Decoherence induced by coupling a system with an environment may display universal features. Here we demostrate that when the coupling to the system drives a quantum phase transition in the environment, the temporal decay of quantum coherences in the system is Gaussian with a width independent of the system-environment coupling strength. The existence of this effect opens the way for a new type of quantum simulation algorithm, where a single qubit is used to detect a quantum phase transition. We discuss possible implementations of such algorithm and we relate our results to available data on universal decoherence in NMR echo experiments.
A low temperature model system consisting of a central spin coupled to a spin-bath is studied to determine whether interaction among bath spins has an effect on central spin dynamics. In the absence of intra-environmental coupling, decoherence of the central spin is fast and irreversible. Strong intra-environmental interaction results in an effective decoupling of the central spin from the bath and suppression of decoherence. Weaker intra-environmental coupling reduces but does not eliminate decoherence. We believe that similar behaviour will be observed in any system with a self-interacting e…
In 1983, Wigner outlined a modified Schrödinger--von-Neumann equation of motion for macroobjects, to describe their typical coupling to the environment. This equation has become a principal model of environmental decoherence which is beleived responsible for the emergence ofclassicality in macroscopic quantum systems. Typically, this happens gradually and asymptotically after a certain characteristic decoherence time. For the Wigner-function, however, one can prove that it evolves perfectly into a classical (non-negative) phase space distribution after a finite time of decoherence.
The simple stationary decoherence of a two-state quantum system is discussed from a new viewpoint of environmental entanglement. My work emphasizes that an unconditional local state must totally be disentangled from the rest of the universe. It has been known for long that the loss of coherence within the given local system is gradual. Also the quantum correlations between the local system and the rest of the universe are being destroyed gradually. I show that, differently from local decoherence, the process of environmental disentanglement may terminate in finite time. The time of perfect dis…
In this contribution I give a brief introduction to the essential concepts and mechanisms of decoherence by the environment. The emphasis will be not so much on technical details but rather on conceptual issues and the impact on the interpretation problem of quantum theory.
We examine the effects of intra-environmental coupling on decoherence by constructing a low temperature spin--spin-bath model of an atomic impurity in a Debye crystal. The impurity interacts with phonons of the crystal through anti-ferromagnetic spin-spin interactions. The reduced density matrix of the central spin representing the impurity is calculated by dynamically integrating the full Schroedinger equation for the spin--spin-bath model for different thermally weighted eigenstates of the spin-bath. Exact numerical results show that increasing the intra-environmental coupling results in sup…
For the case of phase damping (pure decoherence) we investigate the extent to which environmental traits are imprinted on an open quantum system. The dynamics is described using the quantum channel approach. We study what the knowledge of the channel may reveal about the nature of its underlying dynamics and, conversely, what the dynamics tells us about how to consistently model the environment. We find that for a Markov phase-damping channel, that is, a channel compatible with a time-continuous Markovian evolution, the environment may adequately be represented by a mixture of only a few coher…
We review the difference between standard environmental decoherence and 'intrinsic decoherence', which is taken to be an ineluctable process of Nature. Environmental decoherence is typically modeled by spin bath or oscillator modes - we review some of the unanswered questions not captured by these models, and also the application of them to experiments. Finally, a sketch is given of a new theoretical approach to intrinsic decoherence, and this scheme is applied to the discussion of gravitational decoherence.
Using a microscopic master equation to account for the environmental effects, we compute the decoherence culminated during the propagation of a microwave pulse of arbitrary shape through a superconducting qubit. It is shown that the qubit decoherence vanishes and the pulse shape remains absorption-free when the latter adopts a soliton shape with $nπ$ area. Otherwise, the environmental feedback decelerates the velocity of the soliton envelop and induces an monotonic increase of phase in the microwave. A pulse of non-$nπ$ area thus ramifies into a transparent part that travels decoherence-free a…
We reformulate the quantum Monty Hall problem in the presence of decoherence. The decoherence destroys the fairness of the game. A new Nash equilibrium for a particular strategy profile in the presence of decoherence emerges. It is shown that in the presence of decoherence under the action of amplitude damping channel, Bob's winning probability is always higher than three-forth, irrespective of Alice's strategy, if he does not switch to the other door and always wins for a fully decohered case of the channel. Depolarizing channel damps up Bob's winning probability and gets better off if he sti…
The use of rotational degrees of freedom of quantum systems in quantum technologies is limited by environmental effects under decoherence mechanism. Here, we study the mechanism of decoherence based on a new formalism of elastic scattering for a nonspherical quantum system prepared in a superposition of rotational degrees of freedom. We show that for a dielectric ellipsoid immersed in an environment composed of thermal photons the rotational decoherence rate depends on the angular differences between the two configurations of the system and the seventh power of the temperature which is differe…
An unstable quantum state generally decays following an exponential law, as environmental decoherence is expected to prevent the decay products from recombining to reconstruct the initial state. Here we show the existence of deviations from exponential decay in open quantum systems under very general conditions. Our results are illustrated with the exact dynamics under quantum Brownian motion and suggest an explanation of recent experimental observations.
The following statements belonging to the folklore of the theory of environmental decoherence are shown to be incorrect: 1) linear coupling to harmonic oscillator bath is a universal model of decoherence, 2) chaotic environments are more efficient decoherers.
It is shown how environmental decoherence plays an essential and constructive role in a quantum mechanical theory of brain process that has significant explanatory power.
We discuss decrease of coherence in a massive system due to the emission of gravitational waves. In particular we investigate environmental gravitational decoherence in the context of an interference experiment. The time-evolution of the reduced density matrix is solved analytically using the path-integral formalism. Furthermore, we study the impact of a tensor noise onto the coherence properties of massive systems. We discuss that a particular choice of tensor noise shows similarities to a mechanism proposed by Diosi and Penrose.
A fundamental requirement of quantum information processing is the protection from the adverse effects of decoherence and noise. Decoherence-free subspaces and geometric processing are important steps of quantum information protection. Here, we provide a new experimentally feasible scheme to combine decoherence-free subspaces with nonadiabatic geometric manipulations to attain a universal quantum computation. The proposed scheme is different from previous proposals and is based on the typical XY interaction coupling, which can be set up in various nano-engineered systems and therefore open up …
In this article we develop, step by step, the framework for universal dynamical control of two-level systems (TLS) or qubits experiencing amplitude- or phase-noise (AN or PN) due to coupling to a thermal bath. A comprehensive arsenal of modulation schemes is introduced and applied to either AN or PN, resulting in completely analogous formulae for the decoherence rates, thus underscoring the unified nature of this universal formalism. We then address the extension of this formalism to multipartite decoherence control, where symmetries are exploited to overcome decoherence.
We consider a particularly simple exactly solvable model for a qubit coupled to sequentially nested environments. The purpose is to exemplify the coherence conserving effect of a central system, that has been reported as a result of increasing the coupling between near and far environment. The paradigmatic example is the Jaynes-Cummings Hamiltonian, which we introduce into a Kossakowski-Lindblad master equation using alternatively the lowering operator of the oscillator or its number operator as Lindblad operators. The harmonic oscillator is regarded as the near environment of the qubit, while…
We consider a point particle in one dimension initially confined to a finite spatial region whose state is frequently monitored by projection operators onto that region. In the limit of infinitely frequent monitoring, the state never escapes from the region -- this is the Zeno effect. The aim of this paper is to show how the Zeno effect disappears in the classical limit in this and similar examples. We give a general argument showing that the Zeno effect is suppressed in the presence of a decoherence mechanism which kills interference between histories. We show how this works explicitly by cou…
According to the eigenstate thermalization ansatz, matrices representing generic few body observables take on a specific form when displayed in the eigenbasis of a chaotic Hamiltonian. We examine the effect of environmental induced decoherence on the dynamics of observables that conform with said eigenstate thermalization ansatz. The obtained result refers to a description of the dynamics in terms of an integro-differential equation of motion of the Nakajima-Zwanzig form. We find that environmental decoherence is equivalent to an exponential damping of the respective memory kernel. This statem…
We consider the Wigner function evolution of Fock states $|n\rangle$ linearly coupled to a Markovian bath of oscillators. In the absence of environmental coupling, apparent ``quantumness'' increases with $n$, but the presence of any environmental interaction causes high-$n$ states to lose their quantum features more rapidly than low-$n$ states. Using the negative volume of the Wigner function as a metric \cite{kenfack04}, we observe a time-dependent quantumness peak across the eigenstates.
We show that the quantum states generated by universal optimal quantum cloning of a single photon represent an universal set of quantum superpositions resilient to decoherence. We adopt Bures distance as a tool to investigate the persistence ofquantum coherence of these quantum states. According to this analysis, the process of universal cloning realizes a class of quantum superpositions that exhibits a covariance property in lossy configuration over the complete set of polarization states in the Bloch sphere.
We study quantum decoherence of single-qubit and two-qubit Aharonov-Anandan (AA) geometric phase gates realized in a multistep scheme. Each AA gate is also compared with the dynamical phase gate performing the same unitary transformation within the same time period and coupled with the same environment, which is modeled as harmonic oscillators. It is found that the fidelities and the entanglement protection of the AA phase gates are enhanced by the states being superpositions of different eigenstates of the environmental coupling, and the noncommutativity between the qubit interaction and the …
A simple model is considered for an open system consisting of an aggregation of magnetic particles (like greigite) in the presence of a magnetic field (H), and interacting linearly with a bath of 3D harmonic oscillators. Using the Feynman-Vernon formalism, as given in Weiss (termed FVW), the time-evolved reduced density matrix (after eliminating the bath d.o.f.'s), is examined for environmental decoherence as defined in the FVW formalism. While decoherence is usually positive for most two-way couplings with the enviroment, it is found that a $three-way$ interaction involving the system plus ba…
We investigate how to carry out universal quantum computation deterministically with free electrons in decoherence-free subspace by using polarizing beam splitters, charge detectors, and single-spin rotations. Quantum information in our case is encoded in spin degrees of freedom of the electron-pairs which construct a decoherence-free subspace. We design building blocks for two noncommutable single-logic-qubit gates and a logic controlled phase gate, based on which a universal and scalable quantum information processing robust to dephasing is available in a deterministic way.
Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate within a decoherence-free, scalable quantum computer.
In quantum mechanics an incoming particle wave packet with sufficient energy will undergo both transmission and reflection when encountering a barrier of lower energy, but in classical mechanics there is no reflection, only transmission. In this paper we seek to explain the disappearance of quantum-mechanical reflection in the quasi-classical limit, using standard methods of decoherence through environmental interaction. We consider two models. In the first, the incoming particle is classicalized by coupling it to an environment described by a standard Lindblad master equation diagonalizing in…
We consider a universal set of quantum gates encoded within a perturbed decoherence-free subspace of four physical qubits. Using second-order perturbation theory and a measuring device modeled by an infinite set of harmonic oscillators, simply coupled to the system, we show that continuous observation of the coupling agent induces inhibition of the decoherence due to spurious perturbations. We thus advance the idea of protecting or even creating a decoherence-free subspace for processing quantum information.
We consider environment induced decoherence of quantum superpositions to mixtures in the limit in which that process is much faster than any competing one generated by the Hamiltonian $H_{\rm sys}$ of the isolated system. While the golden rule then does not apply we can discard $H_{\rm sys}$. By allowing for simultaneous couplings to different reservoirs, we reveal decoherence as a universal short-time phenomenon independent of the character of the system as well as the bath and of the basis the superimposed states are taken from. We discuss consequences for the classical behavior of the macro…
We study how matter-wave interferometry with Bose-Einstein condensates is affected by hypothetical collapse models and by environmental decoherence processes. Motivated by recent atom fountain experiments with macroscopic arm separations, we focus on the observable signatures of first-order and higher-order coherence for different two-mode superposition states, and on their scaling with particle number. This can be used not only to assess the impact of environmental decoherence on many-body coherence, but also to quantify the extent to which macrorealistic collapse models are ruled out by such…
We consider interactions that generate a universal set of quantum gates on logical qubits encoded in a collective-dephasing-free subspace, and discuss their implementations with trapped ions. This allows for the removal of the by-far largest source of decoherence in current trapped-ion experiments, collective dephasing. In addition, an explicit parametrization of all two-body Hamiltonians able to generate such gates without the system's state ever exiting the protected subspace is provided.
We study the exact decoherence dynamics of the entangled squeezed state of two single-mode optical fields interacting with two independent and uncorrelated environments. We analyze in detail the non-Markovian effects on the entanglement evolution of the initially entangled squeezed state for different environmental correlation time scales. We find that the environments have dual actions on the system: backaction and dissipation. In mparticular, when the environmental correlation time scale is comparable to the time scale for significant change in the system, the backaction would counteract the…
A characteristic action $ΔS$ is defined whose magnitude determines some properties of the expectation value of a general quantum displacement operator. These properties are related to the capability of a given environmental `monitoring' system to induce decoherence in quantum systems coupled to it. We show that the scale for effective decoherence is given by $ΔS\approx\hbar$. We relate this characteristic action with a complementary quantity, $ΔZ$, and analyse their connection with the main features of the pattern of structures developed by the environmental state in different phase space repr…
In this paper, we propose a way to achieve protected universal computation in a neutral atom quantum computer subject to collective dephasing. Our proposal relies on the existence of a Decoherence Free Subspace (DFS), resulting from symmetry properties of the errors. After briefly describing the physical system and the error model considered, we show how to encode information into the DFS and build a complete set of safe universal gates. Finally, we provide numerical simulations for the fidelity of the different gates in the presence of time-dependent phase errors and discuss their performance…
Phosphorus-doped silicon single crystals with 0.19 % <= f <= 99.2 %, where f is the concentration of 29^Si isotopes, are measured at 8 K using a pulsed electron spin resonance technique, thereby the effect of environmental 29^Si nuclear spins on the donor electron spin is systematically studied. The linewidth as a function of f shows a good agreement with theoretical analysis. We also report the phase memory time T_M of the donor electron spin dependent on both f and the crystal axis relative to the external magnetic field.
Decoherence-free subspaces (DFSs) shield quantum information from errors induced by the interaction with an uncontrollable environment. Here we study a model of correlated errors forming an Abelian subgroup (stabilizer) of the Pauli group (the group of tensor products of Pauli matrices). Unlike previous studies of DFSs, this type of errors does not involve any spatial symmetry assumptions on the system-environment interaction. We solve the problem of universal, fault-tolerant quantum computation on the associated class of DFSs.
A unified theory is given of dynamically modified decay and decoherence of field-driven multilevel multipartite entangled states that are weakly coupled to zero-temperature baths or undergo random phase fluctuations. The theory allows for arbitrary local differences in their coupling to the environment. Due to such differences, the optimal driving-field modulation to ensure maximal fidelity is found to substantially differ from conventional ``Bang-Bang'' or $π$-phase flips of the single-qubit evolution.
This article analyzes the decoherence induced on a single qubit by the interaction with a spin chain with nontrivial internal dynamics (XY-type interactions). The aim of the paper is to study the existence and properties of the so-called universal regime, in which the decoherence time scale becomes independent of the strength of the coupling with the environment. It is shown that although such regime does exist, as previously established by Cucchietti \textit{et al} in {\em Phys. Rev. A}, 75:032337 (2007), it is not a clear signature of a quantum phase transition in the environment. In fact, t…
This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as hbar^{2/3} for ch…
We examine the conditions in favor and necessity of a realistic multileveled description of a decohering quantum system. Under these conditions approximate techniques to simplify a multileveled system by its first two levels is unreliable and a realistic multilevel description in the formulation of decoherence is unavoidable. In this regard, our first crucial observation is that, the validity of the two level approximation of a multileveled system is not controlled purely by {\it sufficiently low temperatures}. We demonstrate using three different environmental spectral models that the type of…
A general scheme to perform universal quantum computation within decoherence-free subspaces (DFSs) of a system's Hilbert space is presented. This scheme leads to the first fault-tolerant realization of universal quantum computation on DFSs with the properties that (i) only one- and two-qubit interactions are required, and (ii) the system remains within the DFS throughout the entire implementation of a quantum gate. We show explicitly how to perform universal computation on clusters of the four-qubit DFS encoding one logical qubit each under "collective decoherence" (qubit-permutation-invariant…
We describe exchange-only universal quantum computation and leakage reduction in the 3-qubit decoherence free subsystem (DFS). We discuss the angular momentum structure of the DFS, the proper forms for the DFS CNOT and leakage reduction operators in the total angular momentum basis, and new exchange-only pulse sequences for the CNOT and leakage reduction operators. Our new DFS CNOT sequence requires 22 pulses in 13 time steps. The DFS leakage reduction sequence, the first explicit leakage reduction sequence of its kind, requires 30 pulses in 20 time steps. Although the search for sequences was…
Quantum information protocols are inevitably affected by decoherence which is associated with the leakage of quantum information into an environment. In this paper we address the possibility of recovering the quantum information from an environmental measurement. We investigate continuous variable quantum information, and we propose a simple environmental measurement that under certain circumstances fully restores the quantum information of the signal state although the state is not reconstructed with unit fidelity. We implement the protocol for which information is encoded into conjugate quad…
We theoretically study the non-Markovian dynamics of qubit systems coupled to nonequilibrium environments with nonstationary and non-Markovian statistical properties. The reduced density matrix of the single qubit system satisfies a closed third-order differential equation with all the higher-order environmental correlations taken into account and 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 syst…
Universal quantum computation on decoherence-free subspaces and subsystems (DFSs) is examined with particular emphasis on using only physically relevant interactions. A necessary and sufficient condition for the existence of decoherence-free (noiseless) subsystems in the Markovian regime is derived here for the first time. A stabilizer formalism for DFSs is then developed which allows for the explicit understanding of these in their dual role as quantum error correcting codes. Conditions for the existence of Hamiltonians whose induced evolution always preserves a DFS are derived within this st…
A cavity QED implementation of the non-adiabatic holonomic quantum computation in decoherence-free subspaces is proposed with nitrogen-vacancy centers coupled commonly to the whispering-gallery mode of a microsphere cavity, where a universal set of quantum gates can be realized on the qubits. In our implementation, with the assistant of the appropriate driving fields, the quantum evolution is insensitive to the cavity field state, which is only virtually excited. The implemented non-adiabatic holonomies, utilizing optical transitions in the Λ type of three-level configuration of the nitrogen-v…
It is shown that energy transfer in a homogeneous fully connected quantum network is assisted by a decohering interaction with environmental spins. Analytic expressions for the transfer probabilities are obtained for the zero temperature case, and the effect is shown to persist at physiological temperatures. This model of decoherence-assisted energy transfer is applied to the Fenna-Matthews-Olson complex.
A field configuration utilizing local static and oscillating fields is constructed to achieve universal (but low-order) protection of two-qubit states. That is, two-qubit states can be protected against arbitrary system-environment coupling if the driving field frequency, as compared with the cutoff frequency of the environment, is sufficiently large. Equally important, we show that it is possible to construct driving fields to protect two-qubit entangling gates against decoherence, without assuming any particular form of system-environment coupling. Using a non-Markovian master equation, we f…
We present a series of arguments against the results of the paper "Universal decoherence due to gravitational time dilation" by Pikovski et al. (arXiv:1311.1095).
We propose and analyse a robust quantum state transfer protocol by the use of a combination of coherent quantum coupling and decoherence-free subspaces in a coupled quantum spin chain. Under decoherence, an arbitrary unknown quantum state embedded in a decoherence-free subspace can be perfectly transferred through a noisy channel being weakly coupled to two end registers. The method protects quantum information from both the channel noise and the environmental decoherence. A special case of utilizing two physical qubits to encode one logical qubit is considered as an example and the robustness…
The interaction of quantum emitters with one-dimensional photon-like reservoirs induces strong and long-range dissipative couplings that give rise to the emergence of so-called Decoherence Free Subspaces (DFS) which are decoupled from dissipation. When introducing weak perturbations on the emitters, e.g., driving, the strong collective dissipation enforces an effective coherent evolution within the DFS. In this work, we show explicitly how by introducing single-site resolved drivings, we can use the effective dynamics within the DFS to design a universal set of one and two-qubit gates within t…
We construct a model which describes a recently performed experiment (Phys. Rev. A 64, 050301(R) (2001)) in which an entangled state between two modes of a single cavity is built. Environmental effects are taken into account and the results agree with the experimental findings. Moreover the model predicts, for different conditions of the same experiment, a decoherence-free subspace. These conditions are analyzed and slightly different experiments suggested in order to test its viability.
