Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics are handled through master equations for the density matrix. By embedding elements of this matrix in a higher-dimensional Liouville-Bloch equation, the methods of unitary integration are adapted to solve for the density matrix as a function of time, including the non-unitary effects of dissipation and decoherence. The input requires only solutions of classical, initial value time-dependent equations. Results are illustrated for a damped driven two-level system.
The prototypical Schrödinger cat state, i.e., an initial state corresponding to two widely separated Gaussian wave packets, is considered. The decoherence time is calculated solely within the framework of elementary quantum mechanics and equilibrium statistical mechanics. This is at variance with common lore that irreversible coupling to a dissipative environment is the mechanism of decoherence. Here, we show that, on the contrary, decoherence can in fact occur at high temperature even for vanishingly small dissipation.
We propose a new approach to the implementation of quantum gates in which decoherence during the gate operations is strongly reduced. This is achieved by making use of an environment induced quantum Zeno effect that confines the dynamics effectively to a decoherence-free subspace.
We implement the normal ordering technique to study the quantum dissipation of a single mode harmonic oscillator system. The dynamic evolution of the system is investigated for a reasonable initial state by solving the Schrödinger equation directly through the normal ordering technique. The decoherence process of the system for the cases $T=0K$ and $T\neq0K$ is investigated as an application.
Decoherence is well understood, in contrast to disentanglement. According to common lore, irreversible coupling to a dissipative environment is the mechanism for loss of entanglement. Here, we show that, on the contrary, disentanglement can in fact occur at large enough temperatures $T$ even for vanishingly small dissipation (as we have shown previously for decoherence). However, whereas the effect of $T$ on decoherence increases exponentially with time, the effect of $T$ on disentanglement is constant for all times, reflecting a fundamental difference between the two phenomena. Also, the poss…
The longitudinal coupling of a system to the bath usually induces the pure dephasing of the system. In this paper, we study the collective dephasing induced dissipation and decoherence in a coupled-qubit system with a common bath. It is shown that, compared with the case of the same system with independent baths, the interference between the dephasing processes of different qubits induced by the common bath significantly changes the dissipation of the system. For the system of two coupled qubits, the interference leads to a faster decoherence in the non-single-excitation subspaces and a slower…
Decoherence is a fundamental obstacle to the implementation of large-scale and low-noise quantum information processing devices. In this work, we suggest an approach for suppressing errors by employing pre-processing and post-processing unitary operations, which precede and follow the action of a decoherence channel. In contrast to quantum error correction and measurement-based methods, the suggested approach relies on specifically designed unitary operators for a particular state without the need in ancillary qubits or post-selection procedures. We consider the case of decoherence channels ac…
In a recent article, Ford, Lewis and O'Connell (PRA 64, 032101 (2001)) discuss a thought experiment in which a Brownian particle is subjected to a double-slit measurement. Analyzing the decay of the emerging interference pattern, they derive a decoherence rate that is much faster than previous results and even persists in the limit of vanishing dissipation. This result is based on the definition of a certain attenuation factor, which they analyze for short times. In this note, we point out that this attenuation factor captures the physics of decoherence only for times larger than a certain tim…
We study the behavior of Quantum Darwinism (Zurek, [8]) within the iterative, random unitary operations qubit-model of pure decoherence (Novotny et al, [6]). We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system S from the point of view of its environment E, is not a generic phenomenon, but depends on the specific form of input states and on the type of S-E-interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial input states of environment…
We study the effects of dissipation and decoherence induced on a harmonic oscillator by the coupling to a chaotic system with two degrees of freedom. Using the Feynman-Vernon approach and treating the chaotic system semiclassically we show that the effects of the low dimensional chaotic environment are in many ways similar to those produced by thermal baths. The classical correlation and response functions play important roles in both classical and quantum formulations. Our results are qualitatively similar to the high temperature regime of the Caldeira-Leggett model.
We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four "canonical" system-environment models for decoherence and dissipation. To investigate the influence of further couplings of the environmental spins to a dissipative bath, we also derive the master equation for a harmonic oscillator interacting with a single spin coupled to a bosonic bath. Our models are experimentally motivated by quantum-electromechanical systems an…
A model for a quantum register $\cal R$ made of $N$ replicas of a $d$-dimensional quantum system (cell) coupled with the environment, is studied by means of a Born-Markov Master Equation (ME). Dissipation and decoherence are discussed in various cases in which a sub-decoherent enconding can be rigorously found. For the qubit case ($d=2$) we have solved, for small $N,$ the ME by numerical direct integration and studied, as a function of the coherence length $ξ_c$ of the bath, fidelity and decoherence rates of states of the register. For large enough $ξ_c$ the singlet states of the global $su(2)…
It is commonly stated that decoherence in open quantum systems is due to growing entanglement with an environment. In practice, however, surprisingly often decoherence may equally well be described by random unitary dynamics without invoking a quantum environment at all. For a single qubit, for instance, pure decoherence (or phase damping) is always of random unitary type. Here, we construct a simple example of true quantum decoherence of two qubits: we present a feasible phase damping channel of which we show that it cannot be understood in terms of random unitary dynamics. We give a very int…
We consider N identical oscillators coupled to a single environment and show that the conditions for the existence of decoherence free subspaces are degeneracy of the oscillator frequencies and separability of the coupling with the environment. A formal exact equation for the evolution in the case of two oscillators is found and the decoherence free subspace is explicitly determined. A full analytical solution for any initial condition and general parameters (frequencies and dissipation constants) is given in the markovian approximation and zero temperature. We find that slight relaxation of d…
Distribution functions defined in accord with the quantum theory of measurement are combined with results obtained from the quantum Langevin equation to discuss decoherence in quantum Brownian motion. Closed form expressions for wave packet spreading and the attenuation of coherence of a pair of wave packets are obtained. The results are exact within the context of linear passive dissipation. It is shown that, contrary to widely accepted current belief, decoherence can occur at high temperature in the absence of dissipation. Expressions for the decoherence time with and without dissipation are…
The problem of the quantitative degradation of the performance of a quantum computer due to noisy unitary gates (imperfect external control) is studied. It is shown that quite general conclusions on the evolution of the fidelity can be reached by using the conjecture that the set of states visited by a quantum algorithm can be replaced by the uniform (Haar) ensemble. These general results are tested numerically against quantum computer simulations of two particular periodically driven quantum systems.
The time development of the reduced density matrix for a quantum oscillator damped by coupling it to an ohmic environment is calculated via an identity of the Debye-Waller form. Results obtained some years ago by Hakim and the author in the free particle limit [1] are thus recovered. The evolution of a free particle in a prepared initial state is examined, and a previously published exchange [2,3] is illuminated with figures showing no decoherence without dissipation. [1] V. Hakim and V. Ambegaokar, Phys. Rev. A 32, 423 (1985). [2] G.W. Ford and R.F. O'Connell, Phys. Rev. A 70, 026102 (2004). …
Dissipative processes in physics are usually associated with non-unitary actions. However, the important resource of entanglement is not invariant under general unitary transformations, and is thus susceptible to unitary "dissipation". In this note we discuss both unitary and non-unitary dissipative processes, showing that the former is ultimately of value, since reversible, and enables the production of entanglement; while even in the presence of the latter, more conventional non-unitary and non-reversible, process there exist nonetheless invariant entangled states.
We investigate the time evolution of a superposition of macroscopically distinct quantum states in a system of two-level atoms interacting with a thermal environment of photon modes. We show that the atomic coherent states are robust against decoherence, therefore we call their superpositions atomic Schrödinger cat states. The initial fast regime of the time evolution is associated with the process of decoherence, and it is directed towards the statistical mixture of the constituent coherent states of the original state for most of the initial conditions. However, certain superpositions, calle…
Decoherence is the fundamental obstacle limiting the performance of quantum information processing devices. The problem of transmitting a quantum state (known or unknown) from one place to another is of great interest in this context. In this work, by following the recent theoretical proposal [Opt. Eng. {\bf 59}, 061625 (2020)] we study an application of quantum state-dependent pre- and post-processing unitary operations for protecting the given (multi-qubit) quantum state against the effect of decoherence acting on all qubits. We observe the increase in the fidelity of the output quantum stat…
A perturbative treatment of reduced density operators of quantum subsystems is implemented in the same spirit as Fermi Golden Rule for scattering. Analytic expressions for linear entropy (a measure of purity loss, and in some cases of coherence loss) and for subsystem's energy variations (dissipation) are given. Application to electromagnetic field superposition states in a dissipative cavity is performed. Evaluation of typical field and reservoir time scales ($τ_{F}$ and $τ_{R}$) show that even for small temperatures they are very different. We also indicate the condition on the cutoff temper…
We present and discuss a general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems, able to overcome the intrinsic limitations of the conventional Markov approximation. In particular, the proposed alternative adiabatic scheme does not threaten positivity at any time. The key idea of our approach rests in the temporal symmetrization and coarse graining of the scattering term in the Liouville-von Neumann equation, before applying the reduction procedure over the environment degrees of freedom. The resulting dynamics is genuinely Lindblad-like and …
Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here we propose some compact schemes to implement two- and three-qubit controlled unitary quantum gates and Fredkin gate. For the controlled unitary quantum gates, the unitary operator acting on the target qubit is an arbitrary single-qubit gate operation. The controlled quantum gates can be directly implemented using non-adiabatic holonomy in decoherence-free subspaces and the required resource for the d…
On this work, we consider a particle moving in front of a dielectric plate, and study two of the most relevant effects of the vacuum field fluctuations: the dissipation, and the decoherence of the particle's internal degrees of freedom. We consider the particle to follow a classical, macroscopically-fixed trajectory. To study the dissipative effects, we calculate the in-out effective action by functionally integrating over the vacuum field and the microscopic degrees of freedom of both the plate and the particle. This in-out effective action develops an imaginary part, hence a non-vanishing pr…
Controlling the decoherence induced by the interaction of quantum system with its environment is a fundamental challenge in quantum technology. Utilizing Floquet theory, we explore the constructive role of temporal periodic driving in suppressing decoherence of a spin-1/2 particle coupled to a spin bath. It is revealed that, accompanying the formation of a Floquet bound state in the quasienergy spectrum of the whole system including the system and its environment, the dissipation of the spin system can be inhibited and the system tends to coherently synchronize with the driving. It can be seen…
Repeated closed-loop control operations acting as piecewise-constant Liouville superoperators conditioned on the outcomes of regularly performed measurements may effectively be described by a fixed-point iteration for the density matrix. Even when all Liouville superoperators point to the completely mixed state, feedback of the measurement result may lead to a pure state, which can be interpreted as selective dampening of undesired states. Using a microscopic model, we exemplify this for a single qubit, which can be purified in an arbitrary single-qubit state by tuning the measurement directio…
Decoherence-free Behaviors of Quantum Emitters in Dissipative Photonic Graphene
School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology（华中科技大学物理科学与技术学院量子科学与工程研究院）；Wuhan institute of quantum technology（武汉量子技术研究院）；Quantum Computing Center, RIKEN（理研量子计算中心）；Department of Physics, The University of Michigan（密歇根大学物理系）
The propagation of polarized photons in optical media can be effectively modeled by means of quantum dynamical semigroups. These generalized time evolutions consistently describe phenomena leading to loss of phase coherence and dissipation originating from the interaction with a large, external environment. High sensitive experiments in the laboratory can provide stringent bounds on the fundamental energy scale that characterizes these non-standard effects.
Within the density matrix formalism, it is shown that a simple way to get decoherence is through the introduction of a "quantum" of time (chronon): which implies replacing the differential Liouville--von Neumann equation with a finite-difference version of it. In this way, one is given the possibility of using a rather simple quantum equation to describe the decoherence effects due to dissipation. Namely, the mere introduction (not of a "time-lattice", but simply) of a "chronon" allows us to go on from differential to finite-difference equations; and in particular to write down the quantum-the…
We studied the dispersive dissipation of denegerate-level atom interacting with a single linearly-polarized mode field. It is found that the degeneracy of the atomic level affects the dissipation bahavior of the system as well as the subsystems. The degeneracy of the atomic level augment the periods of entanglement and increase the degree of the maxima statistical mixture states.
The interaction of (two-level) Rydberg atoms with dissipative QED cavity fields can be described classically or quantum mechanically, even for very low temperatures and mean number of photons, provided the damping constant is large enough. We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, analog to the atom-cavity system, in which the atom (field) is represented by a (driven and damped) harmonic oscillator. The maximum value of entanglement is shown to depend on the initial state and the dissipation-rate to coupling-constant ratio.…
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.
That decoherence can take place in the presence of energy conservation seems to be a poorly known fact. That lack of knowledge has for example bedevilled the discussion of the "black hole information" problem. I present a simple model which illustrates such energy free decoherence.
The dynamics of coherent electron-phonon (el-ph) states is investigated for a suspended nanostructure. Exact quantum dynamics calculations reveal that electron and phonons (comprising a thermal bath) couple quantum mechanically to perform coherent oscillations with periods in the range of tens of nanoseconds, despite the finite temperature of the phonon bath. Mechanical energy dissipation due to clamping loss is taken into account in the calculations. Although the lifetime of the coupled el-ph states decreases with the temperature, well defined Rabi oscillations are obtained for temperatures u…
We investigate the influence of dissipation and decoherence on quantum Darwinism by generalizing Zurek's original qubit model of decoherence and the establishment of pointer states (Zurek, Nature Physics 5, 181 - 188 (2009)). Our model allows for repeated multiple qubit-qubit couplings between system and environment which are described by randomly applied two-qubit quantum operations inducing entanglement, dissipation and dephasing. The resulting stationary qubit states of system and environment are investigated. They exhibit the intricate influence of entanglement generation, dissipation and …
We develop in the weak coupling approximation a quasi-non-Markovian master equation and study the phenomenon of decoherence during the operation of a controlled-not (CNOT) quantum gate in a quantum computer model formed by a linear chain of three nuclear spins system with second neighbor Ising interaction between them. We compare with the behavior of the Markovian counterpart for temperature different from zero (thermalization) and at zero temperature for low and high dissipation rates. At low dissipation there is a very small difference between Markovian and quasi no-Markovian at any temperat…
Enviroment - caused dissipation disrupts the hamiltonian evolution of all quantum systems not fully isolated from any bath. We propose and examine a feedback-control scheme to eliminate such dissipation, by tracking the free hamiltonian evolution. We determine a driving-field that maximizes the projection of the actual molecular system onto the freely propagated one. The evolution of a model two level system in a dephasing bath is followed, and the driving field that overcomes the decoherence is calculated. An implementation of the scheme in the laboratory using feedback control is suggested.
We analyse dissipation in quantum computation and its destructive impact on efficiency of quantum algorithms. Using a general model of decoherence, we study the time evolution of a quantum register of arbitrary length coupled with an environment of arbitrary coherence length. We discuss relations between decoherence and computational complexity and show that the quantum factorization algorithm must be modified in order to be regarded as efficient and realistic.
The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, led rapidly to several new quantum algorithms. These all follow unitary quantum evolution, apart from the final measurement. Since logical qubits in a quantum computer must be protected from decoherence by error correction, there is no need to consider decoherence at the level of algorithms. Nonetheless, enlarging the range of quantum dynamics to include non-unitary evolution provides a wider range of possibilities for tuning the properties of quantum walks. For example, small …
These lecture notes address an audience of physicists or mathematicians who have been exposed to a first course in quantum mechanics. We start with a brief discussion of the general "system-bath" paradigm of quantum dissipative systems, analyze in some detail the simplest example of "pure dephasing" of a two-level system, and review the basic concept of the density matrix. We then treat the general dissipative time-evolution, introducing completely positive maps, their relation to entanglement theory, and their Kraus decomposition. Restricting ourselves to Markovian evolution, we discuss the L…
Decoherence can be provided by a dissipative environment as described by the Caldeira-Leggett equation. This equation is foundational to the theory of quantum dissipation. However, no experimental test has been performed that measures for one physical system both the dissipation and the decoherence. Anglin and Zurek predicted that a resistive surface could provide such a dissipative environment for a free electron wave passing close to it. We propose that the electron wave's coherence and energy loss can be measured simultaneously by using Kapitza-Dirac scattering for varying light intensity.
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to the isochronous Galilei group. Mappings describing state transformations both as a consequence of measurement and of dynamical evolution for a closed or open system are considered with respect to the general constraints they have to obey and their covariance properties with respect to symmetry groups. In particular different master equations are analyzed in …
We provide a class of quantum evolution beyond Markovian semigroup. This class is governed by a hybrid Davies like generator such that dissipation is controlled by a suitable memory kernel and decoherence by standard GKLS generator. These two processes commute and both of them commute with the unitary evolution controlled by the systems Hamiltonian. The corresponding memory kernel gives rise to semi-Markov evolution of the diagonal elements of the density matrix. However, the corresponding evolution needs not be completely positive. The role of decoherence generator is to restore complete posi…
We study the behavior of an open quantum system, with an $N$--dimensional space of states, whose density matrix evolves according to a non--unitary map defined in two steps: A unitary step, where the system evolves with an evolution operator obtained by quantizing a classically chaotic map (baker's and Harper's map are the two examples we consider). A non--unitary step where the evolution operator for the density matrix mimics the effect of diffusion in the semiclassical (large $N$) limit. The process of decoherence and the transition from quantum to classical behavior are analyzed in detail b…
Energy dissipation and decoherence are at first glance harmful to acquiring long exciton lifetime desired for efficient photovoltaics. In the presence of both optically forbidden (namely, dark) and allowed (bright) excitons, however, they can be instrumental as suggested in photosynthesis. By simulating quantum dynamics of exciton relaxations, we show that the optimized decoherence that imposes a quantum-to-classical crossover with the dissipation realizes a dramatically longer lifetime. In an example of carbon nanotube, the exciton lifetime increases by nearly two orders of magnitude when the…
It is shown that Non-unitary Newtonian Gravity (NNG) model admits a simple interpretation in terms of Feynman path integral, in which the sum over all possible histories is replaced by a summation over pairs of paths. Correlations between different paths are allowed by a fundamental decoherence mechanism of gravitational origin and can be interpreted as a kind of communication between different branches of the wave function. The ensuing formulation could be used in turn as a motivation to introduce Non-unitary Gravity itself.
The principal obstacle to quantum information processing with many qubits is decoherence. One source of decoherence is spontaneous emission which causes loss of energy and information. Inability to control system parameters with high precision is another possible source of error. As a solution we propose quantum computing experiments using dissipation based on an environment-induced quantum Zeno effect. As an example we present a simple scheme for quantum gate implementations with cold trapped ions in the presence of cooling.
Entanglement between a quantum system and its environment leads to loss of coherence in the former. In general, the temporal fate of coherences is complicated. Here, we establish the connection between decoherence of a central system and fidelity decay in the environment for a variety of situations, including both, energy conserving and dissipative couplings. We show how properties of unitary time evolution of the environment can be inferred from the non-unitary evolution of coherences in the central system. This opens up promising ways for measuring Loschmidt echoes in a variety of situations…
We first present a summary of recent results concerning the phononic energy transport properties of mesoscopic, suspended dielectric wires. We then discuss some related open problems concerning the fundamental lower limits on the vibrational damping rates of submicron-sized cantilever structures and also the possibility to create and detect quantum superpositions of spatially separated states for such structures.
In the framework of an interference setup in which only two outcomes are possible (such as in the case of a Mach-Zehnder interferometer), we discuss in a simple and pedagogical way the difference between a standard, unitary quantum mechanical evolution and the existence of a real collapse of the wave function. Moreover, we also present the Elitzur-Vaidman bomb, the delayed choice experiment, and the effect of decoherence. In the end, we propose two simple experiments to visualize decoherence and to test the role of an entagled particle.
We study the physical implementation of the Photon Carnot engine (PCE) based on the cavity QED system [M. Scully et al, Science, \textbf{299}, 862 (2003)]. Here, we analyze two decoherence mechanisms for the more practical systems of PCE, the dissipation of photon field and the pure dephasing of the input atoms. As a result we find that (I) the PCE can work well to some extent even in the existence of the cavity loss (photon dissipation); and (II) the short-time atomic dephasing, which can destroy the PCE, is a fatal problem to be overcome.
Practical implementations of quantum technology are limited by unavoidable effects of decoherence and dissipation. With achieved experimental control for individual atoms and photons, more complex platforms composed by several units can be assembled enabling distinctive forms of dissipation and decoherence, in independent heat baths or collectively into a common bath, with dramatic consequences for the preservation of quantum coherence. The cross-over between these two regimes has been widely attributed in the literature to the system units being farther apart than the bath's correlation lengt…
The main obstacle for coherent control of open quantum systems is decoherence due to different dissipation channels and the inability to precisely control experimental parameters. To overcome these problems we propose to use dissipation-assisted adiabatic passages. These are relatively fast processes where the presence of spontaneous decay rates corrects for errors due to non-adiabaticity while the system remains in a decoherence-free state and behaves as predicted for an adiabatic passage. As a concrete example we present a scheme to entangle atoms by moving them in and out of an optical cavi…
We construct generally applicable short-time perturbative expansions for some fidelities, such as the input-output fidelity, the entanglement fidelity, and the average fidelity. Successive terms of these expansions yield characteristic times for the damping of the fidelities involving successive powers of the Hamiltonian. The second-order results, which represent the damping rates of the fidelities, are extensively discussed. As an interesting application of these expansions, we use them to study the spatially-correlated dissipation of quantum bits. Spatial correlations in the dissipation are …
The realisation of quantum computers based on molecular electronic spins requires the design of qubits with very long coherence times, T2. Dephasing can proceed over several different microscopic pathways, active at the same time and in different regimes. This makes the rationalisation of the dephasing process not straightforward. Here we present a computational methodology able to address spin decoherence processes for a general ensemble of spins. The method consists in the propagation of the unitary quantum spin dynamics on a reduced Hilbert space. Then we study the dependence of spin dephas…
We study pure phase damping of two qubits due to fluctuating fields. As frequently employed, decoherence is thus described in terms of random unitary (RU) dynamics, i.e., a convex mixture of unitary transformations. Based on a separation of the dynamics into an average Hamiltonian and a noise channel, we are able to analytically determine the evolution of both entanglement and purity. This enables us to characterize the dynamics in a concurrence-purity (CP) diagram: we find that RU phase damping dynamics sets constraints on accessible regions in the CP plane. We show that initial state and dyn…
We study the statistics of quantum interference for completely positive maps. We calculate analytically the mean interference and its second moment for finite dimensional quantum systems interacting with a simple environment consisting of one or several spins (qudits). The joint propagation of the entire system is taken as unitary with an evolution operator drawn from the Circular Unitary Ensemble (CUE). We show that the mean interference decays with a power law as function of the dimension of the Hilbert space of the environment, with a power that depends on the temperature of the environment…
