相关论文: Squash Operator and Symmetry

The anomalous dimension of single and multi-trace composite operators of scalar fields is shown to vanish at all orders of the perturbative series. The proof hold for theories with N=2 supersymmetry with any number of hypermultiplets in a…

The property of cyclicity of a linear operator, or equivalently the property of simplicity of its spectrum, is an important spectral characteristic that appears in many problems of functional analysis and applications to mathematical…

In this paper, we rigorously prove the intuition that in security proofs for BB84 one may regard an incoming signal to Bob as a qubit state. From this result, it follows that all security proofs for BB84 based on a virtual qubit…

Using symmetry properties, we determine the mixing pattern of a class of nonlocal quark bilinear operators containing a straight Wilson line along a spatial direction. We confirm the previous study that mixing among the lowest dimensional…

In this paper we show that when individuals in a bipartite network exclusively choose partners and exchange valued goods with their partners, then there exists a set of exchanges that are pair-wise stable. Pair-wise stability implies that…

Continuous-variable quantum key distribution protocol using coherent states and heterodyne detection, called No-Switching protocol, is widely used in practical systems due to the simple experimental setup without basis switching and easy…

In the present paper we introduce a concept of doubly stochastic quadratic operator. We prove necessary and sufficient conditions for doubly stochasticity of operator. Besides, we prove that the set of all doubly stochastic operators forms…

We show that a symmetric informationally-complete positive operator-valued measure exists in a given dimension $d$ if and only if there exists a $d^2$-dimensional operator system satisfying certain order-theoretic conditions. We also…

It has been widely claimed and believed that many protocols in quantum key distribution, especially the single-photon BB84 protocol, have been proved unconditionally secure at least in principle, for both asymptotic and finite protocols…

Several interesting features of coset models "without fixed points" are easily understood via Chern-Simons theory. In this paper we derive explicit formulae for the handle-squashing operator in these cosets. These operators are fixed,…

The squared Laplace operator acting on symmetric rank-two tensor fields is studied on a (flat) Riemannian manifold with smooth boundary. Symmetry of this fourth-order elliptic operator is obtained provided that such tensor fields and their…

For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…

We address the recently posed question as to whether the nonlocality of a single member of an entangled pair of spin $1/2$ particles can be shared among multiple observers on the other wing who act sequentially and independently of each…

We investigate $\rho$-orthogonality and its local symmetry in the space of bounded linear operators. A characterization of Hilbert space operators with symmetric numerical range is established in terms of $\rho$-orthogonality. Further, we…

Motivated by the controllability/reachability problems for switched linear control systems and some classes of nonlinear (mechanical) control systems we address a related problem of existence of a cyclic vector for an associative (matrix)…

It is well-known that observing nonlocal correlations allows us to draw conclusions about the quantum systems under consideration. In some cases this yields a characterisation which is essentially complete, a phenomenon known as…

The algebraic structures underlying quasi-exact solvability for spin 1/2 Hamiltonians in one dimension are studied in detail. Necessary and sufficient conditions for a matrix second-order differential operator preserving a space of wave…

In this article, we give conditions guaranteeing the commutativity of a bounded self-adjoint operator with an unbounded closed symmetric operator.

Proof of security of cryptographic protocols theoretically establishes the strength of a protocol and the constraints under which it can perform, it does not take into account the overall design of the protocol. In the past model checking…

We describe a general method of detecting valid chains or links of pieces on a two-dimensional grid. Specifically, using the example of the chess variant known as Switch-Side Chain-Chess (SSCC). Presently, no foolproof method of detecting…