We show that whenever a contractive k-tuple T on a finite dimensional space H has a unitary dilation, then for any fixed degree N there is a unitary k-tuple U on a finite dimensional space so that q(T ) = PHq(U)|H for all polynomials q of degree at most N .

A contractive n-tuple A = (A1, . . . , An) has a minimal joint isometric dilation S = (S1, . . . , Sn) where the Si’s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When A acts on a finite dimensional space, the wot-closed nonself-adjoint algebra S generated by S is completely described in terms of the properties of A. This provid...

By making use of M-harmonic function theory, we characterize commuting Toeplitz operators with bounded pluriharmonic symbols on the Bergman space of the unit ball or on the Hardy space of the unit sphere in n-dimensional complex space.

Abstract. A complete set of d + 1 mutually unbiased bases exists in a Hilbert spaces of dimension d, whenever d is a power of a prime. We discuss a simple construction of d+1 disjoint classes (each one having d−1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construc...

We present two pairs of Y(sl2) Yangian symmetries for the trigonometric and hyperbolic versions of the Hubbard model with non-nearest-neighbour hopping. In both cases the Yangians are mutually commuting, hence can be combined into a Y(sl2)⊕Y(sl2) Yangian. Their mutual commutativity is of dynamical origin. The known Yangians of the Haldane-Shastry spin chain and the nearest neighbour Hubbard mod...

Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes repeated experiments. Here we express it as an effective amount (measure) distinct instead. The resulting $\mu$-uncertainties are described by number theory [1] whose central result, existence minimal amount, leads to well-defined notion intrinsic irremovab...

Efficient quantum simulation protocols for any theories demand efficient protection its underlying symmetries. This task is nontrivial gauge as it involves local symmetry/invariance. For non-Abelian theories, protecting all the symmetries generated by a set of mutually non-commuting generators, particularly difficult. In this letter, global symmetry-protection protocol proposed. Using novel loo...

Non-commutative versions of Arveson’s curvature invariant and Euler characteristic for a commuting n-tuple of operators are introduced. The noncommutative curvature invariant is sensitive enough to determine if an ntuple is free. In general both invariants can be thought of as measuring the freeness or curvature of an n-tuple. The connection with dilation theory provides motivation and exhibits...

A d-contraction is a d-tuple (T1, . . . , Td) of mutually commuting operators acting on a common Hilbert space H such that ‖T1ξ1 + T2ξ2 + · · ·+ Tdξd‖ 2 ≤ ‖ξ1‖ 2 + ‖ξ2‖ 2 + · · ·+ ‖ξd‖ 2 for all ξ1, ξ2, . . . , ξd ∈ H. These are the higher dimensional counterparts of contractions. We show that many of the operator-theoretic aspects of function theory in the unit disk generalize to the unit ball...