Physics – Quantum Physics
Scientific paper
2008-02-10
J. Math. Phys. 49, 102104 (2008)
Physics
Quantum Physics
42 pages, 3 figures, Web and paper abstract differ; (v2 contains only minor typo corrections)
Scientific paper
10.1063/1.2953685
Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the structure of degradable quantum channels, including a number of new results as well as alternate proofs of some known results. In the case of qubits, we provide a complete characterization of all degradable channels with two dimensional output, give a new proof that a qubit channel with two Kraus operators is either degradable or anti-degradable and present a complete description of anti-degradable unital qubit channels with a new proof. For higher output dimensions we explore the relationship between the output and environment dimensions ($d_B$ and $d_E$ respectively) of degradable channels. For several broad classes of channels we show that they can be modeled with a environment that is "small" in the sense $d_E \leq d_B$. Perhaps surprisingly, we also present examples of degradable channels with ``large'' environments, in the sense that the minimal dimension $d_E > d_B$. Indeed, one can have $d_E > \tfrac{1}{4} d_B^2$. In the case of channels with diagonal Kraus operators, we describe the subclass which are complements of entanglement breaking channels. We also obtain a number of results for channels in the convex hull of conjugations with generalized Pauli matrices. However, a number of open questions remain about these channels and the more general case of random unitary channels.
Cubitt Toby S.
Ruskai Mary Beth
Smith Graeme
No associations
LandOfFree
The structure of degradable quantum channels does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The structure of degradable quantum channels, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The structure of degradable quantum channels will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-624795