Showing papers in "Journal of Mathematical Physics in 2017"
TL;DR: Based on the completeness relation for the squared solutions of the Lax operator L, the authors showed that a subset of nonlocal equations from the hierarchy of nonlinear Schrodinger equations (NLS) is a completely integrable system.
Abstract: Based on the completeness relation for the squared solutions of the Lax operator L, we show that a subset of nonlocal equations from the hierarchy of nonlocal nonlinear Schrodinger equations (NLS) is a completely integrable system. The spectral properties of the Lax operator indicate that there are two types of soliton solutions. The relevant action-angle variables are parametrized by the scattering data of the Lax operator. The notion of the symplectic basis, which directly maps the variations of the potential of L to the variations of the action-angle variables has been generalized to the nonlocal case. We also show that the inverse scattering method can be viewed as a generalized Fourier transform. Using the trace identities and the symplectic basis, we construct the hierarchy Hamiltonian structures for the nonlocal NLS equations.
106 citations
TL;DR: In this paper, an integrable nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani is shown to be gauge equivalent to a spin-like model.
Abstract: In this paper, we prove that an integrable nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity 29, 915–946 (2016)] is gauge equivalent to a spin-like model. From the gauge equivalence, one can see that there exists significant difference between the nonlocal complex mKdV equation and the classical complex mKdV equation. Through constructing the Darboux transformation for nonlocal complex mKdV equation, a variety of exact solutions including dark soliton, W-type soliton, M-type soliton, and periodic solutions are derived.
100 citations
TL;DR: In this paper, the leading and next-to-leading orders of the 2-point and 4-point functions of the Gurau-Witten tensor model were analyzed in the context of colored SYK models.
Abstract: The Sachdev-Ye-Kitaev (SYK) model is a model of q interacting fermions. Gross and Rosenhaus have proposed a generalization of the SYK model which involves fermions with different flavors. In terms of Feynman graphs, those flavors are reminiscent of the colors used in random tensor theory. This gives us the opportunity to apply some modern, yet elementary, tools developed in the context of random tensors to one particular instance of such colored SYK models. We illustrate our method by identifying all diagrams which contribute to the leading and next-to-leading orders of the 2-point and 4-point functions in the large N expansion and argue that our method can be further applied if necessary. In the second part, we focus on the recently introduced Gurau-Witten tensor model and also extract the leading and next-to-leading orders of the 2-point and 4-point functions. This analysis turns out to be remarkably more involved than in the colored SYK model.
100 citations
TL;DR: In this article, a 16-fold way conjecture for the minimal modular extensions of super-modular categories to spin modular categories is formulated, which is a categorical formulation of gauging the fermion parity.
Abstract: We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin topological quantum field theories at low energy. We formulate a 16-fold way conjecture for the minimal modular extensions of super-modular categories to spin modular categories, which is a categorical formulation of gauging the fermion parity. We investigate general properties of super-modular categories such as fermions in twisted Drinfeld doubles, Verlinde formulas for naive quotients, and explicit extensions of PSU(2)4m+2 with an eye towards a classification of the low-rank cases.
91 citations
TL;DR: In this article, it was shown that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordstrom-de Sitter and Kerr-De Sitter spacetimes.
Abstract: We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner–Nordstrom–de Sitter and Kerr–de Sitter spacetimes and in fact decay exponentially fast to a constant along the Cauchy horizon. We obtain our results by modifying the spacetime beyond the Cauchy horizon in a suitable manner, which puts the wave equation into a framework in which a number of standard as well as more recent microlocal regularity and scattering theory results apply. In particular, the conormal regularity of waves at the Cauchy horizon—which yields the boundedness statement—is a consequence of radial point estimates, which are microlocal manifestations of the blue-shift and red-shift effects.
80 citations
TL;DR: In this paper, it was shown that the Holevo quantity is continuous on the set of all ensembles of m states with respect to all the metrics if either m or the dimension of underlying Hilbert space is finite.
Abstract: We start with Fannes’ type and Winter’s type tight (uniform) continuity bounds for the quantum conditional mutual information and their specifications for states of special types. Then we analyse continuity of the Holevo quantity with respect to nonequivalent metrics on the set of discrete ensembles of quantum states. We show that the Holevo quantity is continuous on the set of all ensembles of m states with respect to all the metrics if either m or the dimension of underlying Hilbert space is finite and obtain Fannes’ type tight continuity bounds for the Holevo quantity in this case. In the general case, conditions for local continuity of the Holevo quantity for discrete and continuous ensembles are found. Winter’s type tight continuity bound for the Holevo quantity under constraint on the average energy of ensembles is obtained and applied to the system of quantum oscillators. The above results are used to obtain tight and close-to-tight continuity bounds for basic capacities of finite-dimensional chann...
70 citations
TL;DR: The elephant random walk (ERW) as mentioned in this paper is a non-Markovian discrete-time random walk on Ω with unbounded memory which exhibits a phase transition from a diffusive to superdiffusive behavior.
Abstract: We study the so-called elephant random walk (ERW) which is a non-Markovian discrete-time random walk on ℤ with unbounded memory which exhibits a phase transition from a diffusive to superdiffusive behavior. We prove a law of large numbers and a central limit theorem. Remarkably the central limit theorem applies not only to the diffusive regime but also to the phase transition point which is superdiffusive. Inside the superdiffusive regime, the ERW converges to a non-degenerate random variable which is not normal. We also obtain explicit expressions for the correlations of increments of the ERW.
69 citations
TL;DR: In this paper, a uniquely determined 1-parameter family of 2D Toda τ-functions of hypergeometric type is shown to consist of generating functions for double Hurwitz numbers enumerating weighted n-sheeted branched coverings.
Abstract: Double Hurwitz numbers enumerating weighted n-sheeted branched coverings of the Riemann sphere or, equivalently, weighted paths in the Cayley graph of Sn generated by transpositions are determined by an associated weight generating function. A uniquely determined 1-parameter family of 2D Toda τ-functions of hypergeometric type is shown to consist of generating functions for such weighted Hurwitz numbers. Four classical cases are detailed, in which the weighting is uniform: Okounkov’s double Hurwitz numbers for which the ramification is simple at all but two specified branch points; the case of Belyi curves, with three branch points, two with specified profiles; the general case, with a specified number of branch points, two with fixed profiles, the rest constrained only by the genus; and the signed enumeration case, with sign determined by the parity of the number of branch points. Using the exponentiated quantum dilogarithm function as a weight generator, three new types of weighted enumerations are introduced. These determine quantum Hurwitz numbers depending on a deformation parameter q. By suitable interpretation of q, the statistical mechanics of quantum weighted branched covers may be related to that of Bosonic gases. The standard double Hurwitz numbers are recovered in the classical limit.
68 citations
TL;DR: In this paper, the authors choose a complete set of square integrable functions as a basis for the expansion of the wave function in configuration space such that the matrix representation of the nonrelativistic time-independent linear wave operator is tridiagonal and symmetric.
Abstract: We choose a complete set of square integrable functions as a basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent linear wave operator is tridiagonal and symmetric. Consequently, the matrix wave equation becomes a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. The recursion relation is then solved exactly in terms of orthogonal polynomials in the energy. Some of these polynomials are not found in the mathematics literature. The asymptotics of these polynomials give the phase shift for the continuous energy scattering states and the spectrum for the discrete energy bound states. Depending on the space and boundary conditions, the basis functions are written in terms of either the Laguerre or Jacobi polynomials. The tridiagonal requirement limits the number of potential functions that yield exact solutions of the wave equation. Nonetheless, the class of exactly solvable prob...
68 citations
TL;DR: In this paper, it was shown that in a Heisenberg chain with n qubits, there is pretty good state transfer between the nodes at the jth and (n − ǫj + 1) positions if n is a power of 2.
Abstract: Pretty good state transfer in networks of qubits occurs when a continuous-time quantum walk allows the transmission of a qubit state from one node of the network to another, with fidelity arbitrarily close to 1. We prove that in a Heisenberg chain with n qubits, there is pretty good state transfer between the nodes at the jth and (n − j + 1)th positions if n is a power of 2. Moreover, this condition is also necessary for j = 1. We obtain this result by applying a theorem due to Kronecker about Diophantine approximations, together with techniques from algebraic graph theory.
51 citations
TL;DR: The SL(2,C) Clebsch-Gordan coefficients appearing in the lorentzian EPRL spin foam amplitudes for loop quantum gravity were studied in this article.
Abstract: We study the SL(2,C) Clebsch-Gordan coefficients appearing in the lorentzian EPRL spin foam amplitudes for loop quantum gravity. We show how the amplitudes decompose into SU(2) nj-symbols at the vertices and integrals over boosts at the edges. The integrals define edge amplitudes that can be evaluated analytically using and adapting results in the literature, leading to a pure state sum model formulation. This procedure introduces virtual representations which, in a manner reminiscent to virtual momenta in Feynman amplitudes, are off-shell of the simplicity constraints present in the theory, but with the integrands that peak at the on-shell values. We point out some properties of the edge amplitudes which are helpful for numerical and analytical evaluations of spin foam amplitudes, and suggest among other things a simpler model useful for calculations of certain lowest order amplitudes. As an application, we estimate the large spin scaling behaviour of the simpler model, on a closed foam with all 4-valent edges and Euler characteristic X, to be N^(X - 5E + V/2). The paper contains a review and an extension of results on SL(2,C) Clebsch-Gordan coefficients among unitary representations of the principal series that can be useful beyond their application to quantum gravity considered here.
TL;DR: In this article, the authors investigated linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators.
Abstract: Linear system games are a generalization of Mermin’s magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob’s measurement operators act on a joint Hilbert space, and Alice’s operators must commute with Bob’s operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.
TL;DR: In this article, a generalisation of joint measurability is derived, which yields a hierarchy for the incompatibility of sets of measurements and a similar hierarchy is defined based on the number of outcomes necessary to perform a simulation of a given measurement.
Abstract: We introduce a framework for simulating quantum measurements based on classical processing of a set of accessible measurements. Well-known concepts such as joint measurability and projective simulability naturally emerge as particular cases of our framework, but our study also leads to novel results and questions. First, a generalisation of joint measurability is derived, which yields a hierarchy for the incompatibility of sets of measurements. A similar hierarchy is defined based on the number of outcomes necessary to perform a simulation of a given measurement. This general approach also allows us to identify connections between different kinds of simulability and, in particular, we characterise the qubit measurements that are projective-simulable in terms of joint measurability. Finally, we discuss how our framework can be interpreted in the context of resource theories.
TL;DR: In this paper, the authors derived new bounds on Herglotz functions that generalize those given in Bernland et al. and Gustafsson and Sjoberg [2010] to a wide class of linear passive systems such as electromagnetic passive materials.
Abstract: Using a sum rule, we derive new bounds on Herglotz functions that generalize those given in Bernland et al [J Phys A: Math Theor 44(14), 145205 (2011)] and Gustafsson and Sjoberg [New J Phys 12(4), 043046 (2010)] These bounds apply to a wide class of linear passive systems such as electromagnetic passive materials Among these bounds, we describe the optimal ones and also discuss their meaning in various physical situations like in the case of a transparency window, where we exhibit sharp bounds Then, we apply these bounds in the context of broadband passive cloaking in the quasistatic regime to refute the following challenging question: is it possible to construct a passive cloaking device that cloaks an object over a whole frequency band? Our rigorous approach, although limited to quasistatics, gives quantitative limitations on the cloaking effect over a finite frequency range by providing inequalities on the polarizability tensor associated with the cloaking device We emphasize that our resul
TL;DR: In this paper, the authors employed the Lie symmetry analysis method to investigate the Lie point symmetries and the one-parameter transformation groups of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system.
Abstract: In this paper, the Lie symmetry analysis method is employed to investigate the Lie point symmetries and the one-parameter transformation groups of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system. By using Ibragimov’s method, the optimal system of one-dimensional subalgebras of this system is constructed. Truncated Painleve analysis is used for deriving the Backlund transformation. The method of constructing lump-type solutions of integrable equations by means of Backlund transformation is first presented. Meanwhile, the lump-type solutions of the (2 + 1)-dimensional Boiti-Leon-Pempinelli system are obtained. The lump-type wave is one kind of rogue wave. The fusion-type N-solitary wave solutions are also constructed. In addition, this system is integrable in terms of the consistent Riccati expansion method.
TL;DR: In this paper, the Hirota direct method was applied to construct complexiton solutions (complexitons) for the Korteweg-de Vries equation, and it was shown that taking pairs of conjugate wave variables in the 2N-soliton solutions generates N-complexion solutions.
Abstract: We apply the Hirota direct method to construct complexiton solutions (complexitons). The key is to use Hirota bilinear forms. We prove that taking pairs of conjugate wave variables in the 2N-soliton solutions generates N-complexion solutions. The general theory is used to construct multi-complexion solutions to the Korteweg–de Vries equation.
TL;DR: In this article, it was shown that unitary 2-designs can be implemented by alternately repeating random unitaries diagonal in the Pauli-Z basis and Pauli X basis.
Abstract: Unitary 2-designs are random unitaries simulating up to the second order statistical moments of the uniformly distributed random unitaries, often referred to as Haar random unitaries. They are used in a wide variety of theoretical and practical quantum information protocols and also have been used to model the dynamics in complex quantum many-body systems. Here, we show that unitary 2-designs can be approximately implemented by alternately repeating random unitaries diagonal in the Pauli-Z basis and Pauli-X basis. We also provide a converse about the number of repetitions needed to achieve unitary 2-designs. These results imply that the process after l repetitions achieves a Θ(d−l)-approximate unitary 2-design. Based on the construction, we further provide quantum circuits that efficiently implement approximate unitary 2-designs. Although a more efficient implementation of unitary 2-designs is known, our quantum circuit has its own merit that it is divided into a constant number of commuting parts, which ...
TL;DR: In this article, it was shown that the tridiagonalization of the hypergeometric operator L yields the generic Heun operator M. The Racah-Heun orthogonal polynomials are introduced as overlap coefficients between the eigenfunctions of the operators L and M. An interpretation in terms of the Racah problem for su(1,1) and separation of variables in a superintegrable system are discussed.
Abstract: It is shown that the tridiagonalization of the hypergeometric operator L yields the generic Heun operator M. The algebra generated by the operators L, M and Z = [L, M] is quadratic and a one-parameter generalization of the Racah algebra. The Racah-Heun orthogonal polynomials are introduced as overlap coefficients between the eigenfunctions of the operators L and M. An interpretation in terms of the Racah problem for su(1,1) and separation of variables in a superintegrable system are discussed.
TL;DR: In this paper, the authors showed that for real frequencies, there are linearly independent fundamental solutions of the radial Teukolsky equation Rhor,Rout, which are purely ingoing at the horizon and purely outgoing at infinity, respectively.
Abstract: A generalization of the mode stability result of Whiting [J. Math. Phys. 30, 1301–1305 (1989)] for the Teukolsky equation is proved for the case of real frequencies. The main result of the paper states that a separated solution of the Teukolsky equation governing massless test fields on the Kerr spacetime, which is purely outgoing at infinity, and purely ingoing at the horizon, must vanish. This has the consequence that for real frequencies, there are linearly independent fundamental solutions of the radial Teukolsky equation Rhor,Rout, which are purely ingoing at the horizon and purely outgoing at infinity, respectively. This fact yields a representation formula for solutions of the inhomogeneous Teukolsky equation and was recently used by Shlapentokh-Rothman [Ann. Henri Poincare 16, 289–345 (2015)] for the scalar wave equation.
TL;DR: In this paper, the authors presented a conjectured family of symmetric informationally complete positive operator valued measures which have an additional symmetry group whose size grows with the dimension of the measure.
Abstract: We present a conjectured family of symmetric informationally complete positive operator valued measures which have an additional symmetry group whose size is growing with the dimension. The symmetry group is related to Fibonacci numbers, while the dimension is related to Lucas numbers. The conjecture is supported by exact solutions for dimensions d = 4, 8, 19, 48, 124, and 323 as well as a numerical solution for dimension d = 844.
TL;DR: In this article, the authors considered the q→0 limit of the deformed Virasoro algebra and that of the level 1, 2 representation of the Ding-Iohara-Miki algebra.
Abstract: In this paper, we consider the q→0 limit of the deformed Virasoro algebra and that of the level 1, 2 representation of the Ding-Iohara-Miki algebra. Moreover, 5D AGT correspondence in this limit is discussed. This specialization corresponds to the limit from Macdonalds functions to Hall-Littlewood functions. Using the theory of Hall-Littlewood functions, some problems are solved. For example, the simplest case of 5D AGT conjectures is proven in this limit, and we obtain a formula for the 4-point correlation function of a certain operator.
TL;DR: In this article, the authors derived an algebraic upper bound for the number of stable fixed points of the locally coupled Kuramoto model with identical frequencies under the assumption that angle differences between connected nodes do not exceed π/2.
Abstract: The number N of stable fixed points of locally coupled Kuramoto models depends on the topology of the network on which the model is defined. It has been shown that cycles in meshed networks play a crucial role in determining N because any two different stable fixed points differ by a collection of loop flows on those cycles. Since the number of different loop flows increases with the length of the cycle that carries them, one expects N to be larger in meshed networks with longer cycles. Simultaneously, the existence of more cycles in a network means more freedom to choose the location of loop flows differentiating between two stable fixed points. Therefore, N should also be larger in networks with more cycles. We derive an algebraic upper bound for the number of stable fixed points of the Kuramoto model with identical frequencies, under the assumption that angle differences between connected nodes do not exceed π/2. We obtain N≤∏k=1c[2⋅Int(nk/4)+1], which depends both on the number c of cycles and on the ...
TL;DR: In this article, a four-parameter system associated with the Wilson and Racah polynomials is presented, where the spectrum states are written in terms of the Wilson polynomial whose asymptotics give the scattering amplitude and phase shift.
Abstract: Using a recent formulation of quantum mechanics without a potential function, we present a four-parameter system associated with the Wilson and Racah polynomials. The continuum scattering states are written in terms of the Wilson polynomials whose asymptotics give the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Racah polynomials.
TL;DR: In this paper, the Jacobi metric derived from the line element by one of the authors is shown to reduce to the standard formulation in the non-relativistic approximation, which is the case for most stationary metrics.
Abstract: The Jacobi metric derived from the line element by one of the authors is shown to reduce to the standard formulation in the non-relativistic approximation. We obtain the Jacobi metric for various stationary metrics. Finally, the Jacobi-Maupertuis metric is formulated for time-dependent metrics by including the Eisenhart-Duval lift, known as the Jacobi-Eisenhart metric.
TL;DR: In this paper, the authors considered the problem of minimizing theta functions on translated lattices, and showed how to reduce the dimension of the problem with respect to the BCC or FCC lattices.
Abstract: We consider the minimization of theta functions $\theta_\Lambda(\alpha)=\sum_{p\in\Lambda}e^{-\pi\alpha|p|^2}$ amongst lattices $\Lambda\subset \mathbb R^d$, by reducing the dimension of the problem, following as a motivation the case $d=3$, where minimizers are supposed to be either the BCC or the FCC lattices. A first way to reduce dimension is by considering layered lattices, and minimize either among competitors presenting different sequences of repetitions of the layers, or among competitors presenting different shifts of the layers with respect to each other. The second case presents the problem of minimizing theta functions also on translated lattices, namely minimizing $(L,u)\mapsto \theta_{L+u}(\alpha)$. Another way to reduce dimension is by considering lattices with a product structure or by successively minimizing over concentric layers. The first direction leads to the question of minimization amongst orthorhombic lattices, whereas the second is relevant for asymptotics questions, which we study in detail in two dimensions.
TL;DR: In this paper, the full hierarchy of loop equations for Laguerre and Jacobi β-ensembles was derived from the theory of the Selberg integral and used to construct the explicit form of the 1/N expansion at low orders.
Abstract: The β-ensembles of random matrix theory with classical weights have many special properties. One is that the loop equations specifying the resolvent and corresponding multipoint correlators permit a derivation at the general order of the correlator via Aomoto’s method from the theory of the Selberg integral. We use Aomoto’s method to derive the full hierarchy of loop equations for Laguerre and Jacobi β-ensembles and use these to systematically construct the explicit form of the 1/N expansion at low orders. This allows us to give the explicit form of corrections to the global density and allows various moments to be computed, complementing results available in the literature motivated by problems in quantum transport.
TL;DR: The generalized Lie symmetry technique is proposed for the derivation of point symmetries for systems of fractional differential equations with an arbitrary number of independent as well as dependent variables as mentioned in this paper.
Abstract: The generalized Lie symmetry technique is proposed for the derivation of point symmetries for systems of fractional differential equations with an arbitrary number of independent as well as dependent variables. The efficiency of the method is illustrated by its application to three higher dimensional nonlinear systems of fractional order partial differential equations consisting of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, (3 + 1)-dimensional Burgers system, and (3 + 1)-dimensional Navier-Stokes equations. With the help of derived Lie point symmetries, the corresponding invariant solutions transform each of the considered systems into a system of lower-dimensional fractional partial differential equations.
TL;DR: In this article, the existence of global bounded classical solution is proved under mild assumptions on the initial data and appropriate conditions on the strength of damping death effects for a two-species chemotaxis system with two chemicals in a smooth bounded domain.
Abstract: In this paper, we investigate the competitive parabolic-elliptic-parabolic-elliptic two-species chemotaxis system with two chemicals in a smooth bounded domain Ω⊂Rn (n≥1). The existence of global bounded classical solution is proved under mild assumptions on the initial data and appropriate conditions on the strength of the damping death effects. Moreover, for the case when both competition parameters a1 and a2 lie in 0,1, it is shown that such solution stabilizes to spatially homogeneous equilibria in the large time limit.
TL;DR: The entropic moments of the probability density of a quantum system in position and momentum spaces describe not only some fundamental and/or experimentally accessible quantities of the system, but also the Entropic uncertainty measures of Renyi type, which allow one to find the most relevant mathematical formalizations of the positionmomentum Heisenberg's uncertainty principle as discussed by the authors.
Abstract: The entropic moments of the probability density of a quantum system in position and momentum spaces describe not only some fundamental and/or experimentally accessible quantities of the system but also the entropic uncertainty measures of Renyi type, which allow one to find the most relevant mathematical formalizations of the position-momentum Heisenberg’s uncertainty principle, the entropic uncertainty relations. It is known that the solution of difficult three-dimensional problems can be very well approximated by a series development in 1/D in similar systems with a non-standard dimensionality D; moreover, several physical quantities of numerous atomic and molecular systems have been numerically shown to have values in the large-D limit comparable to the corresponding ones provided by the three-dimensional numerical self-consistent field methods. The D-dimensional hydrogenic atom is the main prototype of the physics of multidimensional many-electron systems. In this work, we rigorously determine the lea...
TL;DR: In this article, the spectral decomposition of a linear map with respect to an irreducible representation (U) of a finite group (G), whenever U⊗Uc is simply reducible (with Uc being the contragradient representation), is obtained.
Abstract: We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation (U) of a finite group (G), whenever U⊗Uc is simply reducible (with Uc being the contragradient representation). Using the theory of group representations, we obtain the spectral decomposition of any such linear map. The eigenvalues and orthogonal projections arising in this decomposition are expressed entirely in terms of representation characteristics of the group G. This in turn yields necessary and sufficient conditions on the eigenvalues of any such linear map for it to be a quantum channel. We also obtain a wide class of quantum channels which are irreducibly covariant by construction. For two-dimensional irrreducible representations of the symmetric group S(3), and the quaternion group Q, we also characterize quantum channels which are both irreducibly covariant and entanglement breaking.