26 research outputs found
Invariance of quantum correlations under local channel for a bipartite quantum state
We show that the quantum discord and the measurement induced non-locality
(MiN) in a bipartite quantum state is invariant under the action of a local
quantum channel if and only if the channel is invertible. In particular, these
quantities are invariant under a local unitary channel.Comment: 4 pages, no figures, proof of theorm 2 modifie
Bound on Hardy's non-locality from the principle of Information Causality
Recently,the principle of nonviolation of information causality [Nature
461,1101 (2009)], has been proposed as one of the foundational properties of
nature. We explore the Hardy's nonlocality theorem for two qubit systems, in
the context of generalised probability theory, restricted by the principle of
nonviolation of information causality. Applying, a sufficient condition for
information causality violation, we derive an upper bound on the maximum
success probability of Hardy's nonlocality argument. We find that the bound
achieved here is higher than that allowed by quantum mechanics,but still much
less than what the nosignaling condition permits. We also study the Cabello
type nonlocality argument (a generalization of Hardy's argument) in this
context.Comment: Abstract modified, changes made in the conclusion, throughout the
paper we clarified that the condition used by us is protocal based and is
only a sufficient condition for the violation of information causalit
Nonlocality without inequality for almost all two-qubit entangled state based on Cabello's nonlocality argument
Here we deal with a nonlocality argument proposed by Cabello which is more
general than Hardy's nonlocality argument but still maximally entangled states
do not respond. However, for most of the other entangled states maximum
probability of success of this argument is more than that of the Hardy's
argument.Comment: 9 pages, 1 figur
On the degree conjecture for separability of multipartite quantum states
We settle the so-called degree conjecture for the separability of
multipartite quantum states, which are normalized graph Laplacians, first given
by Braunstein {\it et al.} [Phys. Rev. A \textbf{73}, 012320 (2006)]. The
conjecture states that a multipartite quantum state is separable if and only if
the degree matrix of the graph associated with the state is equal to the degree
matrix of the partial transpose of this graph. We call this statement to be the
strong form of the conjecture. In its weak version, the conjecture requires
only the necessity, that is, if the state is separable, the corresponding
degree matrices match. We prove the strong form of the conjecture for {\it
pure} multipartite quantum states, using the modified tensor product of graphs
defined in [J. Phys. A: Math. Theor. \textbf{40}, 10251 (2007)], as both
necessary and sufficient condition for separability. Based on this proof, we
give a polynomial-time algorithm for completely factorizing any pure
multipartite quantum state. By polynomial-time algorithm we mean that the
execution time of this algorithm increases as a polynomial in where is
the number of parts of the quantum system. We give a counter-example to show
that the conjecture fails, in general, even in its weak form, for multipartite
mixed states. Finally, we prove this conjecture, in its weak form, for a class
of multipartite mixed states, giving only a necessary condition for
separability.Comment: 17 pages, 3 figures. Comments are welcom