Decoherence In Quantum Systems Research Articles

Pauli component erasing quantum channels

Decoherence of quantum systems is described by quantum channels. However, a complete understanding of such channels, especially in the multi-particle setting, is still an ongoing difficult task. We propose the family of quantum maps that preserve or completely erase the components of a multi-qubit system in the basis of Pauli strings, which we call Pauli component erasing maps. For the corresponding channels, it is shown that the preserved components can be interpreted as a finite vector subspace, from which we derive several properties and complete the characterization. Moreover, we show that the obtained family of channels forms a semigroup and derive its generators. We use this simple structure to determine physical implementations and connect the obtained family of channels with Markovian processes.

Self-protected adiabatic quantum computation

Recent experiments show the existence of collective decoherence in quantum systems. We study the possibility of quantum computation in decoherence free subspace which is robust against such kind of decoherence processes. This passive protection protocol can be especially advantageous for continuous quantum computation such as quantum annealers. As an example we propose to use decoherence protected adiabatic quantum computation for the Grover search problem. Our proposal contains only two-body interactions, making it feasible in near-term quantum devices.

Measurement and suppression of magnetic field noise of trapped ion qubit

Magnetic field noise is an important factor causing quantum decoherence in quantum systems. In order to suppress the decoherence effect, magnetic field noise needs to be properly measured and controlled. Magnetic field noise power spectrum measurement using a single trapped ion based quantum spectrum analyzer is a very effective way. In this paper, the magnetic field noise measurement based on dynamic decoupling technique is analyzed theoretically. Furthermore, we use magnetically insensitive transition to measure the magnetic field noise, which has the potential to measure stronger magnetic field noise and speed up the measurement process. In our experiment, we suppress the magnetic field noise by using active feedback control and passive compensation, where the required passive compensation amplitude is obtained by measuring the magnetic field noise spectrum of a single 25Mg+ ion. With the magnetic field noise suppressed, the expected contribution of the magnetic field noise to the stability of the 25Mg+–27Al+ ion optical clock can be decreased from to .

Entanglement-Assisted Quantum Codes From Algebraic Geometry Codes

Quantum error-correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error-correcting codes to achieve higher rates than the one obtained by means of the traditional stabilizer formalism. Such codes are called entanglement-assisted quantum error-correcting (EAQEC) codes. In this paper, we utilize algebraic geometry codes to construct several families of EAQEC codes derived from the Euclidean and the Hermitian construction. Three families constructed here consist of codes whose quantum Singleton defect is equal to zero, one, or two. We also construct families of EAQEC codes with an encoding rate exceeding the quantum Gilbert-Varshamov bound. Additionally, asymptotically good towers of linear complementary dual codes are used to obtain asymptotically good families of EAQEC codes consuming maximal entanglement. Furthermore, a simple comparison with the quantum Gilbert-Varshamov bound demonstrates that, by utilizing the proposed construction, it is possible to generate an asymptotically family of EAQEC codes that exceeds this bound.

Master equation incorporating the system-environment correlations present in the joint equilibrium state

We present a general master equation, correct to second order in the system-environment coupling strength, that takes into account the initial system-environment correlations. We assume that the system and its environment are in a joint thermal equilibrium state, and thereafter a unitary operation is performed to prepare the desired initial system state, with the system Hamiltonian possibly changing thereafter as well. We show that the effect of the initial correlations shows up in the second-order master equation as an additional term, similar in form to the usual second-order term describing relaxation and decoherence in quantum systems. We apply this master equation to a generalization of the paradigmatic spin-boson model, namely a collection of two-level systems interacting with a common environment of harmonic oscillators, as well as a collection of two-level systems interacting with a common spin environment. We demonstrate that, in general, the initial system-environment correlations need to be accounted for in order to accurately obtain the system dynamics.

Einselection from incompatible decoherence channels

Decoherence of quantum systems from entanglement with an unmonitored environment is, to date, the most compelling explanation of the emergence of a classical picture from a quantum world. While it is well understood for a single Lindblad operator, the role in the einselection process of a complex system-environment interaction remains to be clarified. In this paper, we analyze an open quantum dynamics inspired by cavity QED experiments with two noncommuting Lindblad operators modeling decoherence in the number basis and dissipative decoherence in the coherent-state basis. We study and solve exactly the problem using quantum trajectories and phase-space techniques. The einselection optimization problem, which we consider to be about finding states that minimize the variation of some entanglement witness at a given energy, is studied numerically. We show that Fock states remain the most robust states to decoherence up to a critical coupling.

Quantum information leakage.

Decoherence in quantum systems compromises the quantum information processing. However, in molecular systems, coherence is not completely lost and residual coherence can provide important information to guide the design of efficient molecular qubits.

Tsallis entropy and decoherence of CsI quantum pseudo dot qubit

Polaron in CsI quantum pseudo dot under an electromagnetic field was considered, and the ground and first excited state energies were derived by employing the combining Pekar variational and unitary transformation methods. With the two-level system obtained, single qubit was envisioned and the decoherence was studied using non-extensive entropy (Tsallis entropy). Numerical results showed: (i) the increase (decrease) of the energy levels (period of oscillation) with the increase of chemical potential, the zero point of pseudo dot, cyclotron frequency, and transverse and longitudinal confinements; (ii) the Tsallis entropy evolved as a wave envelop that increase with the increase of non-extenxive parameter and with the increase of electric field strength, zero point of pseudo dot and cyclotron frequency the wave envelop evolve periodically with reduction of period; (iii) The transition probability increases from the boundary to the centre of the dot where it has its maximum value. It was also noted that the probability density oscillate with period T0=ℏ/ΔΕ with the tunnelling of the chemical potential and zero point of the pseudo dot. These results are helpful in the control of decoherence in quantum systems and may also be useful for the design of quantum computers.

Decoherence in quantum systems in a static gravitational field

A small quantum system is studied which is a superposition of states localized in different positions in a static gravitational field. The time evolution of the correlation between different positions is investigated, and it is seen that there are two time scales for such an evolution (decoherence). Both time scales are inversely proportional to the red shift difference between the two points. These time scales correspond to decoherences which are linear and quadratic, respectively, in time.

Enhancement of phonon backscattering due to confinement of ballistic phonon pathways in silicon as studied with a microfabricated phonon spectrometer

In this work, the mechanism for enhanced phonon backscattering in silicon is investigated. An understanding of phonon propagation through substrates has implications for engineering heat flow at the nanoscale, for understanding sources of decoherence in quantum systems, and for realizing efficient phonon-mediated particle detectors. In these systems, phonons that backscatter from the bottom of substrates, within the crystal or from interfaces, often contribute to the overall detector signal. We utilize a microscale phonon spectrometer, comprising superconducting tunnel junction emitters and detectors, to specifically probe phonon backscattering in silicon substrates (∼500 μm thick). By etching phonon “enhancers” or deep trenches (∼90 μm) around the detectors, we show that the backscattered signal level increases by a factor of ∼2 for two enhancers versus one enhancer. Using a geometric analysis of the phonon pathways, we show that the mechanism of the backscattered phonon enhancement is due to confinement of the ballistic phonon pathways and increased scattering off the enhancer walls. Our result is applicable to the geometric design and patterning of substrates that are employed in phonon-mediated detection devices.

Common reducing unitary subspaces and decoherence in quantum systems

Maps of the form Phi(X) =sum_{i=1}^s A_iXA^*, where A_1, . . . ,A_s are fixed complex n by n matrices and X is any complex n by n matrix are used in quantum information theory as representations of quantum channels. This article deals with computable conditions for the existence of decoherence--free subspaces for Phi. Since the definition of decoherence-free subspace for quantum channels relies only on the matrices A1, . . . ,As, the term of common reducing unitary subspace is used instead of the original one. Among the main results of the paper, there are computable conditions for the existence of common eigenvectors. These are related to common reducing unitary subspaces of dimension one. The new results on common eigenvectors provide new effective condition for the existence of common invariant subspaces of arbitrary dimensions.

Study of Decoherence of Entangled States Made up of Two Basic States in a Linear Chain of Three Qubits

Using Lindblad approach to study decoherence of quantum systems, we study the decoherence and decay of entangled states, formed by two basic states of a chain of thee qubits. We look on these states for a possible regular dependence on their decay as a function of their energy separation between the basic states under different types of environments. We didn’t find regular or significant dependence on this energy separation for the type of environment considered.

Diffusion-assisted selective dynamical recoupling: A new approach to measure background gradients in magnetic resonance

Dynamical decoupling, a generalization of the original NMR spin-echo sequence, is becoming increasingly relevant as a tool for reducing decoherence in quantum systems. Such sequences apply non-equidistant refocusing pulses for optimizing the coupling between systems, and environmental fluctuations characterized by a given noise spectrum. One such sequence, dubbed Selective Dynamical Recoupling (SDR) [P. E. S. Smith, G. Bensky, G. A. Álvarez, G. Kurizki, and L. Frydman, Proc. Natl. Acad. Sci. 109, 5958 (2012)], allows one to coherently reintroduce diffusion decoherence effects driven by fluctuations arising from restricted molecular diffusion [G. A. Álvarez, N. Shemesh, and L. Frydman, Phys. Rev. Lett. 111, 080404 (2013)]. The fully-refocused, constant-time, and constant-number-of-pulses nature of SDR also allows one to filter out "intrinsic" T1 and T2 weightings, as well as pulse errors acting as additional sources of decoherence. This article explores such features when the fluctuations are now driven by unrestricted molecular diffusion. In particular, we show that diffusion-driven SDR can be exploited to investigate the decoherence arising from the frequency fluctuations imposed by internal gradients. As a result, SDR presents a unique way of probing and characterizing these internal magnetic fields, given an a priori known free diffusion coefficient. This has important implications in studies of structured systems, including porous media and live tissues, where the internal gradients may serve as fingerprints for the system's composition or structure. The principles of this method, along with full analytical solutions for the unrestricted diffusion-driven modulation of the SDR signal, are presented. The potential of this approach is demonstrated with the generation of a novel source of MRI contrast, based on the background gradients active in an ex vivo mouse brain. Additional features and limitations of this new method are discussed.

Wave chaos in a randomly inhomogeneous waveguide: Spectral analysis of the finite-range evolution operator

The problem of sound propagation in a randomly inhomogeneous oceanic waveguide is considered. An underwater sound channel in the Sea of Japan is taken as an example. Our attention is concentrated on the domains of finite-range ray stability in phase space and their influence on wave dynamics. These domains can be found by means of the one-step Poincare map. To study manifestations of finite-range ray stability, we introduce the finite-range evolution operator (FREO) describing transformation of a wave field in the course of propagation along a finite segment of a waveguide. Carrying out statistical analysis of the FREO spectrum, we estimate the contribution of regular domains and explore their evanescence with increasing length of the segment. We utilize several methods of spectral analysis: analysis of eigenfunctions by expanding them over modes of the unperturbed waveguide, approximation of level-spacing statistics by means of the Berry-Robnik distribution, and the procedure used by A. Relano and coworkers [Relano et al., Phys. Rev. Lett. 89, 244102 (2002); Relano, Phys. Rev. Lett. 100, 224101 (2008)]. Comparing the results obtained with different methods, we find that the method based on the statistical analysis of FREO eigenfunctions is the most favorable for estimating the contribution of regular domains. It allows one to find directly the waveguide modes whose refraction is regular despite the random inhomogeneity. For example, it is found that near-axial sound propagation in the Sea of Japan preserves stability even over distances of hundreds of kilometers due to the presence of a shearless torus in the classical phase space. Increasing the acoustic wavelength degrades scattering, resulting in recovery of eigenfunction localization near periodic orbits of the one-step Poincaré map.

Strong decoherence in quantum systems undergoing collisions

The decoherence problem in systems with continuous variables is discussed. It is shown that in quantum systems with momentum transfers in the Markovian approximation all pure states strongly decohere making quantum information processing much more complex than in the qubit case. The time scale of the effect is calculated.

Decoherence, entanglement decay, and equilibration produced by chaotic environments

We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the preferential energy eigenbasis are quantum Loschmidt echoes, which in the strong coupling regime are characterized at long time scales by fluctuations around a constant mean value. We show that due to the chaotic dynamics of the environment, the mean value and the width of the Loschmidt-echo fluctuations are inversely proportional to the quantity we define as the effective Hilbert-space dimension of the environment, which in general is smaller than the dimension of the entire available Hilbert space. Nevertheless, in the semiclassical regime this effective Hilbert-space dimension is in general large, in which case even a chaotic environment with few degrees of freedom produces decoherence without revivals. Moreover we show that in this regime the environment leads the central system to equilibrate to the time average of its reduced density matrix, which corresponds to a diagonal state in the preferential energy eigenbasis. For the case of two uncoupled, initially entangled central systems that interact with identical local quantum environments with chaotic underlying classical dynamics, we show that in the semiclassical limit the equilibration state is arbitrarily close to a separable state. We confirm our results with numerical simulations in which the environment is modeled by the quantum kicked rotor in the chaotic regime.

A quantum spectrum analyser

Noise filters based on so-called dynamical decoupling pulse sequences can suppress decoherence in quantum systems. Turning this idea on its head now provides a new technique for studying the noise itself.

Tunneling Splitting of Jahn-Teller Ions in Oxides

The magnitude of tunneling splitting, 3Gamma, that governs decoherence in quantum systems under symmetric potentials, is frequently unknown. Using first-principles calculations, we have obtained 3Gamma for a number of E[symbol:see text]e Jahn-Teller impurities in solids. Calculated values span 6 orders of magnitude on passing from KCl:Ag{2+} to MgO:Cu{2+}. Values associated with Cu2+- and Ag2+-doped MgO are 2 orders of magnitude larger than those previously assumed and consistent with the existence of a dynamic Jahn-Teller effect. The origin and enhancement with pressure of these high 3Gamma values is discussed in detail.

A history of entanglement: Decoherence and the interpretation problem

This paper examines the interweaving of the history of quantum decoherence and the interpretation problem in quantum mechanics through the work of two physicists—H. Dieter Zeh and Wojciech Zurek. In the early 1970s Zeh anticipated many of the important concepts of decoherence, framing it within an Everett-type interpretation. Zeh has since remained committed to this view; however, Zurek, whose papers in the 1980s were crucial in the treatment of the preferred basis problem and the subsequent development of density matrix formalism, has argued that decoherence leads to what he terms the ‘existential interpretation’, compatible with certain aspects of both Everett's relative-state formulation and the Bohr's ‘Copenhagen interpretation’. I argue that these different interpretations can be traced back to the different early approaches to the study of environment-induced decoherence in quantum systems, evident in the early work of Zeh and Zurek. I also show how Zurek's work has contributed to the tendency to see decoherence as contributing to a ‘new orthodoxy’ or a reconstruction of the original Copenhagen interpretation.

Decoherence by engineered quantum baths

Optical lattices can be used to simulate quantum baths and hence they can be of fundamental help to study, in a controlled way, the emergence of decoherence in quantum systems. Here we show how to implement a pure dephasing model for a two-level system coupled to an interacting spin bath. In this scheme it is possible to implement a large variety of spin environments embracing Ising, XY and Heisenberg universality classes. After having introduced the model, we calculate exactly the decoherence for the Ising and the XY spin bath model. We find universal features depending on the critical behaviour of the spin bath, both in the short- and long-time limits. The rich scenario that emerges can be tested experimentally and can be of importance for the understanding of the coherence loss in open quantum systems.