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Physica Scripta

Nonadditivity of quantum capacities of quantum multiple-access channels and the butterfly network

Peng Fei Huang, Guangqiang He, Jun Zhu, Guihua Zeng

Published Sep 22, 2011• 0 citations
Publisher

Abstract

Multipartite quantum information transmission without additional classical resources is investigated. We show purely quantum superadditivity of quantum capacity regions of quantum memoryless multiple-access (MA) channels, which are not entanglement breaking. Also, we find that the superadditivity holds when the MA channel extends to the quantum butterfly network, which can achieve quantum network coding. The present widespread effects for the channels which enable entanglement distribution have not been revealed for multipartite scenarios.

DOI
10.1088/0031-8949/84/04/045013

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Multipartite quantum information transmission without additional classical resources is investigated. We show purely quantum superadditivity of quantum capacity regions of quantum memoryless multiple-access (MA) channels, which are not entanglement breaking. Also, we find that the superadditivity holds when the MA channel extends to the quantum butterfly network, which can achieve quantum network coding. The present widespread effects for the channels which enable entanglement distribution have not been revealed for multipartite scenarios.
We analyze quantum network primitives which are entanglement breaking. We show superadditivity of quantum and classical capacity regions for quantum multiple-access channels and the quantum butterfly network. Since the effects are especially visible at high noise they suggest that quantum information effects may be particularly helpful in the case of the networks with occasional high noise rates. The present effects provide a qualitative borderline between superadditivities of bipartite and multipartite systems.
We analyze quantum network primitives which are entanglement-breaking. We show superadditivity of quantum and classical capacity regions for quantum multiple-access channel and quantum butterfly network. Since the effects are especially visible at high noise they suggest that quantum information effects may be particularly helpful in the case of the networks with occasional high noise rates. To our knowledge the present effects provide the first qualitative borderline between superadditivities of bipartite and multipartite systems.
Entanglement-induced nonadditivity of classical communication capacity in networks consisting of quantum channels is considered. Communication lattices consisting of butterfly-type entanglement-breaking channels augmented, with some probability, by identity channels are analyzed. The capacity superadditivity in the network is manifested in directed correlated bond percolation which we consider in two flavors: simply directed and randomly oriented. The obtained percolation properties show that high-capacity information transfer sets in much faster in the regime of superadditive communication capacity than otherwise possible. As a by-product, this sheds light on a type of entanglement-based quantum capacity percolation phenomenon.
The entanglement-assisted capacity of a quantum channel admits an additive single-letter characterization, implying that joint encodings across channel uses cannot increase the ultimate communication rate. Here, we show that this additive picture does not extend to communication reliability. Specifically, we prove that the Petz-Rényi channel information can be strictly superadditive for every α∈[1/2,1)α\in[1/2,1)α∈[1/2,1), yielding a genuine multi-copy enhancement of the entanglement-assisted random-coding error exponent, even though the entanglement-assisted capacity remains additive. We establish this phenomenon analytically already for measurement channels, which are entanglement-breaking and have additive unassisted capacity. Remarkably, this strict superadditivity is witnessed by a separable, classically correlated two-copy channel-input marginal, demonstrating that no entanglement between the transmitted systems is required. Our results show that, although correlations across channel uses cannot increase the ultimate rate of entanglement-assisted communication, they can enhance its reliability.
We analyze different aspects of multiparty communication over quantum memoryless channels and generalize some of the key results known from bipartite channels to the multiparty scenario. In particular, we introduce multiparty versions of subspace and entanglement transmission fidelities. We also provide alternative, local, versions of fidelities and show their equivalence to the global ones in context of capacity regions defined. An equivalence of two different capacity notions with respect to two types of fidelities is proven. In analogy to the bipartite case it is shown, via sufficiency of isometric encoding theorem, that additional classical forward side channel does not increase capacity region of any quantum channel with kkk senders and mmm receivers which represents a compact unit of general quantum networks theory. The result proves that recently provided capacity region of a multiple access channel [M. Horodecki et al., Nature 436, 673 (2005); J. Yard et al., e-print quant-ph/0501045], is optimal also in a scenario of an additional support of forward classical communication.