Realignment entanglement criterion of phase damped Gaussian states

We derive the realignment entanglement criterion for non-Gaussian states prepared by two mode symmetric Gaussian states undergoing phase damping. The entanglement detecting ability is compared with that of second moment criterion and Fock space criterion of positive partial transpose. New non-Gaussian entangled states are detected.     

Two-mode Gaussian product states in a lossy interferometer

The quantum Fisher information for a two-mode, Gaussian product state in an interferometer subject to photon loss is studied. We obtain the quantum Cramer–Rao bound on the achievable precision in phase estimation using such states. The scaling of the measurement precision with the mean photon number is compared to the shot noise-limited scaling for dual squeezed vacuum states and dual squeezed, displaced vacuum states.     

Generation of entangled coherent-squeezed states: their entanglement and nonclassical properties

In this paper, after a brief review on the coherent states and squeezed states, we introduce two classes of entangled coherent-squeezed states. Next, in order to generate the introduced entangled states, we present a theoretical scheme based on the resonant atom-field interaction. In the proposed model, a \(\varLambda \)-type three-level atom interacts with a two-mode quantized field in the presence of two strong classical fields. Then, we study the amount of entanglement of the generated entangled states using the concurrence and linear entropy. Moreover, we evaluate a few of their nonclassical properties such as photon statistics, second-order correlation function, and quadrature squeezing and establish their nonclassicality features.     

Two-mode squeezing operator in circuit QED

We theoretically investigate the implementation of the two-mode squeezing operator in circuit quantum electrodynamics. Inspired by a previous scheme for optical cavities (Prado et al. in Phys Rev A 73:043803, 2006), we employ a superconducting qubit coupled to two nondegenerate quantum modes and use a driving field on the qubit to adequately control the resonator–qubit interaction. Based on the generation of two-mode squeezed vacuum states, firstly we analyze the validity of our model in the ideal situation and then we investigate the influence of the dissipation mechanisms on the generation of the two-mode squeezing operation, namely the qubit and resonator mode decays and qubit dephasing. We show that our scheme allows the generation of highly squeezed states even with the state-of-the-art parameters, leading to a theoretical prediction of more than 10 dB of two-mode squeezing. Furthermore, our protocol is able to squeeze an arbitrary initial state of the resonators, which makes our scheme attractive for future applications in continuous-variable quantum information processing and quantum metrology in the realm of circuit quantum electrodynamics.     

Elementary quantum gates in different bases

We introduce transformation matrix connecting sets of the displaced states with different displacement amplitudes. Arbitrary pure one-mode state can be represented in new basis of the displaced number (Fock) states (\(\alpha \)-representation) by multiplying the transposed transformation matrix on a column vector of initial state. Analytical expressions of the \(\alpha \)-representation of superposition of vacuum and single photon and two-mode squeezed vacuum are obtained. On the basis of the developed mathematical formalism, we consider the mechanism of interaction between qubits which is based on their displaced properties. Superposed coherent states deterministically displace target state on equal modulo but opposite on sign values. Registration of the single photon in auxiliary mode (probabilistic operation) results in constructive interference and gives birth to entangled hybrid state corresponding to outcome of elementary quantum gates. The method requires minimal number of resource and works in realistic scenario.     

Nonlinear entanglement witnesses based on continuous-variable local orthogonal observables for bipartite systems

In this paper, a nonlinear entanglement witness criterion based on continuous-variable local orthogonal observables for bipartite states is established, which is strictly stronger than the the linear entanglement witnesses criterion introduced by Zhang et al. (Phys. Rev. Lett. 111:190501, 2013). This criterion is particularly applied to two-mode Gaussian states yielding a criterion in terms of the covariance matrix. Comparison with CCNR criterion is discussed.     

Quantum correlations for bipartite continuous-variable systems

Two quantum correlations Q and \(Q_\mathcal P\) for \((m+n)\)-mode continuous-variable systems are introduced in terms of average distance between the reduced states under the local Gaussian positive operator-valued measurements, and analytical formulas of these quantum correlations for bipartite Gaussian states are provided. It is shown that the product states do not contain these quantum correlations, and conversely, all \((m+n)\)-mode Gaussian states with zero quantum correlations are product states. Generally, \(Q\ge Q_{\mathcal P}\), but for the symmetric two-mode squeezed thermal states, these quantum correlations are the same and a computable formula is given. In addition, Q is compared with Gaussian geometric discord for symmetric squeezed thermal states.     

Entanglement detection and distillation for arbitrary bipartite systems

We present an inequality for detecting entanglement and distillability of arbitrary dimensional bipartite systems. This inequality provides a sufficient condition of entanglement for bipartite mixed states, and a necessary and sufficient condition of entanglement for bipartite pure states. Moreover, the inequality also gives a necessary and sufficient condition for distillability.     

Quantification of entanglement of teleportation in arbitrary dimensions

We study bipartite entangled states in arbitrary dimensions and obtain different bounds for the entanglement measures in terms of teleportation fidelity. We find that there is a simple relation between negativity and teleportation fidelity for pure states, but for mixed states, an upper bound is obtained for negativity in terms of teleportation fidelity using convex-roof extension negativity. However, with this, it is not clear how to distinguish between states useful for teleportation and positive partial transpose (PPT) entangled states. Further, there exists a strong conjecture in the literature that all PPT entangled states, in $3 \otimes 3$ systems, have Schmidt rank two. This motivates us to develop measures capable of identifying states useful for teleportation and dependent on the Schmidt number. We thus establish various relations between teleportation fidelity and entanglement measures depending upon Schmidt rank of the states. These relations and bounds help us to determine the amount of entanglement required for teleportation, which we call the “Entanglement of Teleportation.” These bounds are used to determine the teleportation fidelity as well as the entanglement required for teleportation of states modeled by a two-qutrit mixed system, as well as two-qubit open quantum systems.     

An entanglement concentration protocol for cluster states

Cluster class states are entangled states which have several uses in quantum information and computation problems. In this paper we develop an entanglement concentration protocol for partially entangled pure cluster class state with an even number of qubits. We use only local operations for this protocol.     

Entanglement,Purity, and Information Entropies in Continuous Variable Systems

Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal (i.e. referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or, in general, by information entropies, provides an accurate characterization of its entanglement. In particu-lar, for Gaussian states of continuous variable systems, we classify the entanglement of two-mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized p-entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entan-glement in highly symmetric Gaussian states of arbitrary 1 × N-mode partitions.Presented at the International Conference “Entanglement, Information & Noise”, Krzyżowa, Poland, June 14–20, 2004.     

Experimentally identifying the entanglement class of pure tripartite states

We use concurrence as an entanglement measure and experimentally demonstrate the entanglement classification of arbitrary three-qubit pure states on a nuclear magnetic resonance quantum information processor. Computing the concurrence experimentally under three different bipartitions, for an arbitrary three-qubit pure state, reveals the entanglement class of the state. The experiment involves measuring the expectation values of Pauli operators. This was achieved by mapping the desired expectation values onto the local z magnetization of a single qubit. We tested the entanglement classification protocol on twenty-seven different generic states and successfully detected their entanglement class. Full quantum state tomography was performed to construct experimental tomographs of each state and negativity was calculated from them, to validate the experimental results.     

Quantum steering borders in three-qubit systems

We discuss a family of states describing three-qubit systems in a context of quantum steering phenomena. We show that symmetric steering cannot appear between two qubits—only asymmetric steering can appear in such systems. The main aim of this paper is to discuss the possible relations between the entanglement measures and steering parameter for two-mode mixed state corresponding to the qubit–qubit subsystem. We have derived the conditions determining boundary values of the negativity parametrized by concurrence. We show that two-qubit mixed state cannot be steerable when the negativity of such state is smaller than, or equal to, its boundary value. Finally, we have found ranges of the values of the mixedness measure, parametrized by concurrence and negativity for steerable and unsteerable two-qubit mixed states.     

Tripartite entanglement dynamics in the presence of Markovian or non-Markovian environment

We study on the tripartite entanglement dynamics when each party is initially entangled with other parties, but they locally interact with their own Markovian or non-Markovian environment. First we consider three GHZ-type initial states, all of which have GHZ-symmetry provided that the parameters are chosen appropriately. However, this symmetry is broken due to the effect of environment. The corresponding \(\pi \)-tangles, one of the tripartite entanglement measures, are analytically computed at arbitrary time. For Markovian case while the tripartite entanglement for type I exhibits an entanglement sudden death, the dynamics for the remaining cases decays normally in time with the half-life rule. For non-Markovian case the revival phenomenon of entanglement occurs after complete disappearance of entanglement. We also consider two W-type initial states. For both cases the \(\pi \)-tangles are analytically derived. The revival phenomenon also occurs in this case. On the analytical ground the robustness or fragility issue against the effect of environment is examined for both GHZ-type and W-type initial states.     

Quantum information at the interface of light with atomic ensembles and micromechanical oscillators

This article reviews recent research towards a universal light-matter interface. Such an interface is an important prerequisite for long distance quantum communication, entanglement assisted sensing and measurement, as well as for scalable photonic quantum computation. We review the developments in light-matter interfaces based on room temperature atomic vapors interacting with propagating pulses via the Faraday effect. This interaction has long been used as a tool for quantum nondemolition detections of atomic spins via light. It was discovered recently that this type of light-matter interaction can actually be tuned to realize more general dynamics, enabling better performance of the light-matter interface as well as rendering tasks possible, which were before thought to be impractical. This includes the realization of improved entanglement assisted and backaction evading magnetometry approaching the Quantum Cramer-Rao limit, quantum memory for squeezed states of light and the dissipative generation of entanglement. A separate, but related, experiment on entanglement assisted cold atom clock showing the Heisenberg scaling of precision is described. We also review a possible interface between collective atomic spins with nano- or micromechanical oscillators, providing a link between atomic and solid state physics approaches towards quantum information processing.     

Lower bounds of concurrence for <Emphasis Type="Italic">N</Emphasis>-qubit systems and the detection of <Emphasis Type="Italic">k</Emphasis>-nonseparability of multipartite quantum systems

Concurrence, as one of the entanglement measures, is a useful tool to characterize quantum entanglement in various quantum systems. However, the computation of the concurrence involves difficult optimizations and only for the case of two qubits, an exact formula was found. We investigate the concurrence of four-qubit quantum states and derive analytical lower bound of concurrence using the multiqubit monogamy inequality. It is shown that this lower bound is able to improve the existing bounds. This approach can be generalized to arbitrary qubit systems. We present an exact formula of concurrence for some mixed quantum states. For even-qubit states, we derive an improved lower bound of concurrence using a monogamy equality for qubit systems. At the same time, we show that a multipartite state is k-nonseparable if the multipartite concurrence is larger than a constant related to the value of k, the qudit number and the dimension of the subsystems. Our results can be applied to detect the multipartite k-nonseparable states.     

Common entanglement witnesses and their characteristics

We investigate the issue of finding common entanglement witness for certain class of states and extend this study to the case of Schmidt number witnesses. We also introduce the notion of common decomposable and non-decomposable witness operators which is specially useful for constructing a common witness where one of the entangled states is with a positive partial transpose. Our approach is illustrated with the help of suitable examples of qutrit systems.     

General monogamy relations of quantum entanglement for multiqubit <Emphasis Type="Italic">W</Emphasis>-class states

Entanglement monogamy is a fundamental property of multipartite entangled states. We investigate the monogamy relations for multiqubit generalized W-class states. Analytical monogamy inequalities are obtained for the concurrence of assistance, the entanglement of formation, and the entanglement of assistance.     

Entanglement dynamics in two-parameter qubit–qutrit states under Dzyaloshinskii–Moriya interaction

We study entanglement dynamics in two-parameter qubit–qutrit states under the influence of Dzyaloshisnhkii–Moriya (DM) interaction. Our system consists of a qubit–qutrit pair as a closed system initially in two-parameter class of states, and one environmental qubit interacts with the qutrit of the closed system via DM interaction. We divide our analysis into two cases. In the first case, we study the entanglement dynamics in separable region, and in the second case we study the same in non-separable region. The DM interaction produces the entanglement in separable region with entanglement sudden death (ESD) and some states in this region remain unaffected by the same. In non-separable region, all the states are affected by DM interaction. The DM interaction excites the entanglement but does not produce ESD in this region. We observed that probability amplitude of environmental qubit does not affect the entanglement in two-parameter qubit–qutrit states in both the regions.     

Noise effects on entanglement distribution by separable state

We investigate noise effects on the performance of entanglement distribution by separable state. We consider a realistic situation in which the mediating particle between two distant nodes of the network goes through a noisy channel. For a large class of noise models, we show that the average value of distributed entanglement between two parties is equal to entanglement between particular bipartite partitions of target qubits and exchange qubit in intermediate steps of the protocol. This result is valid for distributing two-qubit/qudit and three-qubit entangled states. In explicit examples of the noise family, we show that there exists a critical value of noise parameter beyond which distribution of distillable entanglement is not possible. Furthermore, we determine how this critical value increases in terms of Hilbert space dimension, when distributing d-dimensional Bell states.