Quantum Information Processing, Vol. 4, No. 1, February 2005 (© 2005)
Locality and Information Transfer in Quantum
and Michael D. Westmoreland
Received July 8, 2004; accepted October 14, 2004
We investigate the situation in which no information can be transferred from a
quantum system B to a quantum system A, even though both interact with a com-
mon system C.
KEY WORDS: Quantum locality; quantum subsystems; causality; global uni-
PACS: 03.67.-a, 03.65.Ud.
The universe can be divided up into subsystems that interact with one
another. All parts of the universe are connected, directly or indirectly, by
this web of interactions. Nevertheless, to predict the future state of a small
subsystem A, it is not necessary to specify the past state of the whole uni-
verse. This is what we mean by “locality” of the dynamical evolution of A
within the global system.
Beckman et al.
have investigated a related notion of locality in the
context of quantum operations. Suppose we have a bipartite system AB
whose quantum state evolves according to the map E
. We say that this
map is semicausal if it cannot be used to transfer information from B to
A. That is, if we begin with a joint state ρ
, perform an operation B on
subsystem B, and ﬁnally apply the map E
to the joint system then the
ﬁnal state of A alone is independent of the choice of B.Acausal map is
semicausal in both directions. In Ref. 1, these notions are related to other
Department of Physics, Kenyon College, Gambier, OH 43022, USA. E-mail:
Department of Mathematical Sciences, Denison University, Granville, OH 43023, USA.
To whom correspondence should be addressed.
1570-0755/05/0200-0013/0 © 2005 Springer Science+Business Media, Inc.