The information in quantum computers is often stored in identical two-level systems (spins or pseudo-spins) that are separated by a distance shorter than the characteristic wavelength of a reservoir which is responsible for decoherence. In such a case, the collective spin-reservoir interaction, rather than an individual spin-reservoir interaction, may determine the decoherence characteristics. We use computational basis states, symmetrized spin states and spin coherent states to study collective decoherence in the implementation of various quantum algorithms. A simple method of implementing quantum algorithms using stable subradiant states and avoiding unstable Dicke's superradiant states and Schrodinger's cat states is proposed.
We argue that superradiance (collective emission) due to radiative coupling of qubit states results in non-local noise, and thus introduces an error source that cannot be corrected using current models of fault-tolerant quantum computation.
The symmetric collective states of an atomic spin ensemble (i.e., many-body states that are invariant under particle exchange) are not preserved by decoherence that acts identically but individually on members of the ensemble. We develop a class of collective states in an ensemble of N spin-1/2 particles that is invariant under symmetric local decoherence and find that the dimension of the Hilbert space spanned by these collective states scales only as N^2. We then investigate the open system dynamics of experimentally relevant non-classical collective atomic states, including Schroedinger cat…
We discuss the structure of decoherence-free subsystems for a bosonic channel affected by collective depolarization. A single use of the channel is defined as a transmission of a pair of bosonic modes. Collective depolarization consists in a random linear U(2) transformation of the respective mode operators, which is assumed to be identical for $N$ consecutive uses of the channel. We derive a recursion formula that characterizes the dimensionality of available decoherence-free subsystems in such a setting.
The influence of decoherence on the fidelity of quantum memories for photonic qubits based on dark-state polaritons in atomic ensembles is discussed. It is shown that despite the large entanglement of the collective storage states corresponding to single photons or nonclassical states of light the sensitivity to decoherence does not scale with the number of atoms. This is due to the existence of equivalence classes of storage states corresponding to states with the same number of dark-state polariton excitations but arbitrary excitations in other polariton modes. Several decoherence processes …
We investigate the influence of critical phenomena on two distinct physical processes: the center-of-mass decoherence of a single emitter, and the collective radiation of two emitters. We address these different physical mechanisms with an unified formalism relying on standard perturbation theory. We decompose the decoherence and the collective emission rates as a sum of two contributions, accounting for the spontaneous emission and for interference effects respectively. The former is enhanced by the Purcell effect when the material is in the vicinity of the emitter(s). The latter, associated …
We propose schemes that are efficient when each pair of qubits undergoes some imperfect collective decoherence with different baths. In the proposed scheme, each pair of qubits is first encoded in a decoherence-free subspace composed of two qubits. Leakage out of the encoding space generated by the imperfection is reduced by the quantum Zeno effect. Phase errors in the encoded bits generated by the imperfection are reduced by concatenation of the decoherence-free subspace with either a three-qubit quantum error correcting code that corrects only phase errors or a two-qubit quantum error detect…
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-free subspaces (DFS) in systems of dipole-dipole interacting multi-level atoms are investigated theoretically. It is shown that the collective state space of two dipole-dipole interacting four-level atoms contains a four-dimensional DFS. We describe a method that allows to populate the antisymmetric states of the DFS by means of a laser field, without the need of a field gradient between the two atoms. We identify these antisymmetric states as long-lived entangled states. Further, we show that any single-qubit operation between two states of the DFS can be induced by means of a mic…
We study the generation of spin-squeezing in arrays of long-lived dipoles subject to collective emission, coherent drive, elastic interactions, and spontaneous emission. Counter-intuitively, it is found that the introduction of spontaneous emission leads to an enhancement of the achievable spin-squeezing, relative to that which emerges in the steady-state of the purely collective dynamics for the same model parameters. This behavior is connected to the dynamical self-tuning of the system through a dissipative phase transition that is present in the collective system alone. Our findings will be…
We propose a simple technique for the generation of arbitrary-sized Dicke states in a chain of trapped ions. The method uses global addressing of the entire chain by two pairs of delayed but partially overlapping laser pulses to engineer a collective adiabatic passage along a multi-ion dark state. Our technique, which is a many-particle generalization of stimulated Raman adiabatic passage (STIRAP), is decoherence-free with respect to spontaneous emission and robust against moderate fluctuations in the experimental parameters. Furthermore, because the process is very rapid, the effects of heati…
We propose easy implementable protocols for robust quantum key distribution with the collective dephasing channel or collective rotating channel. In these protocols, Bob only takes passive photon detection to measure the polarization qubits in the random bases. The source for the protocol with collective rotating channel is made by type 2 spontaneous parametric down conversion with random unitary rotation and phase shifter, no quantum disentangler is required. A simple proof for unconditionally security is shown.
We investigate the decoherence of a superposition of symmetric collective internal states of an atomic ensemble due to inhomogeneous coupling to external control fields. For asymptotically large system, we find the characteristic decoherence rate scales as $\sqrt{N}$ with $N$ being the total number of atoms. Our results shed new light on attempts for quantum information processing and storage with atomic ensembles.
We consider decoherence of quantum registers, which consist of the qubits sited approximately periodically in space. The sites of the qubits are permitted to have a small random variance. We derive the explicit conditions under which the qubits can be assumed decohering independently. In other circumstances, the qubits are decohered cooperatively. We describe two kinds of collective decoherence. In each case, a scheme is proposed for reducing the collective decoherence. The schemes operate by encoding the input states of the qubits into some ''subdecoherent'' states.
The problem of dipole-dipole decoherence of nuclear spins is considered for strongly entangled spin cluster. Our results show that its dynamics can be described as the decoherence due to interaction with a composite bath consisting of fully correlated and uncorrelated parts. The correlated term causes the slower decay of coherence at larger times. The decoherence rate scales up as a square root of the number of spins giving the linear scaling of the resulting error. Our theory is consistent with recent experiment reported in decoherence of correlated spin clusters.
We study how the decoherence of macroscopic objects is induced intrisinically by relativistic effect. With the degree of freedom of center of mass (CM) characterizing the collective quantum state of a macroscopic object (MO), it is found that a MO consisting of N particles can decohere with time scale no more than sqrt(N). Here, the special relativity can induce the coupling of the collective motion mode and the relative motion modes in an order of 1/c2, which intrinsically results in the above minimum decoherence.
Decoherence in quantum computer memory due to the inevitable coupling to the external environment is examined. We take the assumption that all quantum bits (qubits) interact with the same environment rather than the assumption of separate environments for different qubits. It is found that the qubits are decohered collectively. For some kinds of entangled input states, no decoherence occurs at all in the memory even if the qubits are interacting with the environment. Based on this phenomenon, a scheme is proposed for reducing the collective decoherence. We also discuss possible implications of…
We analyze the dynamics of entanglement due to decoherence in a system of two identical fermions with spin $3/2$ interacting with a global bosonic environment. We resort to an appropriate measure of the so-called fermionic entanglement to quantify the fermionic correlations, and compare its dynamics with that of a pair of distinguishable qubits immersed in the same environment. According to the system's initial state, three types of qualitatively different dynamics are identified: i) \textit{invariant regime}, corresponding to initial states that belong to a decoherence free subspace (DFS), wh…
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 quantum dynamics of a single qubit coupled to a bath of interacting spins as a model for decoherence in solid state quantum memories. The spin bath is described by the Lipkin-Meshkov-Glick model and the bath spins are subjected to a transverse magnetic field. We investigate the qubit interacting via either an Ising- or an XY-type coupling term to subsets of bath spins of differing size. The large degree of symmetry of the bath allows us to find parameter regimes where the initial qubit state is revived at well defined times after the qubit preparation. These times may become indep…
We present an optical device which is capable of heralding a variety of DFS states which protect against collective noise. Specifically, it can prepare all three basis states which span a DFS qutrit as well as an arbitrarily encoded DFS qubit state. We also discuss an interferometric technique for determining the amplitudes associated with an arbitrary encoding. The heralded state may find use in coherent optical systems which exhibit collective correlations.
We show that errors are not generated correlatedly provided that quantum bits do not directly interact with (or couple to) each other. Generally, this no-qubits-interaction condition is assumed except for the case where two-qubit gate operation is being performed. In particular, the no-qubits-interaction condition is satisfied in the collective decoherence models. Thus, errors are not correlated in the collective decoherence. Consequently, we can say that current quantum error correcting codes which correct single-qubit-errors will work in most cases including the collective decoherence.
Collective decoherence is possible if the departure between quantum bits is smaller than the effective wave length of the noise field. Collectivity in the decoherence helps us to devise more efficient quantum codes. We present a class of optimal quantum codes for preventing collective amplitude damping to a reservoir at zero temperature. It is shown that two qubits are enough to protect one bit quantum information, and approximately $L+ 1/2 \log_2((πL)/2)$ qubits are enough to protect $L$ qubit information when $L$ is large. For preventing collective amplitude damping, these codes are much mor…
We study the dynamics of entanglement in spin gases. A spin gas consists of a (large) number of interacting particles whose random motion is described classically while their internal degrees of freedom are described quantum-mechanically. We determine the entanglement that occurs naturally in such systems for specific types of quantum interactions. At the same time, these systems provide microscopic models for non--Markovian decoherence: the interaction of a group of particles with other particles belonging to a background gas are treated exactly, and differences between collective and non--co…
When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free subspace are known to correct such collective errors. We construct simple quantum circuits, which implement these collective error correction codes, for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and $n=4$, while two logical qubits are encoded with $n=5$. The recursive relations among the subspaces employed in noiseless subs…
We analyze the interplay of chaos, entanglement and decoherence in a system of qubits whose collective behaviour is that of a quantum kicked top. The dynamical entanglement between a single qubit and the rest can be calculated from the mean of the collective spin operators. This allows the possibility of efficiently measuring entanglement dynamics in an experimental setting. We consider a deeply quantum regime and show that signatures of chaos are present in the dynamical entanglement for parameters accessible in an experiment that we propose using cold atoms. The evolution of the entanglement…
Heralded entanglement between collective excitations in two atomic ensembles is probabilistically generated, stored, and converted to single photon fields. By way of the concurrence, quantitative characterizations are reported for the scaling behavior of entanglement with excitation probability and for the temporal dynamics of various correlations resulting in the decay of entanglement. A lower bound of the concurrence for the collective atomic state of 0.9\pm 0.3 is inferred. The decay of entanglement as a function of storage time is also observed, and related to the local dynamics.
The goal of quantum metrology is the precise estimation of parameters using quantum properties such as entanglement. This estimation usually consists of three steps: state preparation, time evolution during which information of the parameters is encoded in the state, and readout of the state. Decoherence during the time evolution typically degrades the performance of quantum metrology and is considered to be one of the major obstacles to realizing entanglement-enhanced sensing. We show, however, that under suitable conditions, this decoherence can be exploited to improve the sensitivity. Assum…
The dynamical evolution of a quantum register of arbitrary length coupled to an environment of arbitrary coherence length is predicted within a relevant model of decoherence. The results are reported for quantum bits (qubits) coupling individually to different environments (`independent decoherence') and qubits interacting collectively with the same reservoir (`collective decoherence'). In both cases, explicit decoherence functions are derived for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: we show that this sensitivity is …
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…
In this thesis we describe methods for avoiding the detrimental effects of decoherence while at the same time still allowing for computation of the quantum information. The philosophy of the method discussed in the first part of this thesis is to use a symmetry of the decoherence mechanism to find robust encodings of the quantum information. Stability, control, and methods for using decoherence-free information in a quantum computer are presented with a specific emphasis on decoherence due to a collective coupling between the system and its environment. Universal quantum computation on such co…
When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under particle relabeling, can be efficiently simulated since they span a subspace whose dimension is linear in the number of spins. However, many open system dynamics break this symmetry, most notably when ensemble members undergo identical, but local, decoherence. In this paper, we extend the definition of symmetric collective states of an ensemble of spin-1/2 parti…
We study distribution schemes for a polarization entangled photon pair based on a decoherence-free subspace over lossy quantum channels and propose an efficient scheme that is robust against not only collective phase noises but also general collective noises for two qubits. While the proposed scheme employs two photons to build the decoherence-free subspace, the success probability is proportional to the channel transmittance of a single photon with the aid of a counter-propagating weak coherent light pulse. The key ingredient in the scheme is found to be the reciprocity of the channel. The pr…
Quantum Fourier transform is of primary importance in many quantum algorithms. In order to eliminate the destructive effects of decoherence induced by couplings between the quantum system and its environment, we propose a robust scheme for quantum Fourier transform over the intrinsic decoherence-free subspaces. The scheme is then applied to the circuit design of quantum Fourier transform over quantum networks under collective decoherence. The encoding efficiency and possible improvements are also discussed.
We propose a method to adiabatically control an atomic ensemble using a decoherence-free subspace (DFS) within a dissipative cavity. We can engineer a specific eigenstate of the system's Lindblad jump operators by injecting a field into the cavity which deconstructively interferes with the emission amplitude of the ensemble. In contrast to previous adiabatic DFS proposals, our scheme creates a DFS in the presence of collective decoherence. We therefore have the ability to engineer states that have high multi-particle entanglements which may be exploited for quantum information science or metro…
We outline a proposal for a method of preparing an encoded two-state system (logical qubit) that is immune to collective noise acting on the Hilbert space of the states supporting it. The logical qubit is comprised of three photonic three-state systems (qutrits) and is generated by the process of spontaneous parametric down conversion. The states are constructed using linear optical elements along with three down-conversion sources, and are deemed successful by the simultaneous detection of six events. We also show how to select a maximally entangled state of two qutrits by similar methods. Fo…
We propose an effective Hamiltonian approach to investigate decoherence of a quantum system in a non-Markovian reservoir, naturally imposing the complete positivity on the reduced dynamics of the system. The formalism is based on the notion of an effective reservoir, i.e., certain collective degrees of freedom in the reservoir that are responsible for the decoherence. As examples for completely positive decoherence, we present three typical decoherence processes for a qubit such as dephasing, depolarizing, and amplitude-damping. The effects of the non-Markovian decoherence are compared to the …
We analyze rigorously the dynamics of the entanglement between two qubits which interact only through collective and local environments. Our approach is based on the resonance perturbation theory which assumes a small interaction between the qubits and the environments. The main advantage of our approach is that the expressions for (i) characteristic time-scales, such as decoherence, disentanglement, and relaxation, and (ii) observables are not limited by finite times. We introduce a new classification of decoherence times based on clustering of the reduced density matrix elements. The charact…
We study a model of a quantum spin register interacting with an environment of spin particles in quantum-measurement limit. In the limit of collective decoherence we obtain the form of state vectors that constitute high-dimensional decoherence-free subspaces (DFS). In a more general setting we present sufficient and necessary conditions for existence of low-dimensional DFSs that can be used to construct subspaces of higher dimension.
We study a model describing competition of interactions between $N$ two-level systems (TLSs) against decoherence. We apply it to analyze dye molecules in an optical microcavity, where molecular vibrations provide a local source for decoherence. Most interesting is the case when decoherence strongly affects each individual TLS, e.g. via broadening of emission lines as well as vibrational satellites, however its influence is strongly suppressed for large $N$ due to the interactions between TLSs. In this interaction dominated regime we find unique signatures in the emission spectrum, including st…
Spin ensemble based hybrid quantum systems suffer from a significant degree of decoherence resulting from the inhomogeneous broadening of the spin transition frequencies in the ensemble. We demonstrate that this strongly restrictive drawback can be overcome simply by burning two narrow spectral holes in the spin spectral density at judiciously chosen frequencies. Using this procedure we find an increase of the coherence time by more than an order of magnitude as compared to the case without hole burning. Our findings pave the way for the practical use of these hybrid quantum systems for the pr…
Scaling theory of decoherence in Dicke superradiance
TU Darmstadt（达姆施塔特工业大学）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；CNRS and Université de Strasbourg（法国国家科学研究中心与斯特拉斯堡大学）
We address the dynamics induced by collective atomic recoil in a Bose-Einstein condensate in presence of radiation losses and atomic decoherence. In particular, we focus on the linear regime of the lasing mechanism, and analyze the effects of losses and decoherence on the generation of entanglement. The dynamics is that of three bosons, two atomic modes interacting with a single-mode radiation field, coupled with a bath of oscillators. The resulting three-mode dissipative Master equation is solved analytically in terms of the Wigner function. We examine in details the two complementary limits …
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…
An ensemble of multilevel atoms is a good candidate for a quantum information storage device. The information is encrypted in the collective ground state atomic coherence, which, in the absence of external excitation, is decoupled from the vacuum and therefore decoherence free. However, in the process of manipulation of atoms with light pulses (writing, reading), one inadvertently introduces a coupling to the environment, i.e. a source of decoherence. The dissipation process is often treated as an independent process for each atom in the ensemble, an approach which fails at large atomic optica…
We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized receiver is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which these secret communications take place is equal to the Holevo-Schumacher-Westmoreland capacity of the quantum channel.
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of $\frac{N-2}{N}$. The proposed scheme is robust against control imprecisions and the non-collective decoherence, …
We compare disentanglement and decoherence rates within two-spin and three-spin entangled systems subjected to all possible combinations of local and collective pure dephasing noise combinations. In all cases, the bipartite entanglement decay rate is found to be greater than or equal to the dephasing-decoherence rates and often significantly greater. This sharpens previous results for two-spin systems [T. Yu and J. H. Eberly Phys. Rev. B 68, 165322 (2003)] and extends them to the three-spin context.
We propose a decoherence-free subspaces (DFS) scheme to realize scalable quantum computation with trapped ions. The spin-dependent Coulomb interaction is exploited, and the universal set of unconventional geometric quantum gates is achieved in encoded subspaces that are immune from decoherence by collective dephasing. The scalability of the scheme for the ion array system is demonstrated, either by an adiabatic way of switching on and off the interactions, or by a fast gate scheme with comprehensive DFS encoding and noise decoupling techniques.
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.
We demonstrate that for an ensemble of qudits, subjected to collective decoherence in the form of perfectly correlated random SU(d) unitaries, quantum superpositions stored in the decoherence free subspace are fully immune against the removal of one particle. This provides a feasible scheme to protect quantum information encoded in the polarization state of a sequence of photons against both collective depolarization and one photon loss, and can be demonstrated with photon quadruplets using currently available technology.
We study the three-dimensional nature of the quantum interface between an ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled through a dispersive interaction. To achieve strong entanglement between the collective atomic spin and the photons, one must match the spatial mode of the collective radiation of the ensemble with the mode of the laser beam while minimizing the effects of decoherence due to optical pumping. For ensembles coupling to a probe field that varies over the extent of the cloud, the set of atoms that indistinguishably radiates into a desired mode of the f…
We present a new method to compute short-time expectation values in large collective spin systems with generic Markovian decoherence. Our method is based on a Taylor expansion of a formal solution to the equations of motion for Heisenberg operators. This expansion can be truncated at finite order to obtain virtually exact results at short times that are relevant for metrological applications such as spin squeezing. In order to evaluate the expansion for Heisenberg operators, we compute the relevant structure constants of a collective spin operator algebra. We demonstrate the utility of our met…
Recent experiments show the existence of collective decoherence in quantum systems. We study the possibility of quantum computation in decoherence free subspace which is robust against such kind of decoherence processes. This passive protection protocol can be especially advantageous for continuous quantum computation such as quantum annealers. As an example we propose to use decoherence protected adiabatic quantum computation for the Grover search problem. Our proposal contains only two-body interactions, making it feasible in near-term quantum devices.
Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, non-adiabatic holonomic quantum computation in decoherence-free subspaces, which avoids long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize non-adiabatic holonomic quantum computation in decoherence-free…
