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

By A. Harrow

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G. g. “N ⊗n can be used to send ≥ n(C − δn ) cbits with error ≤ ǫn ”). However, there is no formal reason that they cannot be used interchangeably. We also can define versions of the dynamic resources with respect to the standard “reference” ′ ′ state τ2A = 11A 2 /2: a qubit in the maximally mixed state. These are denoted as follows: • [q → q : τ ] := id2 : τ2 • [c → c : τ ] := id2 : τ2 CHAPTER 1. 19 (Addition). The addition operation + : R × R → R is defined for α = (αn )n , ′ ′ ′ ′ αn = ((Nn,1 : ωn,1 ), .

The case of the perfect classical channel idd is a classical analogue of the above. 8) holds for any state ρ diagonal in the preferred basis. Now Alice first applies a local ∆ (diagonalizing the input), before proceeding as above. This concludes the proof. Observe that in the above lemma, the final output of N is uncorrelated with the shared randomness that is used. In the QQ formalism, this is immediately apparent from the tensor product between N XA XB and AΦ . Thus we say that the shared randomness is (incoherently) decoupled from the rest of the protocol.

D. resources). ) if αn = (N ⊗n : ω ⊗n ) for some state ω and operation N . We use shorthand notation α = N : ω . g. g. “N ⊗n can be used to send ≥ n(C − δn ) cbits with error ≤ ǫn ”). However, there is no formal reason that they cannot be used interchangeably. We also can define versions of the dynamic resources with respect to the standard “reference” ′ ′ state τ2A = 11A 2 /2: a qubit in the maximally mixed state. These are denoted as follows: • [q → q : τ ] := id2 : τ2 • [c → c : τ ] := id2 : τ2 CHAPTER 1.

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