2018 **Abstract:** We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not restricted. Although our result follows the idea of Azuma et al (2016 Nat. Commun. 7 13523) of splitting the network into two parts, our approach relaxes their strong restriction, consisting of the use of a single entanglement measure in the quantification of the maximum amount o…

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“…For instance, our benchmarks may be used to evaluate performances in relay-assisted QKD protocols such as MDI-QKD and variants [56][57][58]. Related literature and other developments [59][60][61][62][63][64][65][66] are discussed in Supplementary Note 6.…”

confidence: 99%

“…For instance, our benchmarks may be used to evaluate performances in relay-assisted QKD protocols such as MDI-QKD and variants [56][57][58]. Related literature and other developments [59][60][61][62][63][64][65][66] are discussed in Supplementary Note 6.…”

confidence: 99%

“…Proof. For convenience of the reader, we give a complete proof, but we note that some of the essential steps are available in prior works [9,12,14]. From the assumption in (49), it follows that…”

confidence: 99%

“…holds, which is known to occur generally for certain entanglement measures [9,12,16]or for certain channels with particular symmetries [9]. One of the main observations of [9], connected to earlier developments in [10][11][12][13][14], is that the amortized entanglement of a channel serves as an upper bound on the entanglement of the final state ω AB generated by an LOCC-or PPT-P-assisted quantum communication protocol that uses the channel n times:…”

confidence: 98%

“…Given that, even in the case of point-to-point links, entanglement makes the characterization of this optimal value, the capacity, notably more complicated than its classical counterpart, with phenomena such as superactivation [9], it was unclear how much it would be possible to borrow from the theory of classical networks. However, in a series of fundamental works [10][11][12][13] it was established that the capacity of quantum networks for bipartite communication behaves similar to that of classical networks. Namely, given a network of quantum noisy channels and bounds on their capacities satisfying certain properties, one can conceptually construct a classical version of the quantum network where each quantum channel is replaced by a perfect classical channel with capacity given by the bound on the quantum channel capacity.…”

mentioning

confidence: 99%