Quantum Inf Process (2015) 14:979–988
Inseparability criteria based on bipartitions of N-qubit
Received: 13 May 2014 / Accepted: 6 January 2015 / Published online: 17 January 2015
© Springer Science+Business Media New York 2015
Abstract We present a new set of inequalities to detect inseparability in N -qubit
states. These are based on negative partial transposition and involve collective qubit–
qubit correlations of any two partitions of the entire system. They reveal the rich
texture of partial separability for different partitions and can discriminate between
GHZ-type and W-type entanglement, as well. We introduce a new concept of relative
entanglement of two different systems and two different partitions in a qubit-ensemble.
The criteria in its generic form are also applicable to non-symmetric states and states
with odd or even N.
Keywords Inseparability criteria · Many-qubit systems · Partial transposition ·
In recent times, entanglement in many-qubit systems has attracted substantial attention
in view of scalable quantum computation, which relies on such entanglement as a
resource. Therefore, it is important to identify at the outset of an experiment whether
the state under consideration is entangled or not. However, nature of entanglement in
large ensembles is not yet well understood. It is customary to look into entanglement
between different partitions in such case. States of a few qubits, for example, are
Sponsored by the Department of Science and Technology, Govt. of India, under Fast Track Scheme
(Project No. SR/FTP/PS-71/2009).
A. Biswas (
Department of Physics, Indian Institute of Technology Ropar,
Rupnagar 140001, Punjab, India