Operator and Graph Theoretic Techniques for Distinguishing Quantum States via One-Way LOCC

We bring together in one place some of the main results and applications from our recent work on quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time to investigate the topic of distinguishability of sets of quantum states in quantum communication, with particular reference to the framework of one-way local quantum operations and classical communication (LOCC). We also derive a new graph-theoretic description of distinguishability in the case of a single-qubit sender.

Low energy effective field theory operator basis at d ≤ 9

We obtain the complete operator bases at mass dimensions 5, 6, 7, 8, 9 for the low energy effective field theory (LEFT), which parametrize various physics effects between the QCD scale and the electroweak scale. The independence of the operator basis regarding the equation of motion, integration by parts and flavor relations, is guaranteed by our algorithm [1, 2], whose validity for the LEFT with massive fermions involved is proved by a generalization of the amplitude-operator correspondence. At dimension 8 and 9, we list the 35058 (756) and 704584 (3686) operators for three (one) generations of fermions categorized by their baryon and lepton number violations (∆B, ∆L), as these operators are of most phenomenological relevance.

Global well-posedness of a class of dissipative thermoelastic fluids based on fractal theory and thermal science analysis

Thermodynamics and fluid mechanics are used to study the mechanical properties of a class of thermoelastic fluid materials. Using the law of thermodynamics and the law of conservation of energy, thermal science analysis of dissipative thermoelastic fluid materials is performed in a planar 2-D flow field, and a corresponding mathematical model is established. Fractal theory, operator semi-group theory and fractional calculus are used to study the overall well-posedness of a dissipative thermoelastic flow.

A Compositional Shuffle Conjecture Specifying Touch Points of the Dyck Path

We introduce a q, t-enumeration of Dyck paths that are forced to touch the main diagonal at specific points and forbidden to touch elsewhere and conjecture that it describes the action of the Macdonald theory ∇ operator applied to a Hall–Littlewood polynomial. Our conjecture refines several earlier conjectures concerning the space of diagonal harmonics including the “shuffle conjecture” (Duke J. Math. 126 (2005), pp. 195 − 232) for ∇ en[X]. We bring to light that certain generalized Hall–Littlewood polynomials indexed by compositions are the building blocks for the algebraic combinatorial theory of q, t-Catalan sequences, and we prove a number of identities involving these functions.