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Nonadditivity of quantum and classical capacities for quantum networks with entanglement breaking lines

Andrzej Grudka, Paweł Horodecki

Published Jun 6, 2009• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
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.
Superadditivity effects in the classical capacity of discrete multiaccess channels and continuous variable (CV) Gaussian MACs are analyzed. Several examples of the manifestation of superadditivity in the discrete case are provided, including, in particular, a channel which is fully symmetric with respect to all senders. Furthermore, we consider a class of channels for which input entanglement across more than two copies of the channels is necessary to saturate the asymptotic rate of transmission from one of the senders to the receiver. The five-input entanglement of Shor error correction codewords surpass the capacity attainable by using arbitrary two-input entanglement for these channels. In the CV case, we consider the properties of the two channels (a beam-splitter channel and a ``nondemolition'' quadratures coupling sum (XP) gate channel) analyzed in Czekaj et al. [Phys. Rev. A 82, 020302(R) (2010)] in greater detail and also consider the sensitivity of capacity superadditivity effects to thermal noise. We observe that the estimates of the amount of two-mode squeezing required to achieve capacity superadditivity are more optimistic than previously reported.
We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (for minimum entropy output) or superadditivity (for classical capacity) that can occur. One of the more important open questions of quantum information theory is the determination of the capacity of a quantum channel for carrying classical information. This question has been only partially resolved. If entanglement between multiple inputs to the channel is not allowed, a formula for the classical capacity of a quantum channel has indeed been discovered [1, 2]. This capacity formula for a quantum channel Ψ is χ ∗ (Ψ) = max p i,ρ i H Ψ(piρi) − ∑