World Library  

Add to Book Shelf
Flag as Inappropriate
Email this Book

Journal of Mathematical Physics : The structure of degradable quantum channels

By Toby S. Cubitt, Mary Beth Ruskai, and Graeme Smith

Click here to view

Book Id: WPLBN0002169535
Format Type: PDF eBook :
File Size: Serial Publication
Reproduction Date: 8 October 2008

Title: Journal of Mathematical Physics : The structure of degradable quantum channels  
Author: Toby S. Cubitt, Mary Beth Ruskai, and Graeme Smith
Volume: Issue : October 2008
Language: English
Subject: Science, Physics, Natural Science
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Journal of Mathematical Physics Collection
Publication Date:
Publisher: American Institute of Physics


APA MLA Chicago

Cubitt, Mary Beth Ruskai, And Graeme Smit, T. S. (n.d.). Journal of Mathematical Physics : The structure of degradable quantum channels. Retrieved from

Description: 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 (dB and dE, respectively) of degradable channels. For several broad classes of channels we show that they can be modeled with an environment that is “small” in the sense of ΦC. Such channels include all those with qubit or qutrit output, those that map some pure state to an output with full rank, and all those which can be represented using simultaneously diagonal Kraus operators, even in a non-orthogonal basis. Perhaps surprisingly, we also present examples of degradable channels with “large” environments, in the sense that the minimal dimension dE>dB. Indeed, one can have dE>¼dB2. These examples can also be used to give a negative answer to the question of whether additivity of the coherent information is helpful for establishing additivity for the Holevo capacity of a pair of channels. In the case of channels with diagonal Kraus operators, we describe the subclasses that 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.


Click To View

Additional Books

  • Journal of Applied Physics : Effect of g... Volume Issue : November 2008 (by )
  • Journal of Mathematical Physics : Weyl q... Volume Issue : October 2008 (by )
  • Journal of Mathematical Physics : Additi... Volume Issue : October 2008 (by )
  • Applied Physics Letters : Wave propagati... Volume Issue : December 2008 (by )
  • Physics of Fluids : Weakly nonlinear sta... Volume Issue : September 2008 (by )
  • Biblioteca Hispanica : Course of Natural... (by )
  • Chaos : Coherence resonance induced by c... Volume Issue : November 2008 (by )
  • Chaos : Introduction: Fifth Annual Galle... Volume Issue : December 2008 (by )
  • Journal of Applied Physics : Analysis of... Volume Issue : November 2008 (by )
  • Biblioteca Hispanica : Notions of Natura... (by )
  • Physics of Plasmas : Modeling of an adva... Volume Issue : November 2008 (by )
  • Journal of Applied Physics : Vacancy gen... Volume Issue : November 2008 (by )
Scroll Left
Scroll Right


Copyright © World Library Foundation. All rights reserved. eBooks from World Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.