Hamiltonian Composite Dynamics Can Almost Always Lead To Negative Reduced Dynamics

Abstract

Complete positivity is a ubiquitous assumption in the study of quantum systems interacting with the environment, despite repeated efforts to point out that the assumption is not empirically justified. It will be shown that Hamiltonian evolution of a quantum system and its environment can be negative (i.e.\ not completely positive) in the energy basis, by showing that such evolution is {\it almost always} negative for given initial conditions. Ignoring or "correcting" experimental data that is not completely positive may cause the loss of important information regarding system-environment correlations and coupling. A relationship between the negativity of an evolution and the eigenvalues of the Hamiltonian will be shown, and experimental verification of negative reduced dynamics will be proposed.

7 pages, 2 figures; Added a discussion of discord and proposed experimental observations of negativity

References in corpus (5)

• Vanishing quantum discord is necessary and sufficient for completely positive maps
• Completely Positive Maps and Classical Correlations
• Quantum process tomography and Linblad estimation of a solid state qubit
• Open system quantum dynamics with correlated initial states, not completely positive maps and non-Markovianity
• Experimental realization of linear-optical partial SWAP gates

Cited by in corpus (4)

• Violations of the second law of thermodynamics by a non completely positive dynamics
• Complete positivity and thermodynamics in a driven open quantum system
• Complete positivity violation of the reduced dynamics in higher-order quantum adiabatic elimination
• Some aspects of the interplay between bipartite correlations and quantum channels