Series and parallel addition of matrices

Anderson, William N.; Duffin, R. J.

doi:10.1016/0022-247x(69)90200-5

Cited by 312 publications

(158 citation statements)

References 6 publications

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“…3 Finally, we again consider the case of an iid source, and as before, we expect that in the limit of large n, the optimal compression rate 1 n m * (ε) should be characterized by the Shannon entropy. This is in fact an expression of an entropic version of the asymptotic equipartition property, which states that…”

Section: Analysis With Smooth Entropiesmentioning

confidence: 87%

Quantum Information Processing with Finite Resources

Tomamichel¹

2016

SpringerBriefs in Mathematical Physics

276

398

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Section: Analysis With Smooth Entropiesmentioning

confidence: 87%

Quantum Information Processing with Finite Resources

Tomamichel¹

2016

SpringerBriefs in Mathematical Physics

276

398

View full text Add to dashboard Cite

“…The intersection of continuously contained Hilbert spaces is a much more subtle operation that requires the definition of parallel sum of kernels, as introduced for the finite-dimenensional case in [1], and in general in [4] (cf. [7] for a further study).…”

Section: Corollary 33 Let a B ∈ B(h)mentioning

confidence: 99%

Sequential product of quantum effects

Gheondea

Gudder

2003

Proc. Amer. Math. Soc.

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Abstract. Unsharp quantum measurements can be modelled by means of the class E(H) of positive contractions on a Hilbert space H, in brief, quantum effects. For A, B ∈ E(H) the operation of sequential product A•B = A 1/2 BA 1/2 was proposed as a model for sequential quantum measurements. We continue these investigations on sequential product and answer positively the following question: the assumption A • B ≥ B implies AB = BA = B.Then we propose a geometric approach of quantum effects and their sequential product by means of contractively contained Hilbert spaces and operator ranges. This framework leads us naturally to consider lattice properties of quantum effects, sums and intersections, and to prove that the sequential product is left distributive with respect to the intersection.

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“…In previous work, [2,4,5], we have used the model of interconnected electrical networks to define new matrix operations. The series, parallel, and hybrid (a combination of the series and parallel) connections induce series, parallel, and hybrid addition of Hermitian semidefinite (HSD) matrices.…”

Section: Introductionmentioning

confidence: 99%

Parallel Subtraction of Matrices

Anderson

Duffin

Trapp

1972

Proc. Natl. Acad. Sci. U.S.A.

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A new Hermitian semidefinite matrix operation is studied. This operatioin-called parallel subtraction-is developed from the theory of parallel addition. Since the theory of parallel addition is motivated by the analysis of interconnected electrical networks, parallel subraction may be interpreted in terms of the synthesis of electrical networks. The idea of subtraction is also extended to hybrid addition.

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Series and parallel addition of matrices

Cited by 312 publications

References 6 publications

Quantum Information Processing with Finite Resources

Quantum Information Processing with Finite Resources

Sequential product of quantum effects

Parallel Subtraction of Matrices

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