Complementary Channels and the Additivity Problem

By Alexander S. Holevo. 2005

159 citations recorded by the source corpus.

We explore the complementarity between output and environment of a quantum channel (or, more generally, completely positive (CP) map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, the validity of the mutiplicativity/additivity conjecture for a class of CP maps implies its validity for complementary maps. The class of CP maps complementary to entanglement‐breaking ones is described and is shown to contain diagonal CP maps as a proper subclass, resulting in a new class of CP maps (channels) for which the multiplicativity/additivity holds. Covariant and Gaussian channels are discussed briefly in this context.

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

View Paper: https://www.semanticscholar.org/paper/04e6d9bbaad9f01ae7ad6337b133c653758a218a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Vittorio Giovannetti
2. Filippo Caruso
3. Cosmo Lupo
4. Stefano Mancini

In Atomic and Molecular Physics, and Optics

1. Vittorio Giovannetti
2. Filippo Caruso
3. Cosmo Lupo
4. Stefano Mancini

Citations in the corpus

• Quantum channels and memory effects (2012, background): “Moreover, as observed in (Holevo, 2007 a) if a quantum channel is (super)additive for the Holevo information, so is its complementary channel.”
• Ultimate classical communication rates of quantum optical channels (2014, unknown): “These last two have indeed the same minimum output entropy as they are conjugate [37, 38] (more generally, given a generic pure input state |ψ〉, the density operators Aκ0(|ψ〉〈ψ|) and Ãκ0(|ψ〉〈ψ|) have the same nonzero spectra.”