Quantum Information Processing

, Volume 15, Issue 4, pp 1349–1360 | Cite as

Beyond complete positivity

  • Jason M. Dominy
  • Daniel A. LidarEmail author


We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial system-bath states. We describe the space of possibilities admitted by this formulation, namely that, far from being limited to only completely positive (CP) maps, essentially any \({\mathbb {C}}\)-linear, Hermiticity-preserving, trace-preserving map can arise as a legitimate subsystem dynamical map from a joint unitary evolution of a system coupled to a bath. The price paid for this added generality is a trade-off between the set of admissible initial states and the allowed set of joint system-bath unitary evolutions. As an application, we present a simple example of a non-CP map constructed as a subsystem dynamical map that violates some fundamental inequalities in quantum information theory, such as the quantum data processing inequality.


Complete positivity Quantum maps Non-completely positive dynamics Quantum subsystem dynamics 



This research was supported by the ARO MURI Grant W911NF-11-1-0268. The authors thank Iman Marvian for many helpful discussions.

Supplementary material

11128_2015_1228_MOESM1_ESM.pdf (78 kb)
Supplementary material 1 (pdf 78 KB)


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of PhysicsUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.Department of Electrical EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  4. 4.Center for Quantum Information Science & TechnologyUniversity of Southern CaliforniaLos AngelesUSA

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