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V. M. Akulin

Publications and source records attributed to V. M. Akulin.

At least 19 recordsLinked to original sources
arXiv2020

Detecting the event of a single photon loss on quantum signals

We design a scheme for detecting a single photon loss from multi-modal quantum signals transmitted via a fiber or in free space. This consists of a special type of unitary coding transformation, the controlled-squeezing, applied prior to the transmission on the signal composed by information and ancilla modes. At the receiver, the inverse unitary transformation is applied -decoding, and the ancilla modes are measured via photon detection. The outcome reveals whether a photon loss has occurred. Distortion of the information part of the signal caused by an ancilla photon loss can be corrected if the encoding transformation is appropriately selected. Loss of a photon from the information part of the signal can be detected with the probability exponentially close to unity. In contrast to the schemes of decoherence free subspaces and quantum error correction protocols, this methods allows one to make use of entire Hilbert space dimensionality. We discuss possible ways of synthesizing the required encoding-decoding transformations.

quant-ph↗
arXiv2020

Classical and quantum dispersion-free coherent propagation by tailoring multi-modal coupling

It is shown that tailored breaking of the translational symmetry through weak scattering in waveguides and optical fibers can control chromatic dispersions of the individual modes at any order; thereby, it overcomes the problem of coherent classical and quantum signal transmission at long distances. The methodology is based on previously developed quantum control techniques and gives an analytic solution in ideal scattering conditions; it has been also extended to incorporate and correct non-unitary effects in the presence of weak back-scattering. In practice, it requires scatterers able to couple different modes and carefully designed dispersion laws giving a null average quadratic dispersion in the spectral vicinity of the operational frequency.

quant-ph↗
arXiv2018

Quantum compiling with diffusive sets of gates

Given a set of quantum gates and a target unitary operation, the most elementary task of quantum compiling is the identification of a sequence of the gates that approximates the target unitary to a determined precision $\varepsilon$. Solovay-Kitaev theorem provides an elegant solution which is based on the construction of successively tighter `nets' around the unity comprised by successively longer sequences of gates. The procedure for the construction of the nets, according to this theorem, requires accessibility to the inverse of the gates as well. In this work, we propose a method for constructing nets around unity without this requirement. The algorithmic procedure is applicable to sets of gates which are diffusive enough, in the sense that sequences of moderate length cover the space of unitary matrices in a uniform way. We prove that the number of gates sufficient for reaching a precision $\varepsilon$ scales as $ \log (1/\varepsilon )^{\log 3 / log 2} $ while the pre-compilation time is increased as compared to thatof the Solovay-Kitaev algorithm by the exponential factor 3/2.

quant-ph↗
arXiv2018

Nonlinear coupling of photons via a collective mode of transparent superconductor

At the first glance, the expression "transparent superconductor" may seem an oxymoron. Still, the first principle calculations and experiments show that the materials that behave as superconductors at low frequencies and do not absorb in the optical domain may exist. Virtual excitation of the collective electronic modes of such superconductors in a magnetic field appears as an efficient way to realize the nonlinear interaction of light at the level of two single photons. The essence of the effect is in the fact that the pondermotor energy is proportional to the ratio of the charge squared to the mass of the "collective particle" interacting with radiation, $e^2/m$, and therefore, for a "particle" representing a collective motion of many electrons, it scales linearly-, and its second-order correction quadratically with the number of the electrons involved. This general situation is analyzed in detail in the framework of a simple model of a fiber tube waveguide equipped with a clean superconductor layer. It turns out that for realistic parameters, at the micron-scale of the tube diameter and the centimeter-scale of the fiber length, such a system is capable of performing the logic gate operation on the polarization variables of a pair of optical photons.

quant-ph↗
arXiv2017

Universal quantum processor already exists and just waits for the proper programming

A possibility of performing the C-NOT gate operation at the ground and the first excited states of two harmonic oscillators interacting via a two-level system subject to complete control is demonstrated. The system resembles Turing machine, where the result of interaction between oscillators and the two level system is restricted to a certain fixed unitary transformation matrix, while all the control required for the implementation of the gate is provided via manipulations with the two-level system, which remains the only fully-controllable part of the entire system. Each gate operation requires a "Turing programming", - it can be realized as a series of > 63 elementary unitary operations. The result shows a way how one can construct a quantum processor in a multimode microwave cavity equipped with a fully controlled two-level system, such as Josephson junction chip. Parameters of already existing experimental devises could allow one to perform up to 15 gate operations in an ensemble of about 10 qubits.

quant-ph↗
arXiv2015

Neural Control of Redundant (Abundant) Systems as Algorithms Stabilizing Subspaces

We address the problem of stability of motor actions implemented by the central nervous system based on simple algorithms potentially reflecting physical (including physiological) processes within the body. A number of conceptually simple algorithms that solve motor tasks with a high probability of success may be based on feedback schemes that ensure stability of subspaces of neural variables associated with accomplishing those tasks. The task is formulated in terms of linear constrains imposed either on the human body mechanical variables or on neural variables; we discuss three reference frames relevant to these processes. We discuss underlying basic principles of such algorithms, their architecture, and efficiency, and compare the outcomes of implementation of such algorithms with the results of experiments performed on the human hand.

q-bio.NC↗
arXiv2015

The Essentially Entangled Component of Multipartite Mixed Quantum States, its Properties and an Efficient Algorithm for its Extraction

We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled one, which contains no product states components. We show that this convex decomposition can be achieved in practice with the help of an algorithm based on linear programming, which in the general case scales polynomially with the dimension of the multipartite system. Furthermore, we suggest methods for analyzing the multipartite entanglement content of the essentially entangled component and derive analytically an upper bound for its rank. We illustrate the algorithm at an example of a composed system of total dimension 12 undergoing loss of coherence due to classical noise and we trace the time evolution of its essentially entangled component. We suggest a "geometric" description of entanglement dynamics and show how it explains the well-known phenomena of sudden death and revival of multipartite entanglement.

quant-ph↗
arXiv2013

Quantum repeater with Rydberg blocked atomic ensembles in fiber-coupled cavities

We propose and analyze a quantum repeater architecture in which Rydberg blocked atomic ensembles inside optical cavities are linked by optical fibers. Entanglement generation, swapping and purification are achieved through collective laser manipulations of the ensembles and photon transmission. Successful transmission and storage of entanglement are heralded by ionization events rather than by photon detection signal used in previous proposals. We demonstrate how the high charge detection efficiency allows for a shortened average entanglement generation time, and we analyze an implementation of our scheme with ensembles of Cs atoms.

quant-ph↗
arXiv2011

Laplacian growth in self-consistent Laplacian field : Effect of the long-range interparticle interactions on the fractal dimension of structures formed by their aggregation-limited diffusion

We numerically simulate the dynamics of aggregation of interacting atomic clusters deposited on a surface. We show that the shape of the structures resulting from their aggregation-limited random walk is affected by the presence of a binary interparticle Laplacian potential due to, for instance, the surface stress field. We characterize the morphologies we obtain by their Hausdorff fractal dimension as well as the so-called external fractal dimension, which appears more sensitive to the potential. We demonstrate the relevance of our model by comparing it to previously published experimental results for antymony and silver clusters deposited onto graphite surface.

cond-mat.mes-hall↗
arXiv2009

Population Dynamics in Cold Gases Resulting from the Long-Range Dipole-Dipole Interaction

We consider the effect of the long range dipole-dipole interaction on the excitation exchange dynamics of cold two-level atomic gase in the conditions where the size of the atomic cloud is large as compared to the wavelength of the dipole transition. We show that this interaction results in population redistribution across the atomic cloud and in specific spectra of the spontaneous photons emitted at different angles with respect to the direction of atomic polarization.

quant-ph↗
arXiv2009

Universal protection of unitary evolution from slow noise: dynamical control pushed to the extreme

We propose a technique that allows to simultaneously perform universal control of the evolution operator and compensate for the first order contribution of an arbitrary Hermitian constant noise. We show that, at least, a three-valued Hamiltonian is needed in order to protect the system against any such noise. This technique is illystrated by an explicit algorithm for a control sequence that is applied to numerically design a safe two-qubit gate.

quant-ph↗
arXiv2008

Tunneling electro-conductance of atomic Bose condensates

We consider interaction of an electron with a Bose condensate of atoms having electron affinity. Though states of the electron attached to atoms form a continuous band, tunneling through this band is strongly suppressed by quantum fluctuations of the condensate density. We adapt standard field theory methods originally developed for description of a particle propagating trough a disordered potential and present an exactly soluble analytical model of the process. In contrast with the standard description, we take into account inelastic processes associated with quantum transitions in the condensate. Possibilities of the experimental observation of the phenomenon are discussed.

cond-mat.mes-hall↗
arXiv2007

Cooperative behavior of qutrits with dipole-dipole interactions

We have identified a class of many body problems with analytic solution beyond the mean-field approximation. This is the case where each body can be considered as an element of an assembly of interacting particles that are translationally frozen multi-level quantum systems and that do not change significantly their initial quantum states during the evolution. In contrast, the entangled collective state of the assembly experiences an appreciable change. We apply this approach to interacting three-level systems.

quant-ph↗
arXiv2007

Control of multiatom entanglement in a cavity

We propose a general formalism for analytical description of multiatomic ensembles interacting with a single mode quantized cavity field under the assumption that most atoms remain un-excited on average. By combining the obtained formalism with the nilpotent technique for the description of multipartite entanglement we are able to overview in a unified fashion different probabilistic control scenarios of entanglement among atoms or examine atomic ensembles. We then apply the proposed control schemes to the creation of multiatom states useful for quantum information.

quant-ph↗
arXiv2006

Description of Quantum Entanglement with Nilpotent Polynomials

We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging from our approach. We derive the equation of motion for the tanglemeter and, in representative examples of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced idea of generalized entanglement. Possible future developments and applications of the method are discussed.

quant-ph↗
arXiv2005

Coherence protection by the quantum Zeno effect and non-holonomic control in a Rydberg Rubidium isotope

The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error-correction (ancilla adding, coding and decoding) and the Quantum Zeno Effect. A pedagogical demonstration of our method on a simple atomic system, namely a Rubidium isotope, is proposed.

quant-ph↗
arXiv2005

Non-Holonomic Control I

In this paper, we present a universal control technique, the non-holonomic control, which allows us to impose any arbitrarily prescribed unitary evolution to any quantum system through the alternate application of two well-chosen perturbations.

quant-ph↗