Quantum Information Processing

, Volume 12, Issue 12, pp 3725–3744 | Cite as

Dissipative and non-dissipative single-qubit channels: dynamics and geometry

  • S. Omkar
  • R. Srikanth
  • Subhashish Banerjee


Single-qubit dissipative and non-dissipative channels, set in the general scenario of a system’s interaction with a squeezed thermal bath, are compared in the Choi isomorphism framework, to bring out their contrasting rank and geometric properties. The equivalence of commutativity between the signal states and the Kraus operators to that between the system and interaction Hamiltonian, and thus to non-dissipativeness, is pointed out. Two distinct unitarily equivalent Kraus representations of the dissipative channel, one based on the Choi isomorphism, and the other based on an ansatz, are used to illustrate that the orthogonality of Kraus operators under the Hilbert–Schmidt inner product is not a unitary invariant. Unlike the non-dissipative (Pauli) channels, the dissipative (squeezed generalized amplitude damping) channels do not form a convex set. Further, whereas the rank of Pauli channels can be any positive integer up to 4, that of the amplitude damping ones is either 2 or 4. In the latter case, a noise range is identified where environmental squeezing counteracts the effect of thermal decoherence.


Dissipative Single-qubit 



Author S. Omkar acknowledges Manipal University, Manipal, India for accepting this work as a part of Ph.D. thesis.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Poornaprajna Institute of Scientific ResearchBangaloreIndia
  2. 2.Indian Institute of Technology RajasthanJodhpurIndia

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