2018
DOI: 10.1088/1367-2630/aac153
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Abstract: Given an entanglement measure E, the entanglement of a quantum channel is defined as the largest amount of entanglement E that can be generated from the channel, if the sender and receiver are not allowed to share a quantum state before using the channel. The amortized entanglement of a quantum channel is defined as the largest net amount of entanglement Ethat can be generated from the channel, if the sender and receiver are allowed to share an arbitrary state before using the channel. Our main technical resu… Show more

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Cited by 37 publications
(41 citation statements)
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“…where R max (A; B) ρ := inf{λ : ρ AB ≤ 2 λ σ AB , σ AB ∈ PPT (A : B)} denotes the max-Rains information of the state ρ AB [34], with PPT (A : B) denoting the set of all positive semidefinite operators σ AB such that the trace norm T B (σ AB ) 1 ≤ 1 [35]. This observation was made in the case of point-to-point channels [36] and constitutes a contribution of our companion paper [30]. By successive application of the amortization relation in (3) to every use of N in an (n, M, ε)-protocol, it follows that (A : B), it follows by a data-processing argument that…”
mentioning
confidence: 99%
“…where R max (A; B) ρ := inf{λ : ρ AB ≤ 2 λ σ AB , σ AB ∈ PPT (A : B)} denotes the max-Rains information of the state ρ AB [34], with PPT (A : B) denoting the set of all positive semidefinite operators σ AB such that the trace norm T B (σ AB ) 1 ≤ 1 [35]. This observation was made in the case of point-to-point channels [36] and constitutes a contribution of our companion paper [30]. By successive application of the amortization relation in (3) to every use of N in an (n, M, ε)-protocol, it follows that (A : B), it follows by a data-processing argument that…”
mentioning
confidence: 99%
“…The main tool that we used is the formulation of the max-Rains relative entropy and max-Rains information as semi-definite programs [13]- [15]. We discuss in [22] how our strong converse result stands with respect to prior work on strong converses of quantum and private capacities. There, we also provide an elementary proof for the fact that amortization does not enhance a channel's max-relative entropy of entanglement -leading to a strong converse upper bound on the two-way assisted private capacity P ↔ (N ) of any quantum channel N (this latter result was first proven in [8] based on complex interpolation theory).…”
Section: Discussionmentioning
confidence: 99%
“…• For the Rains bound, C = PPT := {σ XY ∈ P(XY ) : σ Y XY 1 ≤ 1} and α = 1 [31], and the version with α = ∞ has also been studied in [4,38]. The notation Y denotes the partial transpose on system Y with respect to some fixed basis.…”
Section: Bounds On Amortized Entanglement Measures and Applicationsmentioning
confidence: 99%