Grunnleggende konsepter
Three measures of dynamical coherence for quantum channels are introduced, which generalize previous results. These measures are based on a generalized distance function between channels and are monotone under free superchannels and convex.
Sammendrag
The paper presents three measures of dynamical coherence for quantum channels, which generalize previous results. The measures are based on a generalized distance function between channels, such as the divergence or a trace-distance. Free operations are considered to be detection-incoherent, creation-incoherent, and detection-creation incoherent. Free superchannels can be expressed using free pre- and post-processing channels.
The three new measures are shown to be coherence measures, meaning they satisfy the properties of non-negativity, monotonicity under free superchannels, and convexity. The measures are defined as:
CDI_f(N) = min_{K∈DI} f(ΔN, ΔK) for detection-incoherent (DI) channels.
CCI_f(N) = min_{K∈CI} f(NΔ, KΔ) for creation-incoherent (CI) channels.
CDCI_f(N) = min_{K∈DCI} f(N, K) for detection-creation incoherent (DCI) channels.
Here, f is a function acting as a distance between channels that satisfies certain properties, such as non-negativity, weak monotonicity, joint convexity, and monotonicity under tensor products.
The paper provides the proofs that these three measures satisfy the coherence measure conditions, including monotonicity under free superchannels and convexity.
Statistikk
The relative entropy of channels, Dre(N||M), satisfies the properties required for the function f.
The trace-one distance of channels, ||N-M||_1, also satisfies the required properties for f.
Sitater
"We present three measures of the dynamical coherence of channels, which are the generalization of several previous results."
"The new measures are monotone under free superchannels and convex."