منابع مشابه
Unitary t-designs
Unitary t-designs provide a method to simplify integrating polynomials of degree less than t over U(d). We prove a classic result the trace double sum inequality and use it to derive the fundamental symmetries of t-designs. As an alternate approach to deriving an asymptotically tight lower bound on the size of t-designs, we introduce a greedy algorithm for constructing designs. Unfortunately, w...
متن کاملUnitary designs and codes
A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find a general lower bound on the size of a unitary t-design in U(d), for any d and t. We also introduce the notion of a unitary code — a subset of U(d) in which...
متن کاملImplementing Unitary 2-Designs Using Random Diagonal-unitary Matrices
Unitary 2-designs are random unitary matrices which, in contrast to their Haar-distributed counterparts, have been shown to be efficiently realized by quantum circuits. Most notably, unitary 2-designs are known to achieve decoupling, a fundamental primitive of paramount importance in quantum Shannon theory. Here we prove that unitary 2-designs can be implemented approximately using random diago...
متن کاملUnitals and Unitary Polarities in Symmetric Designs
We extend the notion of unital as well as unitary polarity from finite projective planes to arbitrary symmetric designs. The existence of unitals in several families of symmetric designs has been proved. It is shown that if a unital in a point-hyperplane design PGd−1(d, q) exists, then d = 2 or 3; in particular, unitals and ovoids are equivalent in case d = 3. Moreover, unitals have been found ...
متن کاملSome Block Designs Constructed from Resolvable Designs
LetD be a resolvable 2−(v, k, λ) design, andD′ be a 2−(v′, k′, λ′) design, such that v′ = v k . Further, let r and r′ be replication numbers of a point in D and D′, respectively. Shrikhande and Raghavarao proved that then there exists a 2 − (v′′, k′′, λ′′) design D′′, such that v′′ = v, k′′ = kk′ and λ′′ = r′λ + (r − λ)λ′. If D′ is resolvable, then D′′ is also resolvable. Applying this result, ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1974
ISSN: 0097-3165
DOI: 10.1016/0097-3165(74)90071-5