Quantum Inf Process (2016) 15:3421–3441
Inﬂuence of environmental noise on the weak value
· Yu-Xiang Zhang
Received: 5 December 2015 / Accepted: 5 May 2016 / Published online: 18 May 2016
© Springer Science+Business Media New York 2016
Abstract Quantum systems are always disturbed by environmental noise. We have
investigated the inﬂuence of the environmental noise on the ampliﬁcation in weak
measurements. Three typical quantum noise processes are discussed in this article.
The maximum expectation values of the observables of the measuring device decrease
sharply with the strength of the depolarizing and phase damping channels, while the
ampliﬁcation effect of weak measurement is immune to the amplitude damping noise.
To obtain signiﬁcantly ampliﬁed signals, we must ensure that the preselection quantum
systems are kept away from the depolarizing and phase damping processes.
Keywords Weak measurement · Weak value · Quantum noise · Ampliﬁcation
In 1988, Aharanov, Albert, and Vaidman showed that the expectation values of the
measuring device in weak measurement could be much larger than the ones in the
traditional measurement . The ampliﬁcation effect of weak measurement has been
conﬁrmed by experiments [2,3]. Weak measurement strategy has been used to imple-
ment a lot of high-precise measurements due to its ampliﬁcation [4–13]. In addition
to its application in improving measurement precision, weak measurement is used to
realize direct quantum tomography [14–20] and explore the fundamental problems
School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China
Hefei National Laboratory for Physical Sciences at Microscale, University of Science
and Technology of China, Hefei 230026, Anhui, China