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39. If α ≥ [c c] and β is pure then α + R [c c] ≥ β can always be derandomized to α ≥ β. Proof. 9) is automatically satisfied. The following theorem tells us that in proving channel coding theorems one only needs to consider the case where the input state is maximally mixed. A similar result was shown in [BKN00] (see also [KW04, YDH05]), though with quite different techniques and formalism. 40 (Absolutization). The following resource inequalities hold: 1. [q → q : τ ] ≥ [q → q] 2. [[c → c : τ ]] ≥ [q → qq] 3.

The sliding protocol shows how working with depth-1 resources is not overly restrictive. Another difficulty with resources is that relative resources are only guaranteed to work properly when given the right sort of input state. Here we show that using shared randomness, some of the standard relative resources can be “absolutized,” removing the restriction to a particular input state. CHAPTER 1. QUANTUM SHANNON THEORY 33 Nl ... N2 N1 m+l−1 ... Nl ... ... Nl N2 N1 N2 N1 m ... Nl ... l N2 N1 Nl ...

5. Bibliographical note: Except where other works are cited, most of the results in this chapter are from [BHLS03] (joint work with Charles Bennett, Debbie Leung and John Smolin). However, this thesis reformulates them in the formalism of Chapter 1, which allows many of the definitions, claims and proofs to be greatly simplified. 1 Background Survey of related work The nonlocal strength of unitary interactions was first discussed within a model of communication complexity, when Nielsen introduced the Schmidt decomposition of a unitary gate (described below) as a measure of its nonlocality[Nie98].

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Appl of Coherent Communication to Quantum Information Theory [thesis] by A. Harrow

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