The Relative Entropy of Entanglement of Schmidt
Correlated States and Distillation
and Dong Yang
Received September 30, 2002; accepted December 26, 2002
We show that a mixed state & ¼
jmihnj can be realized by an ensemble of
pure states f p
ig where j0
jmi. Employing this form, we
discuss the relative entropy of entanglement of Schmidt correlated states. Also, we
calculate the distillable entanglement of a class of mixed states.
KEY WORDS: Relative entropy of entanglement; Schmidt correlated state.
PACS: 03.67.-a; 03.65.Bz; 03.65.Ud.
Quantum entanglement is at the heart of many aspects of quantum infor-
mation theory and responsible for many quantum tasks such as tele-
quantum error correction
etc. In this sense, it
is nowadays viewed as a quantum resource. Intensive theoretical eﬀorts were
made to understand the mathematical structure of entanglement, qualita-
tively and quantitively. Among the entanglement measures, the relative
entropy of entanglement
plays an important role. For general mixed
states, the relative entropy of entanglement is hard to calculate. However, it
can be calculated explicitly for the Schmidt correlated states.
note, employing the particular realization form of mixed states, we easily
deduce the properties of Schmidt correlated states. Generally, orthogonal
states may be distinguished perfectly only by means of global measurements
since the global information of orthogonality may be encoded in entangle-
ment that may not be extracted by local operations and classical commu-
nication (LOCC). Bennett et al.
showed that a set of nine pairwise
1570-0755/02/1000-0389/0 # 2003 Plenum Publishing Corporation
Zhejiang Institute of Modern Physics andDepartment of Physics, Zhejiang University,
Hangzhou 310027, P.R. China
To whom correspondence should be addressed. E-mail: firstname.lastname@example.org
Quantum Information Processing, Vol. 1, No. 5, October 2002 (# 2003)