State And Prove Lami's Theorem Pdf Download [Extra Quality]

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Equation (109) is the first result on the ERE of adaptive protocols for CV quantum communication. The second one is the quantum extension of equation. To prove equation (109), we use several tools from quantum information theory: in particular, we use Stinespring’s theorem, the extended Schmidt decomposition, the Choi-Jamiolkowski isomorphism, and the GNS representation.

The energy-unconstrained case can be treated, essentially, by the methods of [46]. In fact, the proof of equation (108) works for energy-unconstrained protocols as well. Thus the bound applies for the energy-unconstrained case too. In fact, it is a tight bound: for unital channels, the bound is attained by the optimal energy-unconstrained protocol, which is simply teleporte 1 s the remote system by means of an energy-constrained CQME. Furthermore, let us note that the only restriction on the CQME describing the energy-unconstrained protocol is the unitary covariance. Therefore, the bound applies also to quantum teleportation, in which there is no constraint on the initial energy of the system.

Theorem 2(C)DUC maps satisfy the PPT(^2) conjecture.

Proof. We use the GNS representation. We split the proof into three steps. First, we show a weaker version of the PPT(^2) conjecture: i.e., that for any fixed, there exists a map that is both completely positive and diagonal unitary covariant, and such that the Choi matrix satisfies.

We can use a result of Holevo [48] to produce a completely positive map which is diagonal unitary covariant; moreover, it satisfies.

Second, we show that these properties are preserved under the partial trace over the second system. 827ec27edc