Decoherence Function Research Articles

Quantum decoherence dynamics in stochastically fluctuating environments.

We theoretically study the decoherence of a two-level quantum system coupled to noisy environments exhibiting linear and quadratic fluctuations within the framework of a stochastic Liouville equation. It is shown that the intrinsic energy levels of the quantum system renormalize under either the linear or quadratic influence of the environmental noise. In the case of quadratic dependence, the renormalization of the energy levels of the system emerges even if the environmental noise exhibits stationary statistical properties. This is in contrast to the case under linear influence, where the intrinsic energy levels of the system renormalize only if the environmental noise displays nonstationary statistics. We derive the analytical expressions of the decoherence function in the cases where the fluctuation of the frequency difference depends linearly and quadratically on the nonstationary Ornstein-Uhlenbeck noise (OUN) and random telegraph noise (RTN) processes, respectively. In the case of the linear dependence of the OUN, the environmental nonstationary statistical property can enhance the dynamical decoherence. However, the nonstationary statistics of the environmental noise can suppress the quantum decoherence in this case under the quadratic influence of the OUN. In the presence of the RTN, the quadratic influence of the environmental noise does not give rise to decoherence but only causes a determinate frequency renormalization in dynamical evolution. The environmental nonstationary statistical property can suppress the quantum decoherence of the case under the linear influence of the RTN.

Quantum non-Markovianity of a qubit in presence of state dependent bath

In the field of quantum information theory, the intersection of the complex dynamics related to non-Markovianity and information is a crucial frontier. Non-Markovian effects, which take memory and temporal correlations into account, challenge conventional wisdom in the fields of quantum biology, metrology, cryptography, and communication. In this work, we analyze the non-Markovian dynamics of a dephasing model in presence of initial system-bath (SB) correlations. These SB correlations are generated via projective measurements on a predefined equilibrium state. Using the non-Markovian measures based on trace distance and quantum Fisher information, it is shown that these correlations have significant impact in the non-Markovian regime at high temperatures while it does not play any role in the Markovian case. Furthermore, it is shown that the oscillatory behaviour of the decoherence function does not always show non-Markovian behaviour.

Classical analogous quantum coherent superposition through the Hertz-type nonlinearity of elastic granules

The theory of quantum superposition of states is one of the fundamental concepts related to quantum information science and technology (QIST). Two or more pure quantum states can be superposed to get a distinct quantum state, and one of the examples is the quantum bit, or qubit, state. But decoherence makes it easy for the current qubits, the most critical part of QIST platforms, to lose their superposition of states. Therefore, we theoretically propose and experimentally realize a classical analogous to the coherent superposition of energy states through the Hertz-type nonlinearity of elastic granules driven externally. The granules’ nonlinear vibrations depend mutually through phase and form a coherent superposition when projected into linear modes of vibration. We demonstrate how the state vector components can emerge from the amplitudes of coherent states, spanning to the two-dimensional time-dependent parametric Hilbert space. These amplitudes represent an actual amplitude rather than a probability amplitude, which opens the possibility of exploring two-state quantum-like computations through the superposition of states without decoherence and wave function collapse. These characteristics make it possible to understand the material-based quantum analogous information technology through experimentation of elastic bit.

Experimental demonstration of classical analogous time-dependent superposition of states

One of the quantum theory concepts on which quantum information processing stands is superposition. Here we provide experimental evidence for the existence of classical analogues to the coherent superposition of energy states, which is made possible by the Hertz-type nonlinearity of the granules together with the external driving field. The granules’ nonlinear vibrations are projected into the linear modes of vibration, which depend on one another through the phase and form a coherent superposition. We show that the amplitudes of the coherent states form the components of a state vector that spans a two-dimensional Hilbert space, and time enables the system to span its Hilbert space parametrically. Thus, the superposition of states can be exploited in two-state quantum-like computations without decoherence and wave function collapse. Finally, we demonstrate the experimental realization of applying a reversible Hadamard gate to a pure base state that brings the state into a superposition.

Disentanglement Dynamics in Nonequilibrium Environments.

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.

Measure of invertible dynamical maps under convex combinations of noninvertible dynamical maps

We study the convex combinations of the $(d+1)$-generalized Pauli dynamical maps in a Hilbert space of dimension $d$. For certain choices of the decoherence function, the maps are noninvertible, and they remain under convex combinations as well. For the case of dynamical maps characterized by the decoherence function $(1\ensuremath{-}{e}^{\ensuremath{-}ct})/n$ with the decoherence parameter $n$ and decay factor $c$, we evaluate the fraction of invertible maps obtained upon mixing, which is found to increase superexponentially with dimension $d$.

Anti-PT-symmetric qubit: Decoherence and entanglement entropy

We investigate the dynamics of a general two-level based anti-parity-time (anti-$\mathcal{PT}$)-symmetric qubit and study its decoherence as well as entanglement entropy properties. We compare our findings with that of the corresponding parity-time ($\mathcal{PT}$)-symmetric and Hermitian qubits. To begin, we consider the time-dependent Dyson map to find the exact analytical dynamics for a general non-Hermitian qubit system weakly coupled with a thermal bath for pure dephasing, before specializing it to the case of a general anti-$\mathcal{PT}$-symmetric qubit. Basing the comparison under the same coupling strength or increasing the non-Hermiticity, we observe that the decoherence function and entanglement entropy of the anti-$\mathcal{PT}$-symmetric qubit decays and grows more slowly, respectively, compared to the $\mathcal{PT}$-symmetric and Hermitian qubits. Similarly, the corresponding variance and area of Fisher information are much higher compared to the $\mathcal{PT}$-symmetric and Hermitian qubits. These results demonstrate that anti-$\mathcal{PT}$-symmetric qubits may be better suited for quantum computing and quantum information processing applications than conventional Hermitian or even $\mathcal{PT}$-symmetric qubits.

Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath

This work addresses adiabatic quantum decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system–environment interaction Hamiltonian that represents a partition of non-interacting subsystems and highlights the collective correlation that appears exclusively due to the coupling with a common environment. Remarkably, this simple, exactly solvable model encompasses relevant aspects of a many-body open quantum system and features the subtle quantum effects that arise when the size scales up to a macroscopic level. We derive an analytical expression for the time dependence of the density matrix elements (in the preferred basis) without assuming coarse-graining. The resulting decoherence function is eigen-selective and is a complex exponential whose exponent has a real part that introduces a decay similar to that in the spin-boson model. On the contrary, the imaginary part depends on the quantum numbers and geometry of the whole partition and does not reflect the system temperature. Motivated by decoherence in solid-state NMR, and in search of realistic numerical estimations, we apply the theoretical results to a partition of dipole-coupled spin pairs in contact with a common phonon bath, using typical parameters of hydrated salts. The proposal allows estimating the decoherence time scale in terms of the system physical constants: sound velocity and eigenvalue distribution width. As a significant novelty, the decoherence function phase depends on the eigenvalue distribution throughout the sample. It plays the leading role, overshadowing the mechanism associated with the bath thermal state. Finally, we apply the formalism to describe decoherence in the “magic echo” NMR reversal experiment. We find that the system–environment correlation explains the origin of irreversibility, and both the decoherence rate value and its dependence on the dipolar frequency, are remarkably similar to the experiment.

Dynamical decoupling with initial system-environment correlations

Dynamical decoupling (DD) technique is one of the most successful methods to suppress decoherence in qubit systems. In this paper, we studied a solvable pure dephasing model and investigated how DD sequences and initial correlations affect this system. We gave the analytical expressions of decoherence functions and compared the decoherence suppression effects of DD pulses in Ohmic, sub-Ohmic and super-Ohmic environments. Our results show that (1) The initial system-environment correlation will cause additional decoherence. In order to control the dynamic process of open quantum system more accurately and effectively, the initial correlation between the system and reservoir must be considered. (2) High frequency DD pulses can significantly reduce the amplitude of the decoherence function even in the presence of initial system-environment correlations.

Dynamical decoupling-assisted quantum parameter estimation with initial system-environment correlations

Decoherence is the main obstacle to quantum precision measurement. One must adopt appropriate control strategies to suppress decoherence. In this paper, we study the dephasing model of the system-environment with initial correlation, and use the quantum Fisher information (QFI) as the tool to explore the effect of dynamical decoupling pulses on inhibiting decoherence and improving the estimation precision of quantum parameters. We firstly study the influence of the initial correlations and initial quantum state on the dynamical evolution of a single qubit in this mode. Based on numerical calculations, in the Ohmic and the super-Ohmic thermal reservoir, we find that the periodic dynamical decoupling (PDD) sequence can significantly reduce the amplitude of the decoherence function, except for the "anti-Zeno" effect when the number of pulses is relatively small. By a judicious choice of the PDD pulse frequency, the dynamical decoupling pulses can effectively enhance the precision of quantum parameter estimation. And due to the peak structure existing in the decoherence function, the effect of applying Uhrig dynamical decoupling (UDD) sequence on the model is not ideal.

Distributing memory effects in an open two-qubit system

We introduce a method to distribute memory effects among different subspaces of an open two-qubit system's state space. Within the linear optical framework, our system of interest is the polarization of two photons, while the environment consists of their frequency degrees of freedom. By exploiting initially correlated frequency distributions and initial frequency-dependent phase factors, we are able to control all the four decoherence functions for polarization---corresponding to different open-system subspace divisions---almost independently of each other. Hence, our results demonstrate how, in a multipartite dephasing system, Markovian and non-Markovian dynamics can be arbitrarily divided between the subsystems, giving rise to the concept of memory partitions. We also discuss further implications the results have, e.g., on the dynamics of purity and entropy within the two-qubit system.

Photonic dephasing dynamics and the role of initial correlations

Dynamics of open quantum systems depends on different types of initial correlations. On the one hand, when system and environment are both inherently multipartite, initial correlations between the parties of the composite environment make the dynamical map non-local, despite of local nature of the interaction between each party of the system and the environment. On the other hand, initial correlations between the open system and its environment prevents one from defining a completely positive dynamical map. Recently, dephasing dynamics of photons has been used in both of these frameworks - theoretically and experimentally - to demonstrate some fundamental and applicable aspects of open system dynamics and memory effects. However, the earlier studies in this context are often based solely on the concept of decoherence functions. Therefore, we still lack explicit master equation descriptions for dynamics induced by correlated composite initial environmental states. Also, a detailed understanding how initial system-environment correlations influence qubit dynamics in the photonic context is missing. In this paper, we derive generic master equations for the reduced dephasing dynamics of the two-photon polarization state when the bipartite environmental frequency degrees of freedom are initially correlated. We thereby show the explicit dependence of the operator form and the decay rates of the master equation on the initial frequency correlations and the influence of various types of frequency distributions. Furthermore, we use recently developed bath positive decomposition method to treat initially correlated polarization-frequency state of a photon, and demonstrate how this allows new insight and detailed information on how the contributions of different origin influence the photonic dephasing.

Enhancing Quantum Parameter Estimation in Open Quantum System by Dynamical Decoupling Pulses

In this paper, we focus on studying how to enhance the precision of parameter estimation by dynamical decoupling (DD) pulses in an open system. Our results show that, when a qubit is subjected to a zero-temperature Ohmic-like dephasing reservoir, the quantum Fisher information (QFI) is determined by the decoherence function of this qubit. If the appropriate DD pulse frequency is selected, the decoherence in noisy environment can be effectively suppressed and the precision in parameter estimation can be enhanced. Moreover, we make a further comparison for the control effects between Uhrig dynamical decoupling (UDD) sequence and periodic dynamic decoupling (PDD) sequence in the sub-Ohmic and super-Ohmic environments. We find that, when the same DD pulses are applied to this qubit, UDD has obvious advantages over PDD in terms of improving precision of parameter estimation. This is because UDD can completely eliminate the adverse effect of environmental decoherence on parameter estimation.

Control of quantum correlation of high dimensional system in squeezed vacuum reservoir

We study the quantum correlation and entanglement for a high-dimensional spin-S system in a squeezed vacuum reservoir. The exact analytical solution is presented, which shows that the decoherence function governs the quantum correlation and quantum entanglement of corresponding dynamical process. The squeezed amplitude parameter for quantum correlation and quantum entanglement has a negative impact in the whole process, the better the squeezing effect, the greater the negative impact. Furthermore, in the super-Ohmic reservoir, the influence of Ohmic parameter on quantum correlation and quantum entanglement can be divided into two regions in terms of the critical value s=2.5⁡. If s<2.5, the decay rate of quantum correlation slows down obviously, and the environmental decoherence effect is much smaller than that of Ohmic and sub-Ohmic reservoirs. On the contrary, if s>2.5, the decay rate of quantum correlation accelerates obviously, and the decoherence effect surpasses the cases of Ohmic and sub-Ohmic reservoirs greatly.

Schwinger’s picture of quantum mechanics III: The statistical interpretation

Schwinger’s algebra of selective measurements has a natural interpretation in the formalism of groupoids. Its kinematical foundations, as well as the structure of the algebra of observables of the theory, were presented in [F. M. Ciaglia, A. Ibort and G. Marmo, Schwinger’s picture of quantum mechanics I: Groupoids, Int. J. Geom. Meth. Mod. Phys. (2019), arXiv: 1905.12274 [math-ph]. https://doi.org/10.1142/S0219887819501196 . F. M. Ciaglia, A. Ibort and G. Marmo, Schwinger’s picture of quantum mechanics II: Algebras and observables, Int. J. Geom. Meth. Mod. Phys. (2019). https://doi.org/10.1142/S0219887819501366 ]. In this paper, a closer look to the statistical interpretation of the theory is taken and it is found that an interpretation in terms of Sorkin’s quantum measure emerges naturally. It is proven that a suitable class of states of the algebra of virtual transitions of the theory allows to define quantum measures by means of the corresponding decoherence functionals. Quantum measures satisfying a reproducing property are described and a class of states, called factorizable states, possessing the Dirac–Feynman “exponential of the action” form are characterized. Finally, Schwinger’s transformation functions are interpreted similarly as transition amplitudes defined by suitable states. The simple examples of the qubit and the double slit experiment are described in detail, illustrating the main aspects of the theory.

Experimental emulation of quantum non-Markovian dynamics and coherence protection in the presence of information backflow

We experimentally emulate, in a controlled fashion, the non-Markovian dynamics of a pure dephasing spin-boson model at zero temperature. Specifically, we use a randomized set of external radio-frequency fields to engineer a desired noise power-spectrum to effectively realize a non-Markovian environment for a single NMR qubit. The information backflow, characteristic to the non-Markovianity, is captured in the nonmonotonicity of the decoherence function and von Neumann entropy of the system. Using such emulated non-Markovian environments, we experimentally study the efficiency of the Carr-Purcell-Meiboom-Gill dynamical decoupling (DD) sequence to inhibit the loss of coherence. Using the filter function formalism, we design optimized DD sequences that maximize coherence protection for non-Markovian environments and study their efficiencies experimentally. Finally, we discuss DD-assisted tuning of the effective non-Markovianity.

Composing decoherence functionals

Quantum Measure Theory (QMT) is a generalization of quantum theory where physical predictions are computed from a matrix known as \emph{decoherence functional} (DF). Previous works have noted that, in its original formulation, QMT exhibits a problem with composability, since the composition of two decoherence functionals is, in general, not a valid decoherence functional. This does not occur when the DFs in question happen to be positive semidefinite (a condition known as strong positivity). In this paper, we study the concept of composability of DFs and its consequences for QMT. Firstly, we show that the problem of composability is much deeper than originally envisaged, since, for any $n$, there exists a DF that can co-exist with $n-1$ copies of itself, but not with $n$. Secondly, we prove that the set of strongly positive DFs cannot be enlarged while remaining closed under composition. Furthermore, any closed set of DFs containing all quantum DFs can only contain strongly positive DFs.

Decoherence and Loschmidt echo for qubit induced by a reservoir of coupled bosons

We study decoherence of a qubit coupling to the degenerate coupled bosons reservoir (DCBR) and the Loschmidt echo of DCBR. In the weak coupling of the qubit to the reservoir, the decoherence is significantly enhanced with increase of the coupling strength between modes, and the envelope of the decoherence function shows non-Gaussian decay (power-law). But under strong coupling conditions, the decoherence is slightly increased with increase of the coupling strength between modes, and the envelope of the decoherence function shows Gaussian decay for small coupling strength between modes. With increase of the coupling strength between modes, the envelope of the decoherence function shows irregular decay. For quite a long fixed time, change of the Loschmidt echo of DCBR with the mode coupling parameter shows stable multi- peak structure. This indicates that the decoherence will be strengthened for some value of coupling strength between modes.

Entanglement and non-Markovianity of a spin-S system in a dephasing environment

We study the entanglement (measured by negativity) evolution and the non-Markovianity for the dynamical process of a spin-S system embedded in dephasing environments. The exact analytical solution is presented, which shows that the decoherence function governs the evolutions of coherence, entanglement, and the non-Markovianity of the corresponding dynamical processes. For Ohmic and sub-Ohmic reservoirs, the negativity decreases monotonically in time and the corresponding dynamics is Markovian. While for super-Ohmic reservoirs with non-monotonic decoherence function, the negativity appears as the phenomenon of revival and the corresponding dynamics is non-Markovian. The relation between non-Markovianity and the system dimension is studied.

Quantum irreversible decoherence behaviour in open quantum systems with few degrees of freedom: Application to 1H NMR reversion experiments in nematic liquid crystals

An experimental study of NMR spin decoherence in nematic liquid crystals is presented. Decoherence dynamics can be put in evidence by means of refocusing experiments of the dipolar interactions. The experimental technique used in this work is based on the MREV8 pulse sequence. The aim of the work is to detect the main features of the irreversible quantum decoherence in liquid crystals, on the basis of the theory presented by the authors recently. The focus is laid on experimentally probing the eigen-selection process in the intermediate time scale, between quantum interference of a closed system and thermalization, as a signature of the quantum spin decoherence of the open quantum system, as well as on quantifying the effects of non-idealities as possible sources of signal decays which could mask the intrinsic decoherence. In order to contrast experiment and theory, the theory was adapted to obtain the decoherence function corresponding to the MREV8 reversion experiments. Non-idealities of the experimental setting, like external field inhomogeneity, pulse misadjustments, and the presence of non-reverted spin interaction terms are analysed in detail within this framework, and their effects on the observed signal decay are numerically estimated. It is found that though all these non-idealities could in principle affect the evolution of the spin dynamics, their influence can be mitigated and they do not present the characteristic behaviour of the irreversible spin decoherence. As unique characteristic of decoherence, the experimental results clearly show the occurrence of eigen-selectivity in the intermediate timescale, in complete agreement with the theoretical predictions. We conclude that the eigen-selection effect is the fingerprint of decoherence associated with a quantum open spin system in liquid crystals. Besides, these features of the results account for the quasi-equilibrium states of the spin system, which were observed previously in these mesophases, and lead to conclude that the quasi-equilibrium is a definite stage of the spin dynamics during its evolution towards equilibrium.