on liouville integrability of zero curvature equations and the yang hierarchy sufficient conditions for a zero curvature equation ut vx u v 0 being liouville integrable are investigated in the case that the equation is integrable an explicit formula of the poisson bracket h lambda h mu for hamiltonians h is proposed the yang hierarchy is derived and shown to be liouville integrable

structure of states which satisfy strong subadditivity of quantum entropy with equality we give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von neumann entropy by combining a result of petz characterising the equality case for the monotonicity of relative entropy with a recent theorem by koashi and imoto we show that such states will have the form of a so called short quantum markov chain which in turn implies that two of the systems are independent conditioned on the third in a physically meaningful sense this characterisation simultaneously generalises known necessary and sufficient entropic conditions for quantum error correction as well as the conditions for the achievability of the holevo bound on accessible information

continuity of quantum channel capacities we prove that a broad array of capacities of a quantum channel are continuous that is two channels that are close with respect to the diamond norm have correspondingly similar communication capabilities we first show that the classical capacity quantum capacity and private classical capacity are continuous with the variation on arguments varepsilon apart bounded by a simple function of varepsilon and the channel s output dimension our main tool is an upper bound of the variation of output entropies of many copies of two nearby channels given the same initial state the bound is linear in the number of copies our second proof is concerned with the quantum capacities in the presence of free backward or two way public classical communication these capacities are proved continuous on the interior of the set of non zero capacity channels by considering mutual simulation between similar channels

single and double spiral vortex models for a supercavitating non symmetric wedge in a jet the problem of determining the free surface of a jet incident on a rigid wedge and the boundary of a cavity behind the wedge is considered the single and double spiral vortex models by tulin are used to describe the flow at the rear part of the cavity the location of the wedge in the jet and the sides lengths are arbitrary this circumstance makes the flow domain doubly connected for the single vortex model while it is simply connected for the double vortex model both models are solved in closed form by the method of conformal mappings the maps are expressed through the solutions to certain riemann hilbert problems for the former model this problem is formulated on a genus 1 riemann surface the double vortex model requires the solution to a standard riemann hilbert problem on a plane by comparative analysis of the numerical results for the two models it is found that the drag and lift are practically the same while the jet surface the cavity boundary at the rear part and the deflection angle of the jet at infinity are different also the problem of determining the parameters for the conformal mapping in the single vortex model has two solutions it is shown that one of the solutions leads to a non physical shape of the cavity and needs to be disregarded

the capacity of the quantum multiple access channel we define classical quantum multiway channels for transmission of classical information after the previous work by allahverdyan and saakian see quantum computing and quantum communications lecture notes in computer science berlin germany springer verlag vol 1509 1999 bounds on the capacity region are derived in a uniform way which are analogous to the classically known ones simply replacing shannon 1961 entropy with von neumann 1955 entropy for the single receiver case multiple access channel the elect capacity region is determined these results are applied to the case of noisy channels with arbitrary input signal states a second issue of this work is the presentation of a calculus of quantum information quantities based on the algebraic formulation of quantum theory

integrable counterparts of the d kaup newell soliton hierarchy two integrable counterparts of the d kaup newell soliton hierarchy are constructed from a matrix spectral problem associated with the three dimensional special orthogonal lie algebra so 3 r an application of the trace identity presents hamiltonian or quasi hamiltonian structures of the resulting counterpart soliton hierarchies thereby showing their liouville integrability i e the existence of infinitely many commuting symmetries and conserved densities the involved hamiltonian and quasi hamiltonian properties are shown by computer algebra systems

trading classical communication quantum communication and entanglement in quantum shannon theory in this paper we give tradeoffs between classical communication quantum communication and entanglement for processing information in the shannon theoretic setting we first prove a unit resource capacity theorem that applies to the scenario where only the above three noiseless resources are available for consumption or generation the optimal strategy mixes the three fundamental protocols of teleportation superdense coding and entanglement distribution we then provide an achievable rate region and a matching multiletter converse for the direct static capacity theorem this theorem applies to the scenario where a large number of copies of a noisy bipartite state are available in addition to consumption or generation of the above three noiseless resources our coding strategy involves a protocol that we name the classically assisted state redistribution protocol and the three fundamental protocols we finally provide an achievable rate region and a matching multiletter converse for the direct dynamic capacity theorem this theorem applies to the scenario where a large number of uses of a noisy quantum channel are available in addition to the consumption or generation of the three noiseless resources our coding strategy combines the classically enhanced father protocol with the three fundamental unit protocols

riemann hilbert problems for the shapes formed by bodies dissolving melting and eroding in fluid flows the classical stefan problem involves the motion of boundaries during phase transition but this process can be greatly complicated by the presence of a fluid flow here we consider a body undergoing material loss due to either dissolution from molecular diffusion melting from thermodynamic phase change or erosion from fluid mechanical stresses in a fast flowing fluid in each case the task of finding the shape formed by the shrinking body can be posed as a singular riemann hilbert problem a class of exact solutions captures the rounded surfaces formed during dissolution melting as well as the angular features formed during erosion thus unifying these different physical processes under a common framework this study which merges boundary layer theory separated flow theory and riemann hilbert analysis represents a rare instance of an exactly solvable model for high speed fluid flows with free boundaries 2017 wiley periodicals inc

a spectral problem based on so 3 r and its associated commuting soliton equations we present a spectral problem based on the three dimensional real special orthogonal lie algebra so 3 r and construct a hierarchy of commuting bi hamiltonian soliton equations by zero curvature equations associated with the spectral problem an illustrative example of soliton equations is computed together with its associated bi hamiltonian structure

a soliton hierarchy associated with a new spectral problem and its hamiltonian structure a hierarchy of soliton equations together with its hamiltonian structure is constructed from a new spectral problem associated with the three dimensional special orthogonal real lie algebra so 3 the liouville integrability of the presented soliton hierarchy is proved based on the hamiltonian structure

method of riemann surfaces in the study of supercavitating flow around two hydrofoils in a channel abstract in the framework of the tulin model of supercavitating flow the problem of reconstructing the free surface of a channel and the shapes of the cavities behind two hydrofoils placed in an ideal fluid is solved in closed form the conformal map that transforms a parametric plane with three cuts along the real axis into the triple connected flow domain is found by quadratures the use of the theory of riemann surfaces the schottky doubles enables the non linear model problem to be reduced to two separate riemann hilbert problems on a hyperelliptic surface of genus two the solution to the first problem is a rational function with certain zeros and poles on a riemann surface the second problem is solved in terms of singular integrals with the weierstrass kernel the essential singularities of the solution at the infinite points of the surface due to a pole of the kernel are removed by solving a real analogue of the jacobi inversion problem on the surface the unknown parameters of the conformal map are recovered from a system of certain algebraic and transcendental equations

two integrable hamiltonian hierarchies in sl 2 r and so 3 r with three potentials by introducing two specific matrix spectral problems associated with sl 2 r and so 3 r matrix lie algebras we generate two integrable hamiltonian hierarchies with three potentials the computation and analysis on their hamiltonian structures by means of the trace identity show that the resulting hierarchies are liouville integrable namely that each hierarchy consists of commuting hamiltonian soliton equations

motion of a yawed supercavitating wedge beneath a free surface the problem that is studied concerns a yawed wedge under a free surface moving at a uniform speed the model involves a trailing cavity whose boundary is a dividing streamline through the vertex of the wedge the cavity closure mechanism is described according to the tulin terent ev single spiral vortex model a closed form solution to the governing nonlinear boundary value problem is found by the method of conformal mappings the doubly connected flow domain is treated as the image by this map of the exterior of two slits in a parametric plane the mapping function is constructed through the solution to two boundary value problems of the theory of analytic functions the hilbert problem for two slits in a plane and the riemann hilbert problem on an elliptic surface numerical results for the shape of the cavity and the free surface the yaw angle the drag and lift coefficients and the circulation are reported

single spiral vortex model for a cavitating elastic curvilinear foil a two dimensional nonlinear inverse fluid structure interaction problem for a curvilinear elastic hydrofoil is considered a cavity formed behind the foil is modeled according to the single spiral vortex model by tulin the fluid structure problem is decoupled by the method of successive approximations for the cavitation problem the foil is modeled as a polygon the method of conformal mappings and the riemann hilbert problem are employed at this stage the classical detachment mechanism for a smooth arc is satisfied for the polygon approximately the deformation of the smooth foil is described by the governing equations of the thin shell theory with the clamped clamped boundary conditions the loading acting on the middle surface of the foil is prescribed as the difference between the fluid and vapor pressure computed in the fluid problem numerical results include those for the cavity profile the drag coefficient the pressure distribution the speed and the displacements of the elastic foil

a father protocol for quantum broadcast channels a new protocol for quantum broadcast channels based on the fully quantum slepian wolf protocol is presented the protocol yields an achievable rate region for entanglement assisted transmission of quantum information through a quantum broadcast channel that can be considered the quantum analogue of marton s region for classical broadcast channels the protocol can be adapted to yield achievable rate regions for unassisted quantum communication and for entanglement assisted classical communication in the case of unassisted transmission the region we obtain has no independent constraint on the sum rate only on the individual transmission rates regularized versions of all three rate regions are provably optimal

bounds on entanglement distillation and secret key agreement for quantum broadcast channels the squashed entanglement of a quantum channel is an additive function of quantum channels which finds application as an upper bound on the rate at which secret key and entanglement can be generated when using a quantum channel a large number of times in addition to unlimited classical communication this quantity has led to an upper bound of log 1 eta 1 eta on the capacity of a pure loss bosonic channel for such a task where eta is the average fraction of photons that make it from the input to the output of the channel the purpose of this paper is to extend these results beyond the single sender single receiver setting to the more general case of a single sender and multiple receivers a quantum broadcast channel we employ multipartite generalizations of the squashed entanglement to constrain the rates at which secret key and entanglement can be generated between any subset of the users of such a channel along the way developing several new properties of these measures we apply our results to the case of a pure loss broadcast channel with one sender and two receivers

capacity theorems for quantum multiple access channels classical quantum and quantum quantum capacity regions in this paper we consider quantum channels with two senders and one receiver for an arbitrary such channel we give multiletter characterizations of two different two dimensional capacity regions the first region comprises the rates at which it is possible for one sender to send classical information while the other sends quantum information the second region consists of the rates at which each sender can send quantum information for each region we give an example of a channel for which the corresponding region has a single letter description one of our examples relies on a new result proved here perhaps of independent interest stating that the coherent information over any degradable channel is concave in the input density operator we conclude with connections to other work and a discussion on generalizations where each user simultaneously sends classical and quantum information

distillation of secret key and entanglement from quantum states we study and solve the problem of distilling a secret key from quantum states representing correlation between two parties alice and bob and an eavesdropper eve via oneway public discussion we

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

canonical structure of soliton equations i abstract the canonical structure of the nonlinear evolution equations in 1 1 dimensions solvable in terms of an n n inverse scattering problem is discussed the simplest form of the scattering problems that is those containing the spectral parameter linearly is considered it applies to most of the known soliton equations like the korteweg de vries eq the sine gordon eq and the boussinesq eq discussion of various possible reductions of the number of dependent variables by imposing constraints consistent with the hamiltonian flows is given together with the canonical structure of the reduced systems a direct proof of the involutive character of the infinite number of conserved quantities is given for the general case as well as the reduced case the relation between the conserved quantities and symmetry transformations lie backlund transformations becomes very simple in this framework

a soliton hierarchy associated with so 3 r we generate a hierarchy of soliton equations from zero curvature equations associated with the real lie algebra so 3 r and show that each equation in the resulting hierarchy has a bi hamiltonian structure and thus integrable in the liouville sense

on quantum fidelities and channel capacities for the discrete memoryless quantum channel we show the equivalence of two different notions of quantum channel capacity that which uses the entanglement fidelity as its criterion for success in transmission and that which uses the minimum fidelity of pure states in a subspace of the input hilbert space as its criterion as a corollary any source with entropy rate less than the capacity may be transmitted with high entanglement fidelity we also show that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel this enables us to simplify a known upper bound for the channel capacity it also enables us to show that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity

entanglement assisted capacity of quantum multiple access channels we find a regularized formula for the entanglement assisted ea capacity region for quantum multiple access channels qmac we illustrate the capacity region calculation with the example of the collective phase flip channel which admits a single letter characterization on the way we provide a first principles proof of the ea coding theorem based on a packing argument we observe that the holevo schumacher westmoreland theorem may be obtained from a modification of our ea protocol we remark on the existence of a family hierarchy of protocols for multiparty scenarios with a single receiver in analogy to the two party case in this way we relate several previous results regarding qmacs

double cavity flow past a wedge a mathematical model of supercavitating flow past a wedge with sides of arbitrary length is proposed the flow branches at a point on the lower side of the wedge at the vertex of the wedge and at the ends of the wedge the flow breaks away forming a nose bubble and a trailing cavity the closure mechanism is described by the tulin single spiral vortex model the flow domain is mapped into a parametric plane cut along a unit segment the conformal mapping function is reconstructed through the exact solution of two riemann hilbert problems on a genus zero riemann surface to complete the solution one needs to determine five real parameters from a certain system of transcendental equations numerical results are presented for the case when a wedge can rotate about the vertex in the flow domain in this case the flow branches at the vertex and the number of the parameters to be determined is 3

cryptographic distinguishability measures for quantum mechanical states this paper mostly expository in nature surveys four measures of distinguishability for quantum mechanical states this is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions namely the probability of an identification error the kolmogorov distance the bhattacharyya coefficient and the shannon 1948 distinguishability as defined through mutual information these measures have a long history of use in statistical pattern recognition and classical cryptography we obtain several inequalities that relate the quantum distinguishability measures to each other one of which may be crucial for proving the security of quantum cryptographic key distribution in another vein these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states this is a tool that may prove useful in the analysis of various quantum cryptographic protocols

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

one shot marton inner bound for classical quantum broadcast channel we consider the problem of communication over a classical quantum broadcast channel with one sender and two receivers generalizing the classical inner bounds shown by marton and the recent quantum asymptotic version shown by savov and wilde we obtain one shot inner bounds in the quantum setting our bounds are stated in terms of hypothesis testing and one shot max divergences these results give a full justification of the claims of savov and wilde in the classical quantum asymptotic iid setting the techniques also yield similar bounds in the information spectrum setting we obtain these results using a different analysis of the random codebook argument our method yields a classical one shot marton bound with a common message and a classical one shot mutual covering lemma based on rejection sampling

semidirect sums of lie algebras and discrete integrable couplings a relation between semidirect sums of lie algebras and integrable couplings of lattice equations is established and a practicable way to construct integrable couplings is further proposed an application of the resulting general theory to the generalized toda spectral problem yields two classes of integrable couplings for the generalized toda hierarchy of lattice equations the construction of integrable couplings using semidirect sums of lie algebras provides a good source of information on complete classification of integrable lattice equations

quantum broadcast channels we consider quantum channels with one sender and two receivers used in several different ways for the simultaneous transmission of independent messages we begin by extending the technique of superposition coding to quantum channels with a classical input to give a general achievable region we also give outer bounds to the capacity regions for various special cases from the classical literature and prove that superposition coding is optimal for a class of channels we then consider extensions of superposition coding for channels with a quantum input where some of the messages transmitted are quantum instead of classical in the sense that the parties establish bipartite or tripartite ghz entanglement we conclude by using state merging to give achievable rates for establishing bipartite entanglement between different pair of parties with the assistance of free classical communication

hamiltonian and quasi hamiltonian structures associated with semi direct sums of lie algebras the trace variational identity is generalized to zero curvature equations associated with non semi simple lie algebras or equivalently lie algebras possessing degenerate killing forms an application of the resulting generalized variational identity to a class of semi direct sums of lie algebras in the akns case furnishes hamiltonian and quasi hamiltonian structures of the associated integrable couplings three examples of integrable couplings for the akns hierarchy are presented one hamiltonian and two quasi hamiltonian