indispensable ingredient in the next generation of rotation sensors that is now blossoming.

quant-ph↗
arXiv2020

Quantum concepts in optical polarization

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, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincaré space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored and their potential applications in quantum technologies are discussed.

quant-ph↗
arXiv2019

Correspondence rules for Wigner functions over SU(3)/U(2)

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 from the rules of other known cases.

math-ph↗
arXiv2017

Optimal lossy quantum interferometry in phase space

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 derive the asymptotic form of an integral kernel describing the process of photon loss in the phase space in the limit of large photon numbers. The analytic form of this kernel allows one to assess the ultimate precision limit for a lossy interferometer. We also provide a general lower bound on the quantum Fisher information in terms of spin Wigner functions.

quant-ph↗
arXiv2016

Error estimation in the direct state tomography

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 determine the estimation error for any measurement strength, including the weak measurement case, and to obtain an explicit analytic form for the average minimum square errors.

quant-ph↗
arXiv2016

Quantum tomography via Non-orthogonal basis and weak values

Using a relation between a bi-orthogonal 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. With the simple example of a qubit is evidenced the relationship between weak values, measured probabilities and the separation between non-orthogonal bases.

quant-ph↗
arXiv2014

Discrete phase-space approach to mutually orthogonal Latin squares

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 possible operations on the monomial sets into isomorphisms of Latin squares, and find a general form of permutations that map between Latin squares corresponding to unitarily equivalent mutually unbiased sets. We extend this result to a conjecture: MOLS associated to unitarily equivalent MUBs will always be isomorphic, and MOLS associated to unitarily inequivalent MUBs will be non-isomorphic.

quant-ph↗
arXiv2013

Optimal unbiased state characterization

We propose a general approach to characterize states of a bipartite system composed by a fully controllable and an unaccessible subsystems. The method is based on the measuring interference between states of the uncontrollable subsystem obtained after projecting an appropriately transformed bipartite state on the basis of the accessible subsystem by local operations.

quant-ph↗
arXiv2013

Unbiased non-orthogonal bases for tomographic reconstruction

We have developed a general method for constructing a set of non-orthogonal bases with equal separations between all different basis' states in prime dimensions.It results that the corresponding bi-orthogonal counterparts are pairwise unbiased with the components of the original bases. Using these bases we derive an explicit expression for the optimal tomography in non-orthogonal bases. Special two dimensional case is analyzed separately.

quant-ph↗
arXiv2012

Quantum polarization characterization and tomography

We present a complete polarization characterization of any quantum state of two orthogonal polarization modes, and give a systematic measurement procedure to collect the necessary data. Full characterization requires measurements of the photon number in both modes and linear optics. In the situation where only the photon-number difference can be determined, a limited but useful characterization is obtained. The characteristic Stokes moment profiles are given for several common quantum states.

quant-ph↗