2018
DOI: 10.1140/epjd/e2018-90253-1
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## Abstract:We consider the Braunstein-Kimble protocol for continuous variable teleportation and its application for the simulation of bosonic channels. We discuss the convergence properties of this protocol under various topologies (strong, uniform, and bounded-uniform) clarifying some typical misinterpretations in the literature. We then show that the teleportation simulation of an arbitrary single-mode Gaussian channel is uniformly convergent to the channel if and only if its noise matrix has full rank. The various for… Show more

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##### Cited by 14 publications
(17 citation statements)
##### References 105 publications
(161 reference statements)
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“…Therefore, in the limit of many ports M ≫ 1, the M -port PBT channel Γ M tends to an identity channel I, so that Bob's output becomes a perfect replica of Alice's input. Here we prove a stronger result in terms of channel uniform convergence [26,27]. In fact, for any M , we show that the simulation error, expressed in terms of the diamond distance between Γ M and I, is one-to-one with the entanglement fidelity of the PBT channel Γ M .…”
Section: B Pbt and Simulation Of The Identitymentioning
confidence: 55%
See 1 more Smart Citation
“…Therefore, in the limit of many ports M ≫ 1, the M -port PBT channel Γ M tends to an identity channel I, so that Bob's output becomes a perfect replica of Alice's input. Here we prove a stronger result in terms of channel uniform convergence [26,27]. In fact, for any M , we show that the simulation error, expressed in terms of the diamond distance between Γ M and I, is one-to-one with the entanglement fidelity of the PBT channel Γ M .…”
Section: B Pbt and Simulation Of The Identitymentioning
confidence: 55%
“…Consider now two instances (n = 2) of the adaptive protocol. We may bound the trace distance between ρ 2 and ρ M 2 using a "peeling" argument [17,18,[25][26][27]…”
Section: B Propagation Of the Simulation Errormentioning
confidence: 99%
“…It is easy to find Gaussian channels, such as the identity channel (see Appendix A) or the B 1 canonical form (see Ref. [111]), such that the fidelity tends to zero in the limit ofμ → ∞ for any finite µ, i.e.,…”
Section: Considerations For Bosonic Gaussian Channelsmentioning
confidence: 99%
“…if and only if its noise matrix N has full rank, i.e., rank(N) = 2 [111]. For Gaussian channels with rank(N) < 2 and other bosonic channels, we need to replace the uniform convergence of Eq.…”
Section: Topologies Of Convergence In the Bk Protocol And Teleportmentioning
confidence: 99%
“…More precisely, one has to optimize the key-rate over adaptive LOCCs, i.e., local operations (LOs) assisted by unlimited two-way classical communication (CC). The combined use of the relative entropy of entanglement (REE) and teleportation stretching allowed PLOB 38 to upperbound the secret-key capacities of Pauli channels, erasure channels, amplitude damping channels, and bosonic Gaussian channels (see also the follow-up works [39][40][41][42][43] ). Among the Gaussian channels, the thermal loss channel and the thermal amplifier are the most interesting and important.…”
Section: Introductionmentioning
confidence: 99%