separability dynamics of two mode gaussian states in parametric conversion and amplification we give a simplified form of simon s separability criterion for two mode gaussian states showing that for systems whose unitary evolution is governed by arbitrary time dependent quadratic hamiltonians the separability dynamics is completely described in terms of the determinant of the cross covariance matrix as concrete examples we consider the evolution of the inverse negativity coefficient which gives a quantitative estimation of the degree of entanglement for two initially uncoupled modes each being in a squeezed thermal state in the cases of parametric converter parametric amplifier and for a cavity whose boundary oscillates in resonance with two field modes

entanglement criteria for all bipartite gaussian states we provide a necessary and sufficient condition for separability of gaussian states of bipartite systems of arbitrarily many modes the condition provides an operational criterion since it can be checked by simple computation moreover it allows us to find a pure product state decomposition of any given separable gaussian state we also show that all bipartite gaussian states with nonpositive partial transpose are distillable

geometry of gaussian quantum states we study the hilbert schmidt measure on the manifold of mixed gaussian states in multi mode continuous variable quantum systems an analytical expression for the hilbert schmidt volume element is derived its corresponding probability measure can be used to study typical properties of gaussian states it turns out that although the manifold of gaussian states is unbounded an ensemble of gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues from which unitarily invariant properties can be obtained by contrast we find that for an ensemble of one mode gaussian states based on the bures measure the corresponding distribution cannot be normalized as important applications we determine the distribution and the mean value of von neumann entropy and purity for the hilbert schmidt measure

partial scaling transform of multiqubit states as a criterion of separability the partial scaling transform of the density matrix for multiqubit states is introduced to detect entanglement of the quantum state the transform contains partial transposition as a special case the scaling transform corresponds to partial time scaling of a subsystem or partial planck constant scaling which was recently used to formulate a separability criterion for continuous variables a measure of entanglement which is a generalization of negativity measure is introduced being based on tomographic probability description of spin states

exchangeable stationary and entangled chains of gaussian states we explore conditions on the covariance matrices of a consistent chain of mean zero finite mode gaussian states in order that the chain may be exchangeable or stationary for an exchangeable chain our conditions are necessary and sufficient every stationary gaussian chain admits an asymptotic entropy rate whereas an exchangeable chain admits a simple expression for its entropy rate in our examples of stationary chains the same admits an integral formula based on the asymptotic eigenvalue distribution for toeplitz matrices an example of a stationary entangled gaussian chain is given

functorial construction of le barz s triangle space with applications we give a new functorial construction of the space of triangles introduced by le barz this description is used to exhibit the space as a composition of smooth blowups to obtain a space of unordered triangles and to study how the space varies in a family

entanglement detection complexity and shannon entropic criteria entanglement plays a key role in quantum information the separability problem arises how to prove that a given quantum state is entangled covariance matrix based entanglement criteria are the most important and widely used approach to this problem in continuous variable systems here the separability problem is systematically studied in the more experimentally realistic setting that the questioned state is only partly known a simple general formalism is proposed for this variant of the separability problem it builds relations between certain classes of criteria and bounds the power of these criteria in particular it shows the equivalence of many seemingly different covariance matrix based criteria it offers guidance on the study of and reveals the inherent limitations of covariance matrix based criteria also a shannon entropic criterion is proposed for m n mode states it unifies and improves many known covariance matrix based criteria and shannon entropic criteria it is necessary and sufficient for 1 n mode gaussian states and m n mode bisymmetric gaussian states

entropy power uncertainty relations towards a tight inequality for all gaussian pure states we show that a proper expression of the uncertainty relation for a pair of canonically conjugate continuous variables relies on entropy power a standard notion in shannon information theory for real valued signals the resulting entropy power uncertainty relation is equivalent to the entropic formulation of the uncertainty relation due to bialynicki birula and mycielski but can be further extended to rotated variables hence based on a reasonable assumption we give a partial proof of a tighter form of the entropy power uncertainty relation taking correlations into account and provide extensive numerical evidence of its validity interestingly it implies the generalized rotation invariant schrodinger robertson uncertainty relation exactly as the original entropy power uncertainty relation implies heisenberg relation it is saturated for all gaussian pure states in contrast with hitherto known entropic formulations of the uncertainty principle

peres horodecki separability criterion for continuous variable systems the peres horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states the partial transpose operation admits in the continuous case a geometric interpretation as mirror reflection in phase space this recognition leads to uncertainty principles stronger than the traditional ones to be obeyed by all separable states for all bipartite gaussian states the peres horodecki criterion turns out to be a necessary and sufficient condition for separability

hellinger distance as a measure of gaussian discord especially investigated in recent years the gaussian discord can tentatively be quantified by a distance between a given two mode gaussian state gs and the set of all the zero discord two mode gss however as this set consists only of product states such a distance captures all the correlations quantum and classical between modes therefore it is merely an upper bound for the geometric discord no matter which is the employed distance in this work we choose for this purpose the hellinger metric that is known to have many beneficial properties recommending it as a good measure of quantum behaviour in general this metric is determined by affinity a relative of the uhlmann fidelity with which it shares many important features as a first step of our work the affinity of a pair of n mode gss is written then in the two mode case we succeeded in determining exactly the closest gaussian product state and computed the gaussian discord accordingly the obtained general formula is remarkably simple and becomes still friendlier in the significant case of symmetric two mode gss we then analyse in detail two special classes of two mode gss of theoretical and experimental interest as well the squeezed thermal states and the mode mixed thermal ones the former are separable under a well known threshold of squeezing while the latter are always separable it is worth stressing that for symmetric states belonging to either of these classes we find consistency between their geometric hellinger discord and the originally defined discord in the gaussian approach at the same time the gaussian hellinger discord of such a state turns out to be a reliable measure of the total amount of its cross correlations

wigner functions on non standard symplectic vector spaces we consider the weyl quantization on a flat non standard symplectic vector space we focus mainly on the properties of the wigner functions defined therein in particular we show that the sets of wigner functions on distinct symplectic spaces are different but have non empty intersections this extends previous results to arbitrary dimension and arbitrary constant symplectic structure as a by product we introduce and prove several concepts and results on non standard symplectic spaces which generalize those on the standard symplectic space namely the symplectic spectrum williamson s theorem and narcowich wigner spectra we also show how wigner functions on non standard symplectic spaces behave under the action of an arbitrary linear coordinate transformation

quantification of gaussian quantum steering einstein podolsky rosen steering incarnates a useful nonclassical correlation which sits between entanglement and bell nonlocality while a number of qualitative steering criteria exist very little has been achieved for what concerns quantifying steerability we introduce a computable measure of steering for arbitrary bipartite gaussian states of continuous variable systems for two mode gaussian states the measure reduces to a form of coherent information which is proven never to exceed entanglement and to reduce to it on pure states we provide an operational connection between our measure and the key rate in one sided device independent quantum key distribution we further prove that peres conjecture holds in its stronger form within the fully gaussian regime namely steering bound entangled gaussian states by gaussian measurements is impossible

dynamics of bipartite and tripartite entanglement in a dissipative system of continuous variables abstract with the help of the characteristic function and the covariance matrix we study the effect of a dissipative bath on bipartite entanglement in a system of continuous variables with no direct inter mode coupling under the dissipation induced by an agarwal bath the time evolution of entanglement between two oscillators initially in a squeezed state has been examined and an analytical criterion as a function of the squeezing parameter s and the bath temperature n has been derived for bipartite entanglement at long times resulting in an entanglement phase diagram comprising of a sudden death region and a no sudden death region if s n lies in the no sudden death region there will be sustained bipartite entanglement in the long time limit the analysis has been extended to three mode systems including fully symmetric tripartite states and bisymmetric states which are invariant with the exchange of two modes out of the three if two symmetric modes are propagated in separate baths the bipartite entanglement between one of the two and the third mode will vanish in a finite time the disappearance of the entanglement leads to a decrease in cloning fidelities to below the classical value of 0 5 for fully symmetric tripartite states both the separate and common bath cases have been considered it is found that entanglement vanishes in a finite time in the presence of separate baths while it persists for a long time in the presence of a common bath

optimized variable selection via repeated data splitting model selection in high dimensional settings has received substantial attention in recent years however similar advancements in the low dimensional setting have been lacking in this article we introduce a new variable selection procedure for low to moderate scale regressions n p this method repeatedly splits the data into two sets one for estimation and one for validation to obtain an empirically optimized threshold which is then used to screen for variables to include in the final model in an extensive simulation study we show that the proposed variable selection technique enjoys superior performance compared with candidate methods backward elimination via repeated data splitting univariate screening at 0 05 level adaptive lasso scad being amongst those with the lowest inclusion of noisy predictors while having the highest power to detect the correct model and being unaffected by correlations among the predictors we illustrate the methods by applying them to a cohort of patients undergoing hepatectomy at our institution

einstein podolsky rosen like separability indicators for two mode gaussian states we investigate the separability of the two mode gaussian states tmgss by using the variances of a pair of einstein podolsky rosen epr like observables our starting point is inspired by the general necessary condition of separability introduced by duan et al 2000 phys rev lett 84 2722 we evaluate the minima of the normalized forms of both the product and sum of such variances as well as that of a regularized sum making use of simon s separability criterion which is based on the condition of positivity of the partial transpose ppt of the density matrix simon 2000 phys rev lett 84 2726 we prove that these minima are separability indicators in their own right they appear to quantify the greatest amount of epr like correlations that can be created in a tmgs by means of local operations furthermore we reconsider the epr like approach to the separability of tmgss which was developed by duan et al with no reference to the ppt condition by optimizing the regularized form of their epr like uncertainty sum we derive a separability indicator for any tmgs we prove that the corresponding epr like condition of separability is manifestly equivalent to simon s ppt one the consistency of these two distinct approaches epr like and ppt affords a better understanding of the examined separability problem whose explicit solution found long ago by simon covers all situations of interest

on structural physical approximations and entanglement breaking maps very recently a conjecture saying that the so called structural physical approximations spas to optimal positive maps optimal entanglement witnesses give entanglement breaking eb maps separable states has been posed korbicz et al 2008 phys rev a 78 062105 the main purpose of this contribution is to explore this subject first we extend the set of entanglement witnesses supporting the conjecture then we ask whether spas constructed from other than the depolarizing channel maps also lead to eb maps and show that in general this is not the case on the other hand we prove an interesting fact that for any positive map there exists an eb channel such that the spa of constructed with the aid of is again an eb channel finally we ask similar questions in the case of continuous variable systems we provide a simple way of constructing spa and prove that in the case of the transposition map it gives the eb channel

moments of non gaussian wigner distributions and a generalized uncertainty principle i the single mode case the non negativity of the density operator of a state is faithfully coded in its wigner distribution and this coding places on the moments of the wigner distribution constraints arising from the non negativity of the density operator working in a monomial basis for the algebra of operators on the hilbert space of a bosonic mode we formulate these constraints in a canonically covariant form which is both concise and explicit since the conventional uncertainty relation is such a constraint on the first and second moments our result constitutes a generalization of the same to all orders the structure constants of in the monomial basis are shown to be essentially the su 2 clebsch gordan coefficients our results have applications in quantum state reconstruction using optical homodyne tomography and when generalized to the n mode case which will be done in the second part of this work will have applications also for continuous variable quantum information systems involving non gaussian states

inseparability of mixed two mode gaussian states generated with a su 1 1 interferometer we study the entanglement properties of two mode gaussian light emerging from a generic su 1 1 interferometer our tool is the two mode characteristic function which is determined by the 4 4 covariance matrix for an initial product of two mixed single mode gaussian states we investigate the output two mode covariance matrix its structure displays the noise properties of the reduced states as well as the correlations between modes classicality of the output two mode state is characterized by the existence of the glauber sudarshan p representation for testing separability we apply the peres simon criterion requiring preservation of the positivity of the density matrix under partial transposition since inseparability entails nonclassicality the threshold gain above which nonclassicality of the output state becomes manifest is lower than that allowing for its inseparability we find that only for a thermal input do nonclassicality and inseparability of the output have the same threshold gain

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

the space of triangles vanishing theorems and combinatorics abstract we consider compactifications of pn 3 ij the space of triples of distinct points in projective space one such space is a singular variety of configurations of points and lines another is the smooth compactification of fulton and macpherson and a third is the triangle space of schubert and semple we compute the sections of line bundles on these spaces and show that they are equal as gl n representations to the generalized schur modules associated to bad generalized young diagrams with three rows borel weil theorem on the one hand this yields weyl type character and dimension formulas for the schur modules on the other a combinatorial picture of the space of sections cohomology vanishing theorems play a key role in our analysis

entangling oscillators through environment noise we consider two independent bosonic oscillators immersed in a common bath evolving in time with a completely positive markovian quasi free gaussian reduced dynamics we show that an initially separated gaussian state can become entangled as a result of a purely noisy mechanism in certain cases the dissipative dynamics allows the persistence of these bath induced quantum correlations even in the asymptotic equilibrium state