Extremality of Gaussian quantum states

We investigate Gaussian quantum states in view of their exceptional role within the space of all continuous variables states. A general method for deriving extremality results is provided and applied to entanglement measures, secret key distillation and the classical capacity of bosonic quantum channels. We prove that for every given covariance matrix the distillable secret key rate and the entanglement, if measured appropriately, are minimized by Gaussian states. This result leads to a clearer picture of the validity of frequently made Gaussian approximations. Moreover, it implies that Gaussian encodings are optimal for the transmission of classical information through bosonic channels, if the capacity is additive.     

Quantifying non-classical correlations under thermal effects in a double cavity optomechanical system

We investigate the generation of quantum correlations between mechanical modes and optical modes in an optomechanical system,using the rotating wave approximation.The system is composed of two Fabry-Perot cavities separated in space;each of the two cavities has a movable end-mirror.Our aim is the evaluation of entanglement between mechanical modes and optical modes,generated by correlations transfer from the squeezed light to the system,using Gaussian intrinsic entanglement as a witness of entanglement in continuous variables Gaussian states,and the quantification of the degree of mixedness of the Gaussian states using the purity.Then,we quantify nonclassical correlations between mechanical modes and optical modes even beyond entanglement by considering Gaussian geometric discord via the Hellinger distance.Indeed,entanglement,mixdness,and quantum discord are analyzed as a function of the parameters characterizing the system(thermal bath temperature,squeezing parameter,and optomechanical cooperativity).We find that,under thermal effect,when entanglement vanishes,purity and quantum discord remain nonzero.Remarkably,the Gaussian Hellinger discord is more robust than entanglement.The effects of the other parameters are discussed in detail.     

Entanglement generation and protection for two atoms in the presence of two parallel mirrors

We study, in the framework of open quantum systems, the entanglement generation of two atoms in between two parallel mirrors in a thermal bath of quantum scalar fields. We find that the presence of mirrors plays an important role in entanglement generation and protection. The entanglement dynamics is crucially dependent on the geometric configurations of the two-atom system with respect to the mirrors, and the ranges of temperature and interatomic separation within which entanglement can be generated are significantly changed compared with those in a free space. In particular, when the atomic transition wavelength is larger than twice the distance between the two mirrors, the atoms behave as if they were isolated from the environment and the entanglement can persist in the steady state if the atoms are initially entangled and no entanglement can be created if they are initially separable, no matter how the atoms are placed with respect to the mirrors and to each other. This is in sharp contrast to the fact that in a free space, steady-state entanglement is possible only when the two atoms are placed extremely close to each other, while in the presence of one mirror, it is possible when the two atoms placed extremely close to the mirror.     

Gaussification and entanglement distillation of continuous-variable systems: a unifying picture

Distillation of entanglement using only Gaussian operations is an important primitive in quantum communication, quantum repeater architectures, and distributed quantum computing. Existing distillation protocols for continuous degrees of freedom are only known to converge to a Gaussian state when measurements yield precisely the vacuum outcome. In sharp contrast, non-Gaussian states can be deterministically converted into Gaussian states while preserving their second moments, albeit by usually reducing their degree of entanglement. In this work-based on a novel instance of a noncommutative central limit theorem-we introduce a picture general enough to encompass the known protocols leading to Gaussian states, and new classes of protocols including multipartite distillation. This gives the experimental option of balancing the merits of success probability against entanglement produced.     

Monogamy inequality for distributed gaussian entanglement

We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.     

How much quantum noise of amplifiers is detrimental to entanglement

We analyze the effect of the quantum noise of an amplifier on the entanglement properties of an input state. We consider both phase insensitive and phase sensitive amplification and specialize to Gaussian states for which entanglement measures are well developed. In the case of phase insensitive amplification in which both the modes are symmetrically amplified, we find that the entanglement in the output state vanishes if the intensity gain exceeds a limiting value 2/(1+exp[-E_N]) where E_N is the logarithmic negativity of the input state which quantifies the initial entanglement between the two modes. The entanglement between the two modes at the output is found to be more robust if only one mode is amplified.     

Operational quantification of continuous-variable correlations

We quantify correlations (quantum and/or classical) between two continuous-variable modes as the maximal number of correlated bits extracted via local quadrature measurements. On Gaussian states, such "bit quadrature correlations" majorize entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, photon-subtracted states, and mixtures of Gaussian states, the bit correlations are shown to be a monotonic function of the negativity. This quantification yields a feasible, operational way to measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without a complete state tomography.     

Optical implementation and entanglement distribution in Gaussian valence bond states

We study Gaussian valence bond states of continuous variable systems obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites applied at each ofN sites of a harmonic chain. The entanglement distribution in Gaussian valence bond states can be controlled by varying the input amount of entanglement engineered in a (2M+ 1)-mode Gaussian state known as the building block, which is isomorphic to the projector applied at a given site. We show how this mechanism can be interpreted in terms of multiple entanglement swapping from the chain of ancillary bonds, through the building blocks. We provide optical schemes to produce bisymmetric three-mode Gaussian building blocks (which correspond to a single bond, M = 1), and study the entanglement structure in the output Gaussian valence bond states. Finally, the usefulness of such states for quantum communication protocols with continuous variables, like telecloning and teleportation networks, is discussed. The text was submitted by the authors in English.     

Enhancement of next-nearest-neighbouring entanglement in quantum Ising spin chain

Using the method of the Jordan--Wigner transformation for solving different spin--spin correlation functions, we have investigated the generation of next-nearest-neighbouring entanglement in a one-dimensional quantum Ising spin chain with the Gaussian distribution impurities of exchange couplings and external magnetic fields taken into account. The maximal value of entanglement between the next-nearest-neighbouring qubits in the transverse Ising model was analysed in detail by varying the effectively controlled parameters such as interchange coupling, magnetic field and the system impurity. For such systems, where both exchange couplings and external magnetic field disorder appear, we show that it is possible to achieve next-nearest-neighbouring entanglement better than the previously discussed pure Ising spin chain case. We also show that the Gaussian distribution impurity can induce next-nearest-neighbouring entanglement, which can be used as a means to characterize quantum phase transition.     

Entanglement behaviors of two-mode squeezed thermal states in two different environments

We study entanglement properties of two-mode squeezed thermal states subjected to two sources of decoherence: the common reservoirs and the bosonic memory Gaussian channel. For the former one, we find that there exist three different behaviors: no-sudden death, sudden death, and no-creation of entanglement. The range of parameters characterizing these processes is obtained. For the latter one, we obtain a threshold in the degree of squeezing above which the input states remain always entangled. Otherwise, no entanglement is allowed in bosonic Gaussian channel with memory effect. We show that a degree of memory for quantum channel can be help to increase the initial entanglement, while the mean number of added thermal photons is to fasten the decoherence process.     

Detection of macroscopic entanglement by correlation of local observables

We propose a correlation of local observables on many sites in macroscopic quantum systems. By measuring the correlation one can detect, if any, superposition of macroscopically distinct states, which we call macroscopic entanglement, in arbitrary quantum states that are (effectively) homogeneous. Using this property, we also propose an index of macroscopic entanglement.     

Squeezed-state purification with linear optics and feedforward

A scheme for optimal and deterministic linear optical purification of mixed squeezed Gaussian states is proposed and experimentally demonstrated. The scheme requires only linear optical elements and homodyne detectors, and allows the balance between purification efficacy and squeezing degradation to be controlled. One particular choice of parameters gave a tenfold reduction of the thermal noise with a corresponding squeezing degradation of only 11%. We prove optimality of the protocol, and show that it can be used to enhance the performance of quantum informational protocols such as dense coding and entanglement generation.     

Entanglement of formation for symmetric Gaussian states

We show that for a fixed amount of entanglement, two-mode squeezed states are those that maximize Einstein-Podolsky-Rosen-like correlations. We use this fact to determine the entanglement of formation for all symmetric Gaussian states corresponding to two modes. This is the first instance in which this measure has been determined for genuine continuous variable systems.     

Macroscopic entanglement by entanglement swapping

We present a scheme for entangling two micromechanical oscillators. The scheme exploits the quantum effects of radiation pressure and it is based on a novel application of entanglement swapping, where standard optical measurements are used to generate purely mechanical entanglement. The scheme is presented by first solving the general problem of entanglement swapping between arbitrary bipartite Gaussian states, for which simple input-output formulas are provided.