Journal
QUANTUM INFORMATION PROCESSING
Volume 15, Issue 4, Pages 1349-1360Publisher
SPRINGER
DOI: 10.1007/s11128-015-1228-1
Keywords
Complete positivity; Quantum maps; Non-completely positive dynamics; Quantum subsystem dynamics
Funding
- ARO MURI Grant [W911NF-11-1-0268]
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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 -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.
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