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arXiv:0906.1305 · Physical Review A

Nonadditivity of quantum and classical capacities for entanglement breaking multiple-access channels and the butterfly network

Andrzej Grudka, Paweł Horodecki

Published Jun 23, 2010• 73 citations
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Abstract

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.

DOI
10.1103/physreva.81.060305

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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 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.
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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 analyze the quantum adder channel, i.e. the extension of a classical multiple-access additive binary channel to the quantum regime, in which quantum bits (qubits) rather than classical bits are transmitted. Quantum entanglement between different transmitters and/or the receiver results in a significant expansion of the capacity region of the channel, in comparison with its classical counterpart, a property which can be used, e.g., to considerably improve bandwidth efficiency of fiber communication networks in the future.