We introduce the definition of generic bound entanglement for the case of continuous variables. We provide some examples of bound entangled states for that case, and discuss their physical sense in the context of quantum optics. We rise the question of whether the entanglement of these states is generic. As a byproduct we obtain a new many parameter family of bound entangled states with positive partial transpose. We also point out that the ``entanglement witnesses'' and positive maps revealing the corresponding bound entanglement can be easily constructed.
We explore the possibility of entanglement detection in continuous variable systems by entanglement witnesses based on covariance matrices, constructible from random homodyne measurements. We propose new linear constraints characterizing the entanglement witnesses based on second moments, and use them in a semidefinite program providing the optimal entanglement test for given random measurements. We test the method on the class of squeezed vacuum states and study the efficiency of entanglement detection in general unknown covariance matrices.
We introduce a multi-mode squeezing coefficient to characterize entanglement in $N$-partite continuous-variable systems. The coefficient relates to the squeezing of collective observables in the $2N$-dimensional phase space and can be readily extracted from the covariance matrix. Simple extensions further permit to reveal entanglement within specific partitions of a multipartite system. Applications with nonlinear observables allow for the detection of non-Gaussian entanglement.
We propose the definition of the geometric measure of entanglement for continuous variable states. On the basis of this definition we examine entanglement of the graph states obtained as a result of action of a unitary operator on the ground state of a system of $N$ noninteracting harmonic oscillators. We find that the entanglement of a harmonic oscillator with other ones is defined by the value of its vertex degree.
We provide a method to construct entanglement criteria for arbitrary multipartite systems of discrete or continuous variables and hybrid combinations of both. While any set of local operators generates a sufficient condition for entanglement of arbitrary quantum states, a suitable set leads to a necessary and sufficient criterion for pure states. The criteria are readily implementable with existing technology and reveal entanglement that remains undetected by the respective state-of-the-art methods for discrete and continuous variables.
Given a black-box representing an unknown Boolean function $f$ of $n$ variables, in this paper we propose a fast quantum algorithm to test whether or not a certain variable in the function $f$ is a junta variable. The proposed algorithm creates entanglement between the variable under test and an auxiliary qubit, where the entanglement is measured using concurrence measure to decide if the variable is junta. The paper shows applications to the proposed algorithm in learning and categorization of Boolean functions.
We study a proposal of generating macroscopic continuous-variable entanglement with two coupled waveguides respectively carrying optical damping and optical gain. Moreover, a squeezing element is added into one or both waveguides. We show that quantum noise effect existing in the process is essential to the degree of the generated entanglement. It will totally eliminate the entanglement in the setup of adding the squeezing element into the waveguide filled with optical damping material, but will not completely damp the entanglement to zero in the other configurations of having the squeezing el…
Inspired by the discrete-variable pairwise entanglement, in this work, we in theory analyze the continuous-variable pairwise entanglement between microwave modes based on a hybrid optoelectromechanical system, where the multi-pair microwave superconducting circuits simutaneously interact with each other via a mechanical resonator, which forms a Fabry-Pérot cavity along with a standing mirror. With experimentally reachable parameter settings, wanted entanglement can be acheived when the pair number up to 10, and more is also available, which has the potential to be useful in quantum technologie…
The entanglement produced by a bilinear Hamiltonian in continuous variables has been thoroughly studied and widely used. In contrast, the physics of entanglement resulting from nonlinear interaction described by partially degenerate high-order Hamiltonians remains unclear. Here, we derive a hierarchy of sufficient and necessary conditions for the positive-partial-transposition separability of bipartite nonlinear quantum states. The proposed criteria detect the nonpositive-partial-transposition inseparability of higher-order moments of states, which provides a systematic framework for the chara…
An uncertainty relation is introduced for a symmetric arrangement of three mutually unbiased bases in continuous variable phase space, and then used to derive a bipartite entanglement criterion based on the variance of global operators composed of these three phase space variables. We test this criterion using spatial variables of photon pairs, and show that the entangled photons are correlated in three pairs of bases.
We address the non-Markovian entanglement dynamics for bimodal continuous variable quantum systems interacting with two independent structured reservoirs. We derive an analytical expression for the entanglement of formation without performing the Markov and the secular approximations. We observe a variety of qualitative features such as entanglement sudden death, dynamical generation, and protection for two types of Lorentzian spectral densities, assuming the two modes initially excited in a twin-beam state. Our quantitative analysis shows that these cases with different reservoir spectrum, th…
Quantum repeaters have been proposed as a way of extending the reach of quantum communication. First generation approaches use entanglement swapping to connect entangled links along a long distance channel. Recently, there have been proposals for first generation quantum repeaters for continuous variables. In this paper, we present an improved continuous variable repeater scheme using optimal Gaussian entanglement swapping. Our scheme uses the noiseless linear amplifier for entanglement distillation. We show that with the simplest configuration of the noiseless linear amplifier and under the a…
Quantum repeaters are critical to the development of quantum networks, enabling rates of entanglement distribution beyond those attainable by direct transmission. We consider multiple continuous-variable, squeezed light-based entanglement flows through a repeater involving noiseless linear amplification and dual homodyne detection. By analyzing a single-repeater-enhanced channel model with asymmetric losses across the repeater, we determine optimal placements of the central repeater hub in a 4-user hub-and-spoke network such that the rate of each entanglement flow through the hub is enhanced.
