Open Access JMP Weak Values Influenced by Environment

Copyright © 2013 Masashi Ban. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A weak value of an observable is studied for a quantum system which is placed under the influence of an environment, where a quantum system irreversibly evolves from a pre-selected state to a post-selected state. A general expression for a weak value influenced by an environment is provided. For a Markovian environment, the weak value is calculated in terms of the predictive and retrodictive density matrices, or by means of the quantum regression theorem. For a non-Markovian environment, a weak value is examined by making use of exactly solvable models. It is found that although the anomalous property is significantly suppressed by a Markovian environment, it can survive a non-Markovian envi-ronment