2018 **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…

Help me understand this report

View preprint versions

Search citation statements

Paper Sections

Select...

2

1

1

1

Citation Types

0

17

0

Year Published

2018

2019

Publication Types

Select...

3

Relationship

3

0

Authors

Journals

(17 citation statements)

(161 reference statements)

0

17

0

“…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 .…”

confidence: 55%

“…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 .…”

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]…”

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.,…”

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.…”

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.…”

confidence: 99%