multiqubit nonlocality in families of 3 and 4 qubit entangled states we investigate genuine multiqubit nonlocality in families of entangled 3 and 4 qubit pure states by analyzing a bell type inequality that is violated only if all qubits are nonlocally correlated we present detailed numerical studies of the relationship between entanglement and violation of the svetlichny bell type inequality in an experimentally accessible set of 3 qubit pure states and identify the special nonlocality property of the maximal slice states in the space of all 3 qubit pure states we also analyze nonlocal correlations in 3 qubit generalized greenberger horne zeilinger ghz states and extend our analysis to the case of 4 qubit generalized ghz states we show that like the 3 qubit case some 4 qubit generalized ghz states do not violate a bell inequality that tests for genuine 4 qubit nonlocality furthermore the location of the boundary between the states that do violate the inequality and those that do not is the same for the 3 and 4 qubit generalized ghz states

fully nonlocal monogamous and random genuinely multipartite quantum correlations local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal monogamous and with fully random outcomes this makes these states ideal for bipartite cryptographic tasks genuine multipartite nonlocality constitutes a stronger notion of nonlocality in the multipartite case maximal genuine multipartite nonlocality monogamy and random outcomes are thus highly desired properties for genuine multipartite cryptographic scenarios we prove that local measurements on any greenberger horne zeilinger state can produce correlations that are fully genuine multipartite nonlocal monogamous and with fully random outcomes a key ingredient in our proof is a multipartite chained bell inequality detecting genuine multipartite nonlocality which we introduce finally we discuss applications to device independent secret sharing

relativistic gamow vectors the friedrichs model has often been used in order to obtain explicit formulas for eigenvectors associated to complex eigenvalues corresponding to lifetimes such eigenvectors are called gamow vectors and they acquire meaning in extensions of the conventional hilbert space of quantum theory to the so called rigged hilbert space in this paper gamow vectors are constructed for a solvable model of an unstable relativistic field as a result we obtain a time asymmetric relativistic extension of the fock space this extension leads to two distinct poincare semigroups the time reversal transformation maps one semigroup to the other as a result the usual pct invariance should be extended we show that irreversibility as expressed by dynamical semigroups is compatible with the requirements of relativity

an exact approach to the oscillator radiation process in an arbitrarily large cavity starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius r we study the behaviour of the system in free space as the limit of an arbitrarily large radius in the confined solution from a mathematical point of view we show that this way of addressing the problem is not equivalent to considering the system a priori embedded in infinite space in particular the matrix elements of the transformation turning the system to the principal axis do not tend to distributions in the limit of an arbitrarily large sphere as should be the case if the two procedures were mathematically equivalent also we introduce dressed coordinates which allow an exact description of the oscillator radiation process expanding in powers of the coupling constant we recover from our exact expressions the well known decay formulae from perturbation theory

oscillation threshold of a clarinet model a numerical continuation approach this paper focuses on the oscillation threshold of single reed instruments several characteristics such as blowing pressure at threshold regime selection and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion previous works have shown interesting tendencies using analytical expressions with simplified models in the present study a more elaborated physical model is considered the influence of several parameters depending on the reed properties the design of the instrument or the control operated by the player are studied previous results on the influence of the reed resonance frequency are confirmed new results concerning the simultaneous influence of two model parameters on oscillation threshold regime selection and playing frequency are presented and discussed the authors use a numerical continuation approach numerical continuation consists in following a given solution of a set of equations when a parameter varies considering the instrument as a dynamical system the oscillation threshold problem is formulated as a path following of hopf bifurcations generalizing the usual approach of the characteristic equation as used in previous works the proposed numerical approach proves to be useful for the study of musical instruments it is complementary to analytical analysis and direct time domain or frequency domain simulations since it allows to derive information that is hardly reachable through simulation without the approximations needed for analytical approach

looking for symmetric bell inequalities finding all bell inequalities for a given number of parties measurement settings and measurement outcomes is in general a computationally hard task we show that all bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full bell polytope as an illustration of our method we generate 238 885 new bell inequalities and 1085 new svetlichny inequalities we find in particular facet inequalities for bell experiments involving two parties and two measurement settings that are not of the collins gisin linden massar popescu type

stronger two observer all versus nothing violation of local realism we introduce a two observer all versus nothing proof of bell s theorem which reduces the number of required quantum predictions from 9 a cabello phys rev lett 87 010403 2001 z b chen et al phys rev lett 90 160408 2003 to 4 provides a greater amount of evidence against local realism reduces the detection efficiency requirements for a conclusive experimental test of bell s theorem and leads to a bell inequality which resembles mermin s inequality for three observers n d mermin phys rev lett 65 1838 1990 but requires only two observers

a framework for the study of symmetric full correlation bell like inequalities full correlation bell like inequalities represent an important subclass of bell like inequalities that have found applications in both a better understanding of fundamental physics and in quantum information science loosely speaking these are inequalities where only measurement statistics involving all parties play a role in this paper we provide a framework for the study of a large family of such inequalities that are symmetrical with respect to arbitrary permutations of the parties as an illustration of the power of our framework we derive i a new family of svetlichny inequalities for arbitrary numbers of parties settings and outcomes ii a new family of two outcome device independent entanglement witnesses for genuine n partite entanglement and iii a new family of two outcome tsirelson inequalities for arbitrary numbers of parties and settings we also discuss briefly the application of these new inequalities in the characterization of quantum correlations

a purely frequency based floquet hill formulation for the efficient stability computation of periodic solutions of ordinary differential systems abstract since the founding theory established by g floquet more than a hundred years ago computing the stability of periodic solutions has given rise to various numerical methods mostly depending on the way the periodic solutions are themselves determined either in the time domain or in the frequency domain in this paper we address the stability analysis of branches of periodic solutions that are computed by combining a pure harmonic balance method hbm with an asymptotic numerical method anm hbm is a frequency domain method for determining periodic solutions under the form of fourier series and anm is continuation technique that relies on high order taylor series expansion of the solutions branches with respect to a path parameter it is well established now that this hbm anm combination is efficient and reliable provided that the system of ode is first of all recasted with quadratic nonlinearities allowing an easy manipulation of both the taylor and the fourier series in this context hill s method a frequency domain version of floquet theory is revisited so as to become a by product of the hbm applied to a quadratic system allowing the stability analysis to be implemented in an elegant way and with good computing performances the different types of stability changes of periodic solutions are all explored and illustrated through several academic examples including systems that are autonomous or not conservative or not free or forced

multipartite nonlocality as a resource and quantum correlations having indefinite causal order the characterization of quantum correlations in terms of information theoretic resource has been a fruitful approach to understand the power of quantum correlations as a resource while bipartite entanglement and bell inequality violation in this setting have been extensively studied relatively little is known about their multipartite counterpart in this paper we apply and adapt the recently proposed definitions of multipartite nonlocality bancal et al 2013 phys rev a 88 014102 to the three and four partite scenarios to gain new insight on the resource aspect of multipartite nonlocal quantum correlations specifically we show that reproducing certain tripartite quantum correlations requires mixtures of classical resources be it the ability to change the groupings or the time orderings of measurements thus when seen from the perspective of biseparable one way classical signaling resources certain tripartite quantum correlations do not admit a definite causal order in the four partite scenario we obtain a superset description of the set of biseparable correlations which can be produced by allowing two groups of bipartite non signaling resources quantum violation of the resulting bell like inequalities is investigated as a byproduct we obtain some new examples of device independent witnesses for genuine four partite entanglement and also device independent witnesses that allow one to infer the structure of the underlying multipartite entanglement this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

method of convex rigid frames and applications in studies of multipartite qunit pure states in this letter we suggest a method of convex rigid frames in the studies of multipartite qunit pure states we illustrate what the convex rigid frames are and what is their method as applications we use this method to solve some basic problems and give some new results three theorems the problem of the partial separability of the multipartite qunit pure states and its geometric explanation the problem of the classification of multipartite qunit pure states giving a perfect explanation of the local unitary transformations thirdly we discuss the invariants of classes and give a possible physical explanation

multigraph approach to quantum non locality non contextuality nc and bell inequalities can be expressed as bounds for positive linear combinations s of probabilities of events exclusive events in s can be represented as adjacent vertices of a graph called the exclusivity graph of s in the case that events correspond to the outcomes of quantum projective measurements quantum probabilities are intimately related to the grotschel lovasz schrijver theta body of the exclusivity graph then one can easily compute an upper bound to the maximum quantum violation of any nc or bell inequality by optimizing s over the theta body and calculating the lovasz number of the corresponding exclusivity graph in some cases this upper bound is tight and gives the exact maximum quantum violation however in general this is not the case the reason is that the exclusivity graph does not distinguish among the different ways exclusivity can occur in bell inequality and similar scenarios an interesting question is whether there is a graph theoretical concept which accounts for this problem here we show that for any given n partite bell inequality an edge coloured multigraph composed of n single colour graphs can be used to encode the relationships of exclusivity between each party s parts of the events then the maximum quantum violation of the bell inequality is exactly given by a refinement of the lovasz number that applies to these edge coloured multigraphs we show how to calculate upper bounds for this number using a hierarchy of semi definite programs and calculate upper bounds for i3 i3322 and the three bipartite bell inequalities whose exclusivity graph is a pentagon the multigraph theoretical approach introduced here may remove some obstacles in the program of explaining quantum correlations from first principles this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

bell type inequalities for partial separability in n particle systems and quantum mechanical violations we derive n particle bell type inequalities under the assumption of partial separability i e that the n particle system is composed of subsystems which may be correlated in any way e g entangled but which are uncorrelated with respect to each other these inequalities provide upon violation experi mentally accessible sufficient conditions for full n particle entanglement i e for n particle entanglement that cannot be reduced to mixtures of states in which a smaller number of particles are entangled the inequalities are shown to be maximally violated by the n particle greenberger horne zeilinger states

flute like musical instruments a toy model investigated through numerical continuation abstract self sustained musical instruments bowed string woodwind and brass instruments can be modelled by nonlinear lumped dynamical systems among these instruments flutes and flue organ pipes present the particularity to be modelled as a delay dynamical system in this paper such a system a toy model of flute like instruments is studied using numerical continuation equilibrium and periodic solutions are explored with respect to the blowing pressure with focus on amplitude and frequency evolutions along the different solution branches as well as jumps between periodic solution branches the influence of a second model parameter namely the inharmonicity on the behaviour of the system is addressed it is shown that harmonicity plays a key role in the presence of hysteresis or quasiperiodic regime throughout the paper experimental results on a real instrument are presented to illustrate various phenomena and allow some qualitative comparisons with numerical results

tripartite entanglement versus tripartite nonlocality in three qubit greenberger horne zeilinger class states we analyze the relationship between tripartite entanglement and genuine tripartite nonlocality for three qubit pure states in the greenberger horne zeilinger class we consider a family of states known as the generalized greenberger horne zeilinger states and derive an analytical expression relating the three tangle which quantifies tripartite entanglement to the svetlichny inequality which is a bell type inequality that is violated only when all three qubits are nonlocally correlated we show that states with three tangle less than 1 2 do not violate the svetlichny inequality on the other hand a set of states known as the maximal slice states does violate the svetlichny inequality and exactly analogous to the two qubit case the amount of violation is directly related to the degree of tripartite entanglement we discuss further interesting properties of the generalized greenberger horne zeilinger and maximal slice states

all versus nothing inseparability for two observers a recent proof of bell s theorem without inequalities a cabello phys rev lett 86 1911 2001 is formulated as a greenberger horne zeilinger type proof involving just two observers on one hand this new approach allows us to derive an experimentally testable bell inequality which is violated by quantum mechanics on the other hand it leads to a new state independent proof of the kochen specker theorem and provides a wider perspective on the relations between the major proofs of no hidden variables

quantifying multipartite nonlocality the nonlocal correlations of multipartite entangled states can be reproduced by a classical model if sufficiently many parties join together or if sufficiently many parties broadcast their measurement inputs the maximal number m of groups and the minimal number k of broadcasting parties that allow for the reproduction of a given set of correlations quantify their multipartite nonlocal content we show how upper bounds on m and lower bounds on k can be computed from the violation of the mermin svetlichny inequalities while n partite greenberger horne zeilinger states violate these inequalities maximally we find that w states violate them only by a very small amount

joint measurements and svetlichny s inequality we prove that svetlichny s inequality can be derived from the existence of joint measurements and the principle of no signaling then we show that on the basis of the assumption of quantum measurement it would imply the breach of causality if the magnitude of violation of svetlichny s inequality exceeds the quantum bound

response of an artificially blown clarinet to different blowing pressure profiles using an artificial mouth with an accurate pressure control the onset of the pressure oscillations inside the mouthpiece of a simplified clarinet is studied experimentally two time profiles are used for the blowing pressure in a first set of experiments the pressure is increased at constant rates then decreased at the same rate in a second set of experiments the pressure rises at a constant rate and is then kept constant for an arbitrary period of time in both cases the experiments are repeated for different increase rates numerical simulations using a simplified clarinet model blown with a constantly increasing mouth pressure are compared to the oscillating pressure obtained inside the mouthpiece both show that the beginning of the oscillations appears at a higher pressure values than the theoretical static threshold pressure a manifestation of bifurcation delay experiments performed using an interrupted increase in mouth pressure show that the beginning of the oscillation occurs close to the stop in the increase of the pressure experimental results also highlight that the speed of the onset transient of the sound is roughly the same independently of the duration of the increase phase of the blowing pressure

explicit mapping of acoustic regimes for wind instruments this paper proposes a methodology to map the various acoustic regimes of wind instruments the maps can be generated in a multidimensional space consisting of design control parameters and initial conditions the boundaries of the maps are obtained explicitly in terms of the parameters using a support vector machine svm classifier as well as a dedicated adaptive sampling scheme the approach is demonstrated on a simplified clarinet model for which several maps are generated based on different criteria examples of computation of the probability of occurrence of a specific acoustic regime are also provided in addition the approach is demonstrated on a design optimization example for optimal intonation

nonclassical correlations from randomly chosen local measurements we show that correlations inconsistent with any locally causal description can be a generic feature of measurements on entangled quantum states specifically spatially separated parties who perform local measurements on a maximally entangled state using randomly chosen measurement bases can with significant probability generate nonclassical correlations that violate a bell inequality for n parties using a greenberger horne zeilinger state this probability of violation rapidly tends to unity as the number of parties increases we also show that even with both a randomly chosen two qubit pure state and randomly chosen measurement bases a violation can be found about 10 of the time among other applications our work provides a feasible alternative for the demonstration of bell inequality violation without a shared reference frame

linear modal stability analysis of bowed strings linearised models are often invoked as a starting point to study complex dynamical systems besides their attractive mathematical simplicity they have a central role for determining the stability properties of static or dynamical states and can often shed light on the influence of the control parameters on the system dynamical behaviour while the bowed string dynamics has been thoroughly studied from a number of points of view mainly by time domain computer simulations this paper proposes to explore its dynamical behaviour adopting a linear framework linearising the friction force near an equilibrium state in steady sliding conditions and using a modal representation of the string dynamics starting from the simplest idealisation of the friction force given by coulomb s law with a velocity dependent friction coefficient the linearised modal equations of the bowed string are presented and the dynamical changes of the system as a function of the bowing parameters are studied using linear stability

bell klyshko inequalities to characterize maximally entangled states of n qubits this letter presents the first rigorous proof of the conjecture raised by gisin and bechmann pasquinucci phys lett a 246 1 1998 that the greenberger horne zeilinger states of n qubits and the states obtained from them by local unitary transformations are the unique states that maximally violate the bell klyshko inequalities the proof is obtained by using the certain algebraic properties that pauli s matrices satisfy and some subtle mathematical techniques since all states obtained by local unitary transformations of a maximally entangled state are equally valid entangled states we thus give a characterization of maximally entangled states of n qubits in terms of the bell type inequality

quantum correlations are tightly bound by the exclusivity principle it is a fundamental problem in physics of what principle limits the correlations as predicted by our current description of nature based on quantum mechanics one possible explanation is the global exclusivity principle recently discussed in phys rev lett 110 060402 2013 in this work we show that this principle actually has a much stronger restriction on the probability distribution we provide a tight constraint inequality imposed by this principle and prove that this principle singles out quantum correlations in scenarios represented by any graph our result implies that the exclusivity principle might be one of the fundamental principles of nature

dressed coordinates the path integral approach the recently introduced dressed coordinates are studied in the path integral approach these coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and it is shown that in this model the dressed coordinates appear as a coordinate transformation preserving the path integral functional measure the analysis also generalizes the sum rules established in a previous work

device independent witnesses of genuine multipartite entanglement we consider the problem of determining whether genuine multipartite entanglement was produced in an experiment without relying on a characterization of the systems observed or of the measurements performed we present an n partite inequality that is satisfied by all correlations produced by measurements on biseparable quantum states but which can be violated by n partite entangled states such as greenberger horne zeilinger states in contrast to traditional entanglement witnesses the violation of this inequality implies that the state is not biseparable independently of the hilbert space dimension and of the measured operators violation of this inequality does not imply however genuine multipartite nonlocality we show more generically how the problem of identifying genuine tripartite entanglement in a deviceindependent way can be addressed through semidefinite programming

multipartite separability inequalities exponentially stronger than local reality inequalities i show that separability of n partite quantum states implies new inequalities on bell correlations which are stronger than the corresponding mermin roy singh local reality inequalities by a factor of 2 n 1 2

separability problem for multipartite states of rank at most 4 one of the most important problems in quantum information is the separability problem which asks whether a given quantum state is separable we investigate multipartite states of rank at most 4 which are ppt i e all their partial transposes are positive semidefinite we show that any ppt state of rank 2 or 3 is separable and has length at most 4 for separable states of rank 4 we show that they have length at most 6 it is six only for some qubit qutrit or multiqubit states it turns out that any ppt entangled state of rank 4 is necessarily supported on a 3 3 or a 2 2 2 subsystem we obtain a very simple criterion for the separability problem of the ppt states of rank at most 4 such a state is entangled if and only if its range contains no product vectors this criterion can be easily applied since a four dimensional subspace in the 3 3 or 2 2 2 system contains a product vector if and only if its plucker coordinates satisfy a homogeneous polynomial equation the chow form of the corresponding segre variety we have computed an explicit determinantal expression for the chow form in the former case while such an expression was already known in the latter case