We discuss fluctuations in the measurement process and how these fluctuations are related to the dissipational parameter characterising quantum damping or decoherence. On the example of the measuring current of the variable-barrier or QPC problem we show there is an extra noise or fluctuation connected with the possible different outcomes of a measurement. This noise has an enhanced short time component which could be interpreted as due to ``telegraph noise'' or ``wavefunction collapses''. Furthermore the parameter giving the the strength of this noise is related to the parameter giving the rate of damping or decoherence.
We consider one source of decoherence for a single trapped ion due to intensity and phase fluctuations in the exciting laser pulses. For simplicity we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. This master equation is averaged over the noise, and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. Our results are in good qualitative agreement with r…
We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of the interference pattern. One might naively expect that a particle ensemble suffers a greater loss of quantum coherence by interacting with an increasingly randomized distribution of shifts. As we shall see, this is not always true.
We analyze the coherence properties of neutron wave packets, after they have interacted with a phase shifter undergoing different kinds of statistical fluctuations. We give a quantitative (and operational) definition of decoherence and compare it to the standard deviation of the distribution of the phase shifts. We find that in some cases the neutron ensemble is more coherent, even though it has interacted with a wider (i.e. more disordered) distribution of shifts. This feature is independent of the particular definition of decoherence: this is shown by proposing and discussing an alternative …
A general expression is derived for the momentum diffusion constant of a small polarizable particle in blackbody radiation, and is shown to be closely related to the long-wavelength collisional decoherence rate for such a particle in a thermal environment. We show how this diffusion constant appears in the steady-state photon emission rate of two dipoles induced by blackbody radiation. We consider in addition the Einstein--Hopf drag force on a small polarizable particle moving in a blackbody field, and derive its fully relativistic form from the Lorentz transformation of forces.
It is shown that the noise process in quantum computation can be described by spatially correlated decoherence and dissipation. We demonstrate that the conventional quantum error correcting codes correcting for single-qubit errors are applicable for reducing spatially correlated noise.
In this paper we investigate the short-time decoherence from Ohmic and 1/f noise of single Josephson charge qubit (JCQ). At first, we use the short-time approximation to obtain the dynamics of the open JCQ. Then we calculate the decoherence the measure of which is chosen as the maximum norm of the deviation density operator. It is shown that the decoherence from 1/f noise plays the central role. The total decoherence from Ohmic and 1/f noise is serious at present experiential conditions according to the DiVincenzo criterion.
Quantum decoherence arises due to uncontrollable entanglement between a system with its environment. However the effects of decoherence are often thought of and modeled through a simpler picture in which the role of the environment is to introduce classical noise in the system's degrees of freedom. Here we establish necessary conditions that the classical noise models need to satisfy to quantitatively model the decoherence. Specifically, for pure-dephasing processes we identify well-defined statistical properties for the noise that are determined by the quantum many-point time correlation func…
The interaction between particles and the electromagnetic field induces decoherence generating a small suppression of fringes in an interference experiment. We show that if a double slit--like experiment is performed in the vicinity of a conducting plane, the fringe visibility depends on the position (and orientation) of the experiment relative to the conductor's plane. This phenomenon is due to the change in the structure of vacuum induced by the conductor and is closely related to the Casimir effect. We estimate the fringe visibility both for charged and for neutral particles with a permanen…
In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations.
We study non-perturbatively the time evolution of a qubit subject to amplitude-damping noise. We show that at strong coupling the qubit decoherence can be quenched owing to large environment feedbacks, such that the qubit can evolve coherently even in the long-time limit. As an application, we show that for a quantum channel that consists of two independent qubits subject to uncorrelated local amplitude-damping noises, it can maintain at strong coupling finite entanglement and better than classical teleportation fidelity at long times.
We discuss decoherence due to electromagnetic fluctuations in charge qubits formed by two lateral quantum dots. We use an effective circuit model to evaluate correlations of voltage fluctuations in the qubit setup. These correlations allows us to estimate energy (T1) and phase (T2) relaxation times of the the qubit system. Our theoretical estimate of the quality factor due to dephasing by electromagnetic fluctuations yields values much higher than those found in recent experiments, indicating that other sources of decoherence play a dominant role.
The elimination of decoherence of a multiphoton two-state quantum system by using an appropriate external driving field is considered. The multiphoton process caused by the noise field has a supersymmetric Lie algebraic structure. The time-evolution equations for the off-diagonal elements of the density operator of the two-state system are derived in the interaction picture. A simple explicit formula is given for the time-dependent external driving field used to eliminate the decoherence of the multiphoton two-state system.
In this paper, we investigate the exact decoherence dynamics of a superconducting resonator coupled to an electromagnetic reservoir characterized by the $1/f$ noise at finite temperature, where a full quantum description of the environment with $1/f^{x}$ noise (with $x \approx 1$) is presented. The exact master equation and the associated non-equilibrium Green's functions are solved exactly for such an open system. We show a clear signal of non-Markovian dynamics induced purely by $1/f$ noise. Our analysis is also applicable to another nano/micro mechanical oscillators. Finally, we demonstrate…
The radiation pressure coupling with vacuum fluctuations gives rise to energy damping and decoherence of an oscillating particle. Both effects result from the emission of pairs of photons, a quantum effect related to the fluctuations of the Casimir force. We discuss different alternative methods for the computation of the decoherence time scale. We take the example of a spherical perfectly-reflecting particle, and consider the zero and high temperature limits. We also present short general reviews on decoherence and dynamical Casimir effect.
In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. The transition from quantum to classical behaviour of the considered system is analyzed and it is shown that the classicality takes place during a finite interval of time. We calculate also the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations.
In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. The transition from quantum to classical behaviour of the considered system is analyzed and it is shown that the classicality takes place during a finite interval of time. We calculate also the decoherence time and show that it has the same scale as the time after which statistical fluctuations become comparable with quantum fluctuations.
We relate disentanglement and decoherence rates in a pair of three-level atoms subjected to multi-local and collective pure dephasing noise acting in a preferred basis. The bipartite entanglement decay rate, as bounded from above by the negativity, is found to be greater than or equal to the dephasing-decoherence rates characterized by the decay of off-diagonal elements in the corresponding full density matrix describing the system or the reduced density matrix describing either qutrit, extending previous results for qubit pairs subject to such noise.
Quantum error correction is a solution to preserve the fidelity of quantum information encoded in physical systems subject to noise. However, unfavorable correlated errors could be induced even for non-interacting qubits through the environment (bath), when they are "packed" together. The question is, to what extent can we treat the noise induced by the bath as independent? In the context of the spin-boson model, we show that, under some reasonable constraints, the independent noise approximation could be valid. On the other hand, in the strongly correlated limit, we show how the method of dec…
A relationship between the time scales of quantum coherence loss and short-time solvent response for a solute/bath system is derived for a Gaussian wave packet approximation for the bath. Decoherence and solvent response times are shown to be directly proportional to each other, with the proportionality coefficient given by the ratio of the thermal energy fluctuations to the fluctuations in the system-bath coupling. The relationship allows the prediction of decoherence times for condensed phase chemical systems from well developed experimental methods.
Noise and decoherence are two major obstacles to the implementation of large-scale quantum computing. Because of the no-cloning theorem, which says we cannot make an exact copy of an arbitrary quantum state, simple redundancy will not work in a quantum context, and unwanted interactions with the environment can destroy coherence and thus the quantum nature of the computation. Because of the parallel and distributed nature of classical neural networks, they have long been successfully used to deal with incomplete or damaged data. In this work, we show that our model of a quantum neural network …
We examine a stochastic noise process that has a decohering effect on the average evolution of qubits in the quantum register of the solid state quantum computer proposed by Kane. We consider the effects of this process on the single qubit operations necessary to perform quantum logical gates and derive an expression for the fidelity of these gates in this system. We then calculate an upper bound on the level of this stochastic noise tolerable in a workable quantum computer.
The use of distributed amplifiers may have some potential advantages for the transmission of quantum information through optical fibers. In addition to the quantum noise introduced by the amplifiers, entanglement between atoms in the amplifying media and the optical field corresponds to which-path information that can further reduce the coherence. Here we analyze the effects of decoherence in a phase-insensitive distributed amplifier by using perturbation theory to calculate the state of the entire system including the atomic media. For an initial coherent state, tracing over the atomic states…
We consider the description of quantum noise within the framework of the standard Copenhagen interpretation of quantum mechanics applied to a composite system environment setting. Averaging over the environmental degrees of freedom leads to a stochastic quantum dynamics, described by equations complying with the constraints arising from the statistical structure of quantum mechanics. Simple examples are considered in the framework of open system dynamics described within a master equation approach, pointing in particular to the appearance of the phenomenon of decoherence and to the relevance o…
We propose and study a realistic model for the decoherence of topological qubits, based on Majorana fermions in one-dimensional topological superconductors. The source of decoherence is the fluctuating charge on a capacitively coupled gate, modeled by non-interacting electrons. In this context, we clarify the role of quantum fluctuations and thermal fluctuations and find that quantum fluctuations do not lead to decoherence, while thermal fluctuations do. We explicitly calculate decay times due to thermal noise and give conditions for the gap size in the topological superconductor and the gate …
We calculate the two-qubit disentanglement due to classical random telegraph noise using the quasi-Hamiltonian method. This allows us to obtain analytical results even for strong coupling and mixed noise, important when the qubits have tunable working point. We determine when entanglement sudden death and revival occur as functions of qubit working point, noise coupling strength and initial state entanglement. For extended Werner states, we show that the concurrence is related to the difference of two functions: one is related to dephasing and the other longitudinal relaxation. A physical inte…
In previous work, we have proposed an entanglement indicator for a general multiqubit state, which can be "learned" by a quantum system, acting as a neural network. The indicator can be used for a pure or a mixed state, and it need not be "close" to any particular state; moreover, as the size of the system grows, the amount of additional training necessary diminishes. Here, we show that the indicator is stable to noise and decoherence.
We investigate the meaning of gravity-induced decoherence in quantum theory, known as `intrinsic' or `fundamental' decoherence in the literature. We explore a range of issues relevant to this problem, including the meaning of modified uncertainty relations, the interpretations of the Planck scale, the distinction between quantum and stochastic fluctuations and the role of the time variable in quantum mechanics. We examine the specific physical assumptions that enter into different approaches to the subject. In particular, we critique two representative approaches that identify time fluctuation…
Momentum Diffusion, Decoherence and Drag Force on a Magnetic Nanoparticle
Van Swinderen Institute for Particle Physics and Gravity, University of Groningen（格罗宁根大学范斯温德伦粒子物理与引力研究所）；Departemen Fisika, FMIPA, Universitas Indonesia（印度尼西亚大学理学院物理系）
We consider two different kinds of fluctuations in an ion trap potential: external fluctuating electrical fields, which cause statistical movement (``wobbling'') of the ion relative to the center of the trap, and fluctuations of the spring constant, which are due to fluctuations of the ac-component of the potential applied in the Paul trap for ions. We write down master equations for both cases and, averaging out the noise, obtain expressions for the heating of the ion. We compare our results to previous results for far-off resonance optical traps and heating in ion traps. The effect of fluctu…
We show a completely analytical approach to the decoherence induced by a zero temperature environment on a Brownian test particle. We consider an Omhic environment bilinearly coupled to an oscillator and compute the master equation. From diffusive coefficients, we evaluate the decoherence time for the usual quantum Brownian motion and also for an upside-down oscillator, as a toy model of a quantum phase transition.
Electromagnetic field fluctuations are responsible for the destruction of electron coherence (dephasing) in solids and in vacuum electron beam interference. The vacuum fluctuations are modified by conductors and dielectrics, as in the Casimir effect, and hence, bodies in the vicinity of the beams can influence the beam coherence. We calculate the quenching of interference of two beams moving in vacuum parallel to a thick plate with permittivity $ε(ω)=ε_{0}+i 4πσ/ω$. In case of an ideal conductor or dielectric $(|ε|=\infty)$ the dephasing is suppressed when the beams are close to the surface of…
Common philosophy in control theory is the control of disorder by order. It is not exceptional for strategies suppressing quantum decoherence. Here we predict an anomalous quantum phenomenon. Suppression of decoherence can be made via more disordered white noise field, in particular white Poissonian noise. The phenomenon seems to be another anomaly in quantum mechanics, and may offer a new strategy in quantum control practices.
We study the three-player Prisoner's Dilemma game under the effect of decoherence and correlated noise. It is seen that the quantum player is always better off over the classical players. It is also seen that the game's Nash equilibrium does not change in the presence of correlated noise in contradiction to the effect of decoherence in multiplayer case. Furthermore, it is shown that for maximum correlation the game does not behave as a noiseless game and the quantum player is still better off for all values of the decoherence parameter p which is not possible in the two-player case. In additio…
We develop dynamical non-Markovian description of quantum computing in weak coupling limit, in lowest order approximation. We show that long range memory of quantum reservoir produces strong interrelation between structure of noise and quantum algorithm, implying nonlocal attacks of noise. We then argue that the quantum error correction method fails to protect quantum computation against electromagnetic or phonon vacuum which exhibit $1/t^4$ memory. This shows that the implicit assumption of quantum error correction theory -- independence of noise and self-dynamics -- fails in long time regime…
The external control circuits of quantum gates inevitably introduce a small but finite noise to the operation of quantum computers. The complex modes of decoherence introduced by this noise are not covered by the common error models. Using the controlled-phase gate as an example, the effect of gate control noise on decoherence is investigated for different quantum computer architectures. It is shown that the decoherence rate rises faster than linearly with the length of a quantum register for most cases considered, adding to the challenge of implementing proposed error correcting and fault tol…
Liquid-state NMR quantum computer has demonstrated the possibility of quantum computation and supported its development. Using NMR quantum computer techniques, we observed phase decoherence under two kinds of artificial noise fields; one a noise with a long period, and the other with shorter random period. The first one models decoherence in a quantum channel while the second one models transverse relaxation. We demonstrated that the bang-bang control suppresses decoherence in both cases.
In this article, we study the dynamics of quantum correlation measures such as entanglement and measurement-induced nonlocality (MIN). Starting from an arbitrary Bell diagonal mixed states under Markovian local noise such as bit-phase flip, depolarizing and generalized amplitude damping channel, we provide the decays of the entanglement measured by concurrence and quantum correlation captured by different forms of MIN (trace distance, Hilbert-Schmidt norm and relative entropy) as a function of the decoherence parameters. The effect of local noises on the dynamical behaviors of quantum correlat…
Decoherence phenomenon has been widely studied in different types of quantum walks. In this work we show how to model decoherence inspired by percolation on staggered quantum walks. Two models of unitary noise are described: breaking polygons and breaking vertices. The evolution operators subject to these noises are obtained and the equivalence to the coined quantum walk model is presented. Further, we numerically analyze the effect of these decoherence models on the two-dimensional grid of $4$-cliques. We examine how these perturbations affect the quantum walk based search algorithm in this g…
Decoherence-free states protect quantum information from collective noise, the predominant cause of decoherence in current implementations of quantum communication and computation. Here we demonstrate that spontaneous parametric down-conversion can be used to generate four-photon states which enable the encoding of one qubit in a decoherence-free subspace. The immunity against noise is verified by quantum state tomography of the encoded qubit. We show that particular states of the encoded qubit can be distinguished by local measurements on the four photons only.
In quantum key distribution, one conservatively assumes that the eavesdropper Eve is restricted only by physical laws, whereas the legitimate parties, namely the sender Alice and receiver Bob, are subject to realistic constraints, such as noise due to environment-induced decoherence. In practice, Eve too may be bound by the limits imposed by noise, which can give rise to the possibility that decoherence works to the advantage of the legitimate parties. A particular scenario of this type is one where Eve can't replace the noisy communication channel with an ideal one, but her eavesdropping chan…
We consider the case when decoherence is due to the fluctuations of some classical variable or parameter of a system and not to its entanglement with the environment. Under few and quite general assumptions, we derive a model-independent formalism for this non-dissipative decoherence, and we apply it to explain the decoherence observed in some recent experiments in cavity QED and on trapped ions.
One of the biggest problems faced by those attempting to combine quantum theory and general relativity is the experimental inaccessibility of the unification scale. In this paper we show how incoherent conformal waves in the gravitational field, which may be produced by quantum mechanical zero-point fluctuations, interact with the wavepackets of massive particles. The result of this interaction is to produce decoherence within the wavepackets which could be accessible in experiments at the atomic scale. Using a simple model for the coherence properties of the gravitational field we derive an e…
The central issue in this article is to transmit a quantum state in such a way that after some decoherence occurs, most of the information can be restored by a suitable decoding operation. For this purpose, we incorporate redundancy by mapping a given initial quantum state to a messenger state on a larger-dimensional Hilbert space via a $C^*$-algebra embedding. Our noise model for the transmission is a phase damping channel which admits a noiseless or decoherence-free subspace or subsystem. More precisely, the transmission channel is obtained from convex combinations of a set of lowest rank ye…
The ultimate stability of atomic clocks is limited by the quantum noise of the atoms. To reduce this noise it has been suggested to use entangled atomic ensembles with reduced atomic noise. Potentially this can push the stability all the way to the limit allowed by the Heisenberg uncertainty relation, which is denoted the Heisenberg limit. In practice, however, entangled states are often more prone to decoherence, which may prevent reaching this performance. Here we present an adaptive measurement protocol that in the presence of a realistic source of decoherence enables us to get near Heisenb…
For many implementations of quantum computing, 1/f and other types of broad-spectrum noise are an important source of decoherence. An important step forward would be the ability to back out the characteristics of this noise from qubit measurements and to see if it leads to new physical effects. For certain types of qubits, the working point of the qubit can be varied. Using a new mathematical method that is suited to treat all working points, we present theoretical results that show how this degree of freedom can be used to extract noise parameters and to predict a new effect: noise-induced lo…
We study three methods of obtaining an approximation of unitary evolution of a quantum system under decoherence. We use three methods of optimizing the control pulses: genetic optimization, approximate evolution method and approximate gradient method. To model the noise in the system we use the Lindblad equaiton. We obtain results showing that genetic optimization may give a better approximation of a unitary evolution in the case of high noise.
We discuss recent experimental evidence of decoherence in a laboratory mesoscopic system in a cavity, from which we draw analogies with the decoherence that we argue is induced by microscopic quantum-gravity fluctuations in the space-time background. We emphasize the parallel rôles played in both cases by dissipation through non-trivial vacuum fluctuations that trigger the collapse of an initially coherent quantum state. We review a phenomenological parametrization of possible effects of this kind in the neutral kaon system, where they would induce CPT violation, and describe some epxerimental…
We study the decoherence effect of charge noise on a single flip-flop qubit and two dipole-coupled qubits. We find that a single flip-flop qubit is highly resistant to charge noise at its sweet spots. However, due to the proximity of the charge excited states to the flip-flop logical states, the presence of charge noise greatly reduces the fidelity of two-qubit operations. We identify leakage from the qubit Hilbert space as the main culprit for the reduced gate fidelity. We also explore different bias conditions to mitigate this decoherence channel.
Quantum correlations typically decrease with increasing noise, although classical correlators (CCors) may rise for a particular class of states with noise. To analyse the behavior of classical correlation (CC) in the presence of local noise, we scrutinize the set of classical correlators, axiomatic CC measures like classical discord, and local work for Haar uniformly generated states. Like quantum correlation measures, we illustrate that when noise levels rise, the average value of the CC measures for noisy output states obtained from random input states decreases for most of the channels. We …
The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The standard coherent Gaussian model is compared with an alternative photon gas model which represents lack of a shared phase reference between transmitter and receiver. At any frequency, information rates over the photon gas model essentially coincide with those over the Gaussian model when the signal-to-noise ratio is below a threshold. Only above the threshold does decoherence cause a loss in information rates; the loss can amount to half of the capacity. The thr…
