Decoherence effect on quantum entanglement of two optical qubits in a lossy cavity interacting with a nonlinear medium (Kerr nonlinearity) is analyzed. The qubits are assumed to be initially in the maximally entangled states (Bell or Bell-like states) or the maximally entangled mixed states, on the example of Werner and Werner-like states. Two kinds of measures of the entanglement are considered: the concurrence to describe a decay of the entanglement of formation of the qubits, and the negativity to determine a decay of the entanglement cost under positive-partial-transpose-preserving operations. It is observed that the Kerr nonlinearity, in the discussed decoherence model, does not affect the entanglement of the qubits initially in the Bell or Werner states, although the evolution of the qubits can depend on this nonlinearity explicitly. However, it is shown that for the initial Bell-like state and the corresponding Werner-like state, the loss of the entanglement can be periodically reduced by inserting the Kerr nonlinearity in the lossy cavity. Moreover, the relativity of the entanglement measures is demonstrated, to our knowledge for the first time, as a result of a physical process.
We propose and demonstrate a scheme for boosting up the efficiency of entanglement distribution based on a decoherence-free subspace (DFS) over lossy quantum channels. By using backward propagation of a coherent light, our scheme achieves an entanglement-sharing rate that is proportional to the transmittance T of the quantum channel in spite of encoding qubits in multipartite systems for the DFS. We experimentally show that highly entangled states, which can violate the Clauser-Horne-Shimony-Holt inequality, are distributed at a rate proportional to T.
In the viewpoint of quasi normal modes, we describe a novel decoherence mechanism of charge qubit of Josephson Junctions (JJ) in a lossy micro-cavity, which can appear in the realistic experiment for quantum computation based on JJ qubit. We show that the nonlinear coupling of a charge qubit to quantum cavity field can result in an additional dissipation of resonant mode due to its effective interaction between those non-resonant modes and a resonant mode, which is induced by the charge qubit itself. We calculate the characterized time of the novel decoherence by making use of the system plus …
By use of external periodic driving sources, we demonstrate the possibility of controlling the coherent as well as the decoherent dynamics of a two-level atom placed in a lossy cavity. The control of the coherent dynamics is elucidated for the phenomenon of coherent destruction of tunneling (CDT), i.e., the coherent dynamics of a driven two-level atom in a quantum superposition state can be brought practically to a complete standstill. We study this phenomenon for different initial preparations of the two-level atom. We then proceed to investigate the decoherence originating from the interacti…
We investigate cat codes that can correct multiple excitation losses and identify two types of logical errors: bit-flip errors due to excessive excitation loss and dephasing errors due to quantum back-action from the environment. We show that selected choices of logical subspace and coherent amplitude can efficiently reduce dephasing errors. The trade-off between the two major errors enables optimized performance of cat codes in terms of minimized decoherence. With high coupling efficiency, we show that one-way quantum repeaters with cat codes feature drastically boosted secure communication r…
Self-interactions and interaction with the environment tend to push quantum systems toward states of maximal entanglement. This is a definition of decoherence. We argue that these maximally entangled states fall into the well-defined classes that can be uniquely described by the values of certain entanglement invariants. After discussing these ideas we present examples of maximally entangled states for a number of generic systems, construct compact states in the most entangled classes for tripartite systems, and suggest how they may be constructed for other $n$-partite systems. We study random…
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.
Reducing decoherence is an essential step toward realizing general-purpose quantum computers beyond the present noisy intermediate-scale quantum (NISQ) computers. To this end, dynamical decoupling (DD) approaches in which external fields are applied to qubits are often adopted. We numerically study DD using a two-level model system (qubit) under the influence of Markovian decoherence by using quantum optimal control theory with slightly modified settings, in which the physical objective is to maximally create and maintain a specified superposition state in a specified control period. An optima…
In this paper, the master equation for the coupled lossy waveguides is solved using the thermofield dynamics(TFD) formalism. This formalism allows the use of the underlying symmetry algebras SU(2) and SU(1,1), associated with the Hamiltonian of the coupled lossy waveguides,to compute entanglement and decoherence as a function of time for various input states such as NOON states and thermal states.
Entanglement can be considered as a special quantum correlation, but not the only kind. Even for a separable quantum system, it is allowed to exist non-classical correlations. Here we propose two dissipative schemes for generating a maximally correlated state of two qubits in the absence of quantum entanglement, which was raised by [F. Galve, G. L. Giorgi, and R. Zambrini, {\color{blue}Phys. Rev. A {\bf 83}, 012102 (2011)}]. These protocols take full advantages of the interaction between four-level atoms and strongly lossy optical cavities. In the first scenario, we alternatively change the ph…
It is known that maximally entangled Bell state and three-qubit W-type states are very useful in various quantum information processing task. Thus the problem of preparation of these type of states is very important in quantum information theory. But the factor which prohibit the generation of the above mentioned pure states shared between two and three distant partners is decoherence. When we send one qubit, from a two qubit state, through decoherence channel like amplitude damping channel, the purity of the qubit is lost and it ends up with a mixed state. Therefore it is very difficult to ke…
The "Ping-Pong" (PP) protocol is a two-way quantum key protocol based on entanglement. In this protocol, Bob prepares one maximally entangled pair of qubits, and sends one qubit to Alice. Then, Alice performs some necessary operations on this qubit and sends it back to Bob. Although this protocol was proposed in 2002, its security in the noisy and lossy channel has not been proven. In this report, we add a simple and experimentally feasible modification to the original PP protocol, and prove the security of this modified PP protocol against collective attacks when the noisy and lossy channel i…
Maximally predictive states, as defined in recent work by Zurek, Habib and Paz, are studied for more elaborate environment models than a linear coupling. An environment model which includes spatial correlations in the noise is considered in the non-dissipative regime. The Caldeira-Leggett model is also reconsidered in the context of an averaging procedure which produces a completely positive form for the quantum master equation. In both cases, the maximally predictive states for the harmonic oscillator are the coherent states, which is the same result found by Zurek,Habib and Paz for the Calde…
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 present a general theoretical method to generate maximally entangled mixed states of a pair of photons initially prepared in the singlet polarization state. This method requires only local operations upon a single photon of the pair and exploits spatial degrees of freedom to induce decoherence. We report also experimental confirmation of these theoretical results.
We study two quantum versions of the Eddington clock-synchronization protocol in the presence of decoherence. The first protocol uses maximally entangled states to achieve the Heisenberg limit for clock synchronization. The second protocol achieves the limit without using entanglement. We show the equivalence of the two protocols under any single-qubit decoherence model that does not itself provide synchronization information.
In some off-resonant cases, the reduced density matrix of two atoms symmetrically coupled with an optical cavity can very approximately approach to maximally entangled mixed states or maximal Bell violation mixed states in their evolution. The influence of phase decoherence on the generation of maximally entangled mixed state is also discussed. PACS numbers: 03.67.-a, 03.65.Ud
Nonclassical states are essential for optics-based quantum information processing, but their fragility limits their utility for practical scenarios in which loss and noise inevitably degrade, if not destroy, nonclassicality. Exploiting nonclassical states in quantum metrology yields sensitivity advantages over all classical schemes delivering the same energy per measurement interval to the sample being probed. These enhancements, almost without exception, are severely diminished by quantum decoherence. Here, we experimentally demonstrate an entanglement-enhanced sensing system that is resilien…
Every entangled state can be perturbed, for instance by decoherence, and stay entangled. For a large class of pure entangled states, we show how large the perturbation can be. Our class includes all pure bipartite and all maximally entangled states. For an entangled state, E, the constucted neighborhood of entangled states is the region outside two parallel hyperplanes, which sandwich the set of all separable states. The states for which these neighborhoods are largest are the maximally entangled ones. As the number of particles, or the dimensions of the Hilbert spaces for two of the particles…
The 1996 Brune {\it et al.} experiment on vacuum Rabi oscillation is analyzed by means of alternative models of atom-reservoir interaction. Agreement with experimental Rabi oscillation data can be obtained if one defines jump operators in the dressed-state basis, and takes into account thermal fluctuations between dressed states belonging to the same manifold. Such low-frequency transitions could be ignored in a closed cavity, but the cavity employed in the experiment was open, which justifies our assumption. The cavity quality factor corresponding to the data is $Q=3.31\cdot 10^{10}$, whereas…
The system of an atom couples to two distinct optical cavities with phase decoherence is studied by making use of a dynamical algebraic method. We adopt the concurrence to characterize the entanglement between atom and cavities or between two optical cavities in the presence of the phase decoherence. It is found that the entanglement between atom and cavities can be controlled by adjusting the detuning parameter. Finally, we show that even if the atom is initially prepared in a maximally mixed state, it can also entangle the two mode cavity fields.
We investigate the decay of entanglement, due to decoherence, of multi-qubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own, independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness optimization problem, only involving states equivalent under local unitary transformations to the |G…
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…
Subtle quantum properties offer exciting new prospects in optical communications. Quantum entanglement enables the secure exchange of cryptographic keys and the distribution of quantum information by teleportation. Entangled bright beams of light attract increasing interest for such tasks, since they enable the employment of well-established classical communications techniques. However, quantum resources are fragile and undergo decoherence by interaction with the environment. The unavoidable losses in the communication channel can lead to a complete destruction of useful quantum properties -- …
This Letter studies the decoherence in a system of two antiferromagnetically coupled spins that interact with a spin bath environment. Systems are considered that range from the rotationally invariant to highly anisotropic spin models, have different topologies and values of parameters that are fixed or are allowed to fluctuate randomly. We explore the conditions under which the two-spin system clearly shows an evolution from the initial spin-up - spin-down state towards the maximally entangled singlet state. We demonstrate that frustration and, especially, glassiness of the spin environment s…
We report on exciton-acoustic-phonon coupling effects on the generation of exciton maximally entangled states in N=2 and 3 quantum dot systems. In particular, we address the question of the combined effect of laser pulses, appropriate for generating Bell and Greenberger-Horne-Zeilinger entangled states, together with decoherence mechanisms as provided by a phonon reservoir. By solving numerically the master equation for the optically driven exciton-phonon kinetics, we show that the generation of maximally entangled exciton states is preserved over a reasonable parameter window.
Single-photon entanglement may be the simplest type of entanglement but it is of vice importance in quantum communication. Here we present a practical protocol for distilling the single-photon entanglement from both photon loss and decoherence. With the help of some local single photons, the probability of single photon loss can be decreased and the less-entangled state can also be recovered to maximally entangled state simultaneously. It only requires some linear optical elements which makes it feasible in current experiment condition. This protocol might find applications in current quantum …
We show that a simple experimental setting of a locally pumped and lossy array of two-level quantum systems can stabilize states with strong long-range coherence. Indeed, by explicit analytic construction, we show there is an extensive set of steady-state density operators, from minimally to maximally entangled, despite this being an interacting open many-body problem. Such nonequilibrium steady states arise from a hidden symmetry that stabilizes Bell pairs over arbitrarily long distances, with unique experimental signatures. We demonstrate a protocol by which one can selectively prepare these…
The Lindblad generators of the master equation define which kind of decoherence happens in an open quantum system. We are working with a two qubit system and choose the generators to be projection operators on the eigenstates of the system and unitary bilocal rotations of them. The resulting decoherence modes are studied in detail. Besides the general solutions we investigate the special case of maximally entangled states - the Bell singlet states. The results are depicted in the so-called spin geometry picture which allows to illustrate the evolution of the (nonlocal) correlations stored in a…
We design an effect protocol for protecting the single-photon entanglement from photon loss and decoherence. The protocol only requires some auxiliary single photons and the linear optical elements. By operating the protocol, the photon loss can be effectively decreased and the less entangled single photon state can be recovered to the maximally entangled state with some probability. Moreover, the polarization information encoded in the single photon state can be perfectly contained. The protocol can be realized under current experimental condition. As the single photon entanglement is quite i…
We study and experimentally implement a double-slit quantum eraser in the presence of a controlled decoherence mechanism. A two-photon state, produced in a spontaneous parametric down conversion process, is prepared in a maximally entangled polarization state. A birefringent double-slit is illuminated by one of the down-converted photons, and it acts as a single-photon two-qubits controlled not gate that couples the polarization with the transversal momentum of these photons. The other photon, that acts as a which-path marker, is sent through a Mach-Zehnder-like interferometer. When the interf…
The entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in the presence of intrinsic decoherence is studied. The usefulness of such system for performance of the quantum teleportation protocol ${\cal T}_0$ and entanglement teleportation protocol ${\cal T}_1$ is also investigated. The results depend on the initial conditions and the parameters of the system. For the product and maximally entangled initial states, increasing the size of spin-orbit interaction parameter $D$ amplifies the effects of dephasing and hence decreases the asymptotic entanglement and fidelity of telep…
In the present article, the robustness of entanglement in two qubits maximally entangled mixed states (MEME) have been studied under quantum decoherence channels. Here we consider bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels. To quantify the entanglement, the concurrence has been used as an entanglement measure. During this study interesting results have been found for sudden death and birth of entanglement under bit flip and bit-phase-flip channels. While amplitude damping channel produces entanglement sudden death and does not allow re-bi…
We study the nonlocal properties of two-qubit maximally-entangled and N-qubit Greenberger-Horne-Zeilinger states under local decoherence. We show that the (non)resilience of entanglement under local depolarization or dephasing is not necessarily equivalent to the (non)resilience of Bell-inequality violations. Apart from entanglement and Bell-inequality violations, we consider also nonlocality as quantified by the nonlocal content of correlations, and provide several examples of anomalous behaviors, both in the bipartite and multipartite cases. In addition, we study the practical implications o…
We present a three-cavity network model with two modes in each cavity and a non-linear medium that generates a Kerr type interaction via both self-phase and cross-phase modulation processes. We have two main goals. The first one is to generate a multipartite Maximally Entangled State (MES), starting from the ground state of the system. We address the problem both without and with dissipation. Secondly, we want to protect the MES from decoherence. While studying the MES, we analyze different bipartite and multipartite entanglement measures. We also study the effect of an Avoided Level Crossing …
A simplified Bogoliubov transform reduces a fully-interacting many-fermion spin-1/2 system-plus-environment to a more tractable many-to-one variant. The transform additionally yields exact solutions for bosonic multi-particle interactions sans the approximation introduced by using discrete time steps to deal with quantum parallelism. The decohering effect of relatively general finite environments is therewith modeled and compared to the decohering effect of an infinite environmental "bath." The anti-symmetric singlet state formed by two maximally-entangled two-state particles is shown to be in…
Giant atoms are a new paradigm of quantum optics going beyond the usual local coupling. Building on this, a new type of decoherence-free (DF) many-body Hamiltonians was shown in a broadband waveguide. Here, these are incorporated in a general framework (not relying on master equations) and contrasted to dispersive DF Hamiltonians with normal atoms: the two schemes are shown to correspond to qualitatively different ways to match the same general condition for suppressing decoherence. Next, we map the giant atoms dynamics into a cascaded collision model (CM), providing an intuitive interpretatio…
Quantum technologies able to manipulating single quantum systems, are presently developing. Among the dowries of the quantum realm, entanglement is one of the basic resources for the novel quantum revolution. Within this context, one is faced with the problem of protecting the entanglement when a system state is manipulated. In this paper, we investigate the effect of the classical driving field on the generation entanglement between two qubits interacting with a bosonic environment. We discuss the effect of the classical field on the generation of entanglement between two (different) qubits a…
We investigate the non-dissipative decoherence of three qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Modelling the environment as a set of noninteracting harmonic oscillators, analytical expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state, and the population inversion have been obtained. The pointer observable is the energy of the isolated quantum system. Coupling to environment results in exponential decay of off diagonal matrix elements of the state operator …
We revisit the protocols to create maximally entangled states between two Josephson junction (JJ) charge phase qubits coupled to a microwave field in a cavity as a quantum data bus. We devote to analyze a novel mechanism of quantum decoherence due to the adiabatic entanglement between qubits and the data bus, the off-resonance microwave field. We show that even through the variable of the data bus can be adiabatically eliminated, the entanglement between the qubits and data bus remains and can decoher the superposition of two-particle state. Fortunately we can construct a decoherence-free subs…
In spin-based architectures of quantum devices, the hyperfine interaction between the electron spin qubit and the nuclear spin environment remains one of the main sources of decoherence. This paper provides a short review of the current advances in the theoretical description of the qubit decoherence dynamics. Next, we study the qubit-environment entanglement using negativity as its measure. For an initial maximally mixed state of the environment, we study negativity dynamics as a function of environment size, changing the numbers of environmental nuclei and the total spin of the nuclei. Furth…
We investigate the effect of common bath decoherence on the qubits of Alice in the usual teleportation protocol. The system bath interaction is studied under the central spin model, where the qubits are coupled to the bath spins through isotropic Heisenberg interaction. We have given a more generalized representation of the protocol in terms of density matrices and calculated the average fidelity of the teleported state for different Bell state measurements performed by Alice. The common bath interaction differentiates the outcome of various Bell state measurements made by Alice. There will be…
The dynamics of two two-level dipole-dipole interacting atoms coupled to a common electromagnetic bath and closely located inside a lossy cavity, is reported. Initially injecting only one excitation in the two atoms-cavity system, loss mechanisms asymptotically drive the matter sample toward a stationary maximally entangled state. The role played by the closeness of the two atoms with respect to such a cooperative behaviour is carefully discussed. Stationary radiation trapping effects are found and transparently interpreted.
Maintaining coherence of a qubit is of vital importance for realizing a large-scale quantum computer in practice. In this work, we study the central spin decoherence problem in the $XXX$ central spin model (CSM) and focus on the quantum states with different initial entanglement, namely intra-bath entanglement or system-bath entanglement. We analytically obtain their evolutions of fidelity, entanglement, and quantum coherence. When the initial bath spins constitute an $N$-particle entangled state (the Greenberger-Horne-Zeilinger-bath or the $W$-bath), the leading amplitudes of their fidelity e…
We propose practical schemes for concentrating entanglement of a pair of unknown partially entangled Bell states and three-photon W states with cross-Kerr nonlinearity. In the schemes, utilizing local operations and classical communication, two separated parties can obtain one maximally entangled photon pair from two previously shared partially entangled photon pairs, and three separated parties can obtain one maximally entangled three-photon W state and a maximally entangled cluster state from two identical partially entangled three-photon W state with a certain success probability. Finally, …
By exactly solving the underlying Schödinger equation we show that one and the same resonant cavity can be used as a catalyst to maximally entangle atoms of two nonidentical groups. The generation scheme is realistic and advantageous in the sense that it is deterministic, efficient, scalable and immune from decoherence effects.
We employ the technique of weak measurement in order to enable preservation of teleportation fidelity for two-qubit noisy channels. We consider one or both qubits of a maximally entangled state to undergo amplitude damping, and show that the application of weak measurement and a subsequent reverse operation could lead to a fidelity greater than $2/3$ for any value of the decoherence parameter. The success probability of the protocol decreases with the strength of weak measurement, and is lower when both the qubits are affected by decoherence. Finally, our protocol is shown to work for the Wern…
Bounds of the minimum evolution time between two distinguishable states of a system can help to assess the maximal speed of quantum computers and communication channels. We study the quantum speed limit time of a composite quantum states in the presence of nondissipative decoherence. For the initial states with maximally mixed marginals, we obtain the exactly expressions of quantum speed limit time which mainly depend on the parameters of the initial states and the decoherence channels. Furthermore, by calculating quantum speed limit time for the time-dependent states started from a class of i…
We address the time evolution of the quantum correlations ($QCs$) such as entanglement, purity, and coherence for a model of two non-interacting qubits initially prepared as a maximally entangled bipartite state. We contrast the comparative potential of the classical fields to preserve these $QCs$ in the noisy and noiseless realms. We also disclose the characteristic dynamical behavior of the $QCs$ of the two-qubit state under the static noisy effects originating from the common and different configuration models. We show that there is a direct connection between the fluctuations allowed by an…
The time evolution of a maximally entangled bipartite systems is presented in this paper. The distillability criterion is given in terms of Kraus operators. Using the criterion, we discuss the distillability of $2\times 2$ and $n\times n (n>2)$ systems in their evolution process. There are two distinguished processes, dissipation and decoherence, which may destroy the distillability. We discuss the effects of those processes on distillability in details.
An exactly solvable model for the decoherence of one and two-qubit states interacting with a spin-bath, in the presence of a time-dependent magnetic field is studied. The magnetic field is static along $\hat{z}$ direction and oscillatory in the transverse plane. The transition probability and Rabi oscillations between the spin-states of a single qubit is shown to depend on the size of bath, the distribution of qubit-bath couplings and the initial bath polarization. In contrast to the fast Gaussian decay for short times, the polarization of the qubit shows an oscillatory power-law decay for lon…
