Additivity of the classical capacity of entanglement-breaking quantum channels

By Peter W. Shor. 2002

255 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4ef4e20dc2aa9be7d37a2c56d6d95c71be503863

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Entanglement Breaking Channels (2003, background): “Shor [20] then proved the additivity of minimal entropy and Holevo capacity when Φ is EBT and Ω arbitrary.”
A Survey on Quantum Channel Capacities (2018, background): “About the additivity of the capacity of quantum channels see [165], [271], [474].”
Properties of Conjugate Channels with Applications to Additivity and Multiplicativity (2005, background): “t most drather than d2 is quite remarkable. 3 Conjugates of entanglement breaking maps Inthis section wereview theclass ofentanglement-breaking maps. Anentanglementbreaking trace-preserving (EBT) map [33] is a CPT map Φ for which (I⊗Φ)(ρ) is 10 separable for all ρ. A number of equivalent criteria ar”
Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy (2013, background): “If Nx , Mx ≥ 0 for all x , then we say that the map is entanglement-breaking [31,32,34,62], and one can also verify that it is completely positive as well.”
Quantum channels and memory effects (2012, methodology): “…notwithstanding the fact that the Holevo information is generally superadditive, it has been proven to be additive for certain classes of quantum channels (Amosov and Mancini, 2009; Hiroshima, 2006), among which, qubit unital channels (King, 2002), entanglement breaking channels (Shor, 2002a).”
Geometry of Quantum States: Index (2007, background): “This was known to hold for some particular class of channels [32, 530, 836], so it was tempting to speculate that it is true in general.”
Qubit Entanglement Breaking Channels (2003, background): “I owe a particularly large debt to Peter Shor for stimulating my interest in this topic by communicating the results of [17] prior to publication.”