arXiv subjects

S. N. Filippov

Publications and source records attributed to S. N. Filippov.

At least 37 records · Page 2Linked to original sources

arXiv2019

Simulation complexity of open quantum dynamics: Connection with tensor networks

The difficulty to simulate the dynamics of open quantum systems resides in their coupling to many-body reservoirs with exponentially large Hilbert space. Applying a tensor network approach in the time domain, we demonstrate that effective small reservoirs can be defined and used for modeling open quantum dynamics. The key element of our technique is the timeline reservoir network (TRN), which contains all the information on the reservoir's characteristics, in particular, the memory effects timescale. The TRN has a one-dimensional tensor network structure, which can be effectively approximated in full analogy with the matrix product approximation of spin-chain states. We derive the sufficient bond dimension in the approximated TRN with a reduced set of physical parameters: coupling strength, reservoir correlation time, minimal timescale, and the system's number of degrees of freedom interacting with the environment. The bond dimension can be viewed as a measure of the open dynamics complexity. Simulation is based on the semigroup dynamics of the system and effective reservoir of finite dimension. We provide an illustrative example showing scope for new numerical and machine learning-based methods for open quantum systems.

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arXiv2019

Measurement of the $K^+\rightarrow{μ^+}{ν_μ}γ$ decay form factors in the OKA experiment

A precise measurement of the vector and axial-vector form factors difference $F_V-F_A$ in the $K^+\rightarrow{μ^+}{ν_μ}γ$ decay is presented. About 95K events of $K^+\rightarrow{μ^+}{ν_μ}γ$ are selected in the OKA experiment. The result is $F_V-F_A=0.134\pm0.021(stat)\pm0.027(syst)$. Both errors are smaller than in the previous $F_V-F_A$ measurements.

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arXiv2019

Study of the decay $K^{+}\toπ^{+}π^{-}π^{+}γ$ in the OKA experiment

A high statistics data sample of the decays of $K^+$ mesons to three charged particles was accumulated by the OKA experiment in 2012 and 2013. This allowed to select a clean sample of about 450 events with $K^{+}\toπ^{+}π^{-}π^{+}γ$ decays with the energy of the photon in the kaon rest frame greater than 30 MeV. The measured branching fraction of the $K^{+}\toπ^{+}π^{-}π^{+}γ$, with $E_γ^{*}$ > 30 MeV is $(0.71 \pm 0.05) \times 10^{-5}$. The measured energy spectrum of the decay photon is compared with the prediction of the chiral perturbation theory to O$(p^{4})$. A search for an up-down asymmetry of the photon with respect to the hadronic system decay plane is also performed.

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arXiv2018

Search for heavy neutrino in $K^{+} \to μ^{+} ν_{H}$ decay

A high statistics data sample of the $K^{+}\toμ^{+}ν_μ$ decay was accumulated by the OKA experiment in 2012. The missing mass analysis was performed to search for the decay channel $K^{+}\toμ^{+}ν_{H}$ with a hypothetic stable heavy neutrino in the final state. The obtained missing mass spectrum does not show peaks which could be attributed to existence of stable heavy neutrinos in the mass range (220 $< m_{ν_{H}} <$ 375) MeV$/c^{2}$. As a result, we obtain upper limits on the branching ratio and on the value of the mixing element $|U_{μH}|^{2}$.

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arXiv2018

Dimension truncation for open quantum systems in terms of tensor networks

We present novel and simple estimation of a minimal dimension required for an effective reservoir in open quantum systems. Using a tensor network formalism we introduce a new object called a reservoir network (RN). The reservoir network is the tensor network in the form of a Matrix Product State, which contains all effects of open dynamics. This object is especially useful for understanding memory effects. We discuss possible applications of the reservoir network and the estimation of dimension to develop new numerical and machine learning based methods for open quantum systems.

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arXiv2017

$K_{e3}$ decay studies in OKA experiment

Recent results from OKA setup concerning form factor studies in $K_{e3}$ decay are presented. About 5.25M events are selected for the analysis. The linear and quadratic slopes for the decay formfactor $f_{+}(t)$ are measured: $λ'_{+}=(26.1 \pm 0.35 \pm 0.28 )\times 10^{-3}$, $λ"_{+}=(1.91 \pm 0.19 \pm 0.14)\times 10^{-3}$. The scalar and tensor contributions are compatible with zero. Several alternative parametrizations are tried: the Pole fit parameter is found to be $M_V = 891 \pm 2.0$ MeV ; the parameter of the Dispersive parametrization is measured to be $Λ_+ =(24.58 \pm 0.18) \times 10^{-3}$. The presented results are considered as preliminary.

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arXiv2017

Divisibility of quantum dynamical maps and collision models

Divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under infinitesimal perturbations, and characterize Pauli dynamical semigroups exhibiting such a property. We construct collision models with factorized environment particles, which realize additivity and multiplicativity of generators of CP divisible maps. A mixture of dynamical maps is obtained with the help of correlated environment. Mixture of ultimate CP divisible processes is shown to result in a new class of eternal CP indivisible evolutions. We explicitly find collision models leading to weakly and essentially non-Markovian Pauli dynamical maps.

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arXiv2017

Quantum evolution in the stroboscopic limit of repeated measurements

We consider a quantum system dynamics caused by successive selective and non-selective measurements of the probe coupled to the system. For the finite measurement rate $τ^{-1}$ and the system-probe interaction strength $γ$ we derive analytical evolution equations in the stroboscopic limit $τ\rightarrow 0$ and $γ^2 τ= {\rm const}$, which can be considered as a deviation from the Zeno subspace dynamics on a longer timescale $T \sim (γ^2 τ)^{-1} \gg γ^{-1}$. Non-linear quantum dynamics is analyzed for selective stroboscopic projective measurements of an arbitrary rank. Non-selective measurements are shown to induce the semigroup dynamics of the system-probe aggregate. Both non-linear and decoherent effects become significant at the timescale $T \sim (γ^2 τ)^{-1}$, which is illustrated by a number of examples.

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arXiv2013

Bipartite entanglement-annihilating maps: necessary and sufficient conditions

We fully characterize bipartite entanglement-annihilating (EA) channels that destroy entanglement of any state shared by subsystems and, thus, should be avoided in any entanglement-enabled experiment. Our approach relies on extending the problem to EA positive maps, the cone of which remains invariant under concatenation with partially positive maps. Due to this invariancy, positive EA maps adopt a well characterization and their intersection with completely positive trace-preserving maps results in the set of EA channels. In addition to a general description, we also provide sufficient operational criteria revealing EA channels. They have a clear physical meaning since the processes involved contain stages of classical information transfer for subsystems. We demonstrate the applicability of derived criteria for local and global depolarizing noises, and specify corresponding noise levels beyond which any initial state becomes disentangled after passing the channel. The robustness of some entangled states is discussed.

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arXiv2013

Single photon-added coherent states: estimation of parameters and fidelity of the optical homodyne detection

Travelling modes of single-photon-added coherent states (SPACS) are characterized via optical homodyne tomography. Given a set of experimentally measured quadrature distributions, we estimate parameters of the state and also extract information about the detector efficiency. The method used is a minimal distance estimation between theoretical and experimental quantities, which additionally allows to evaluate the precision of estimated parameters. Given experimental data, we also estimate the lower and upper bounds on fidelity. The results are believed to encourage preciser engineering and detection of SPACS.

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arXiv2012

Towards higher precision and operational use of optical homodyne tomograms

We present the results of an operational use of experimentally measured optical tomograms to determine state characteristics (purity) avoiding any reconstruction of quasiprobabilities. We also develop a natural way how to estimate the errors (including both statistical and systematic ones) by an analysis of the experimental data themselves. Precision of the experiment can be increased by postselecting the data with minimal (systematic) errors. We demonstrate those techniques by considering coherent and photon-added coherent states measured via the time-domain improved homodyne detection. The operational use and precision of the data allowed us to check for the first time purity-dependent uncertainty relations and uncertainty relations for Shannon and Rényi entropies.

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arXiv2011

Star product and ordered moments of photon creation and annihilation operators

We develop a star-product scheme of symbols defined by the normally ordered powers of the creation and annihilation photon operators, (a†)^m a^n. The corresponding phase space is a two-dimensional lattice with nodes (m,n) given by pairs of nonnegative integers. The star-product kernel of symbols on the lattice and intertwining kernels to other schemes are found in explicit form. Analysis of peculiar properties of the star-product kernel results in new sum relations for factorials. Advantages of the developed star-product scheme for describing dynamics of quantum systems are discussed and time evolution equations in terms of the ordered moments are derived.

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arXiv2011

Optical tomography of Fock state superpositions

We consider optical tomography of photon Fock state superpositions in connection with recent experimental achievements. The emphasis is put on the fact that it suffices to represent the measured tomogram as a main result of the experiment. We suggest a test for checking the correctness of experimental data. Explicit expressions for optical tomograms of Fock state superpositions are given in terms of Hermite polynomials. Particular cases of vacuum and low photon-number state superposition are considered as well as influence of thermal noise on state purity is studied.

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arXiv2011

Unitary and Non-Unitary Matrices as a Source of Different Bases of Operators Acting on Hilbert Spaces

Columns of d^2 x N matrices are shown to create different sets of N operators acting on $d$-dimensional Hilbert space. This construction corresponds to a formalism of the star-product of operator symbols. The known bases are shown to be partial cases of generic formulas derived by using d^2 x N matrices as a source for constructing arbitrary bases. The known examples of the SIC-POVM, MUBs, and the phase-space description of qubit states are considered from the viewpoint of the developed unified approach. Star-product schemes are classified with respect to associated d^2 x N matrices. In particular, unitary matrices correspond to self-dual schemes. Such self-dual star-product schemes are shown to be determined by dequantizers which do not form POVM.

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arXiv2010

Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics

Symmetric informationally complete positive operator valued measures (SIC-POVMs) are studied within the framework of the probability representation of quantum mechanics. A SIC-POVM is shown to be a special case of the probability representation. The problem of SIC-POVM existence is formulated in terms of symbols of operators associated with a star-product quantization scheme. We show that SIC-POVMs (if they do exist) must obey general rules of the star product, and, starting from this fact, we derive new relations on SIC-projectors. The case of qubits is considered in detail, in particular, the relation between the SIC probability representation and other probability representations is established, the connection with mutually unbiased bases is discussed, and comments to the Lie algebraic structure of SIC-POVMs are presented.

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arXiv2010

Mutually unbiased bases: tomography of spin states and star-product scheme

Mutually unbiased bases (MUBs) are considered within the framework of a generic star-product scheme. We rederive that a full set of MUBs is adequate for a spin tomography, i.e. knowledge of all probabilities to find a system in each MUB-state is enough for a state reconstruction. Extending the ideas of the tomographic-probability representation and the star-product scheme to MUB-tomography, dequantizer and quantizer operators for MUB-symbols of spin states and operators are introduced, ordinary and dual star-product kernels are found. Since MUB-projectors are to obey specific rules of the star-product scheme, we reveal the Lie algebraic structure of MUB-projectors and derive new relations on triple- and four-products of MUB-projectors. Example of qubits is considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is discussed.

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arXiv2010

MuSR method and tomographic probability representation of spin states

Muon spin rotation/relaxation/resonance (MuSR) technique for studying matter structures is considered by means of a recently introduced probability representation of quantum spin states. A relation between experimental MuSR histograms and muon spin tomograms is established. Time evolution of muonium, anomalous muonium, and a muonium-like system is studied in the tomographic representation. Entanglement phenomenon of a bipartite muon-electron system is investigated via tomographic analogues of Bell number and positive partial transpose (PPT) criterion. Reconstruction of the muon-electron spin state as well as the total spin tomography of composed system is discussed.

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arXiv2010

Inverse spin-s portrait and representation of qudit states by single probability vectors

Using the tomographic probability representation of qudit states and the inverse spin-portrait method, we suggest a bijective map of the qudit density operator onto a single probability distribution. Within the framework of the approach proposed, any quantum spin-j state is associated with the (2j+1)(4j+1)-dimensional probability vector whose components are labeled by spin projections and points on the sphere. Such a vector has a clear physical meaning and can be relatively easily measured. Quantum states form a convex subset of the 2j(4j+3) simplex, with the boundary being illustrated for qubits (j=1/2) and qutrits (j=1). A relation to the (2j+1)^2- and (2j+1)(2j+2)-dimensional probability vectors is established in terms of spin-s portraits. We also address an auxiliary problem of the optimum reconstruction of qudit states, where the optimality implies a minimum relative error of the density matrix due to the errors in measured probabilities.

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