56 research outputs found
Are all maximally entangled states pure?
We study if all maximally entangled states are pure through several
entanglement monotones. In the bipartite case, we find that the same conditions
which lead to the uniqueness of the entropy of entanglement as a measure of
entanglement, exclude the existence of maximally mixed entangled states. In the
multipartite scenario, our conclusions allow us to generalize the idea of
monogamy of entanglement: we establish the \textit{polygamy of entanglement},
expressing that if a general state is maximally entangled with respect to some
kind of multipartite entanglement, then it is necessarily factorized of any
other system.Comment: 5 pages, 1 figure. Proof of theorem 3 corrected e new results
concerning the asymptotic regime include
Schmidt balls around the identity
Robustness measures as introduced by Vidal and Tarrach [PRA, 59, 141-155]
quantify the extent to which entangled states remain entangled under mixing.
Analogously, we introduce here the Schmidt robustness and the random Schmidt
robustness. The latter notion is closely related to the construction of Schmidt
balls around the identity. We analyse the situation for pure states and provide
non-trivial upper and lower bounds. Upper bounds to the random Schmidt-2
robustness allow us to construct a particularly simple distillability
criterion. We present two conjectures, the first one is related to the radius
of inner balls around the identity in the convex set of Schmidt number
n-states. We also conjecture a class of optimal Schmidt witnesses for pure
states.Comment: 7 pages, 1 figur
Reflections upon separability and distillability
We present an abstract formulation of the so-called Innsbruck-Hannover
programme that investigates quantum correlations and entanglement in terms of
convex sets. We present a unified description of optimal decompositions of
quantum states and the optimization of witness operators that detect whether a
given state belongs to a given convex set. We illustrate the abstract
formulation with several examples, and discuss relations between optimal
entanglement witnesses and n-copy non-distillable states with non-positive
partial transpose.Comment: 12 pages, 7 figures, proceedings of the ESF QIT Conference Gdansk,
July 2001, submitted to special issue of J. Mod. Op
Separable approximation for mixed states of composite quantum systems
We describe a purely algebraic method for finding the best separable
approximation to a mixed state of a composite 2x2 quantum system, consisting of
a decomposition of the state into a linear combination of a mixed separable
part and a pure entangled one. We prove that, in a generic case, the weight of
the pure part in the decomposition equals the concurrence of the state.Comment: 13 pages, no figures; minor changes; accepted for publication in PR
Separability in 2xN composite quantum systems
We analyze the separability properties of density operators supported on
\C^2\otimes \C^N whose partial transposes are positive operators. We show
that if the rank of equals N then it is separable, and that bound
entangled states have rank larger than N. We also give a separability criterion
for a generic density operator such that the sum of its rank and the one of its
partial transpose does not exceed 3N. If it exceeds this number we show that
one can subtract product vectors until decreasing it to 3N, while keeping the
positivity of and its partial transpose. This automatically gives us a
sufficient criterion for separability for general density operators. We also
prove that all density operators that remain invariant after partial
transposition with respect to the first system are separable.Comment: Extended version of quant-ph/9903012 with new results. 11 page
Optimal Lewenstein-Sanpera Decomposition for some Biparatite Systems
It is shown that for a given bipartite density matrix and by choosing a
suitable separable set (instead of product set) on the separable-entangled
boundary, optimal Lewenstein-Sanpera (L-S) decomposition can be obtained via
optimization for a generic entangled density matrix. Based on this, We obtain
optimal L-S decomposition for some bipartite systems such as and
Bell decomposable states, generic two qubit state in Wootters
basis, iso-concurrence decomposable states, states obtained from BD states via
one parameter and three parameters local operations and classical
communications (LOCC), Werner and isotropic states, and a one
parameter state. We also obtain the optimal decomposition for
multi partite isotropic state. It is shown that in all systems
considered here the average concurrence of the decomposition is equal to the
concurrence. We also show that for some Bell decomposable states
the average concurrence of the decomposition is equal to the lower bound of the
concurrence of state presented recently in [Buchleitner et al,
quant-ph/0302144], so an exact expression for concurrence of these states is
obtained. It is also shown that for isotropic state where
decomposition leads to a separable and an entangled pure state, the average
I-concurrence of the decomposition is equal to the I-concurrence of the state.
Keywords: Quantum entanglement, Optimal Lewenstein-Sanpera decomposition,
Concurrence, Bell decomposable states, LOCC}
PACS Index: 03.65.UdComment: 31 pages, Late
Separable approximations of density matrices of composite quantum systems
We investigate optimal separable approximations (decompositions) of states
rho of bipartite quantum systems A and B of arbitrary dimensions MxN following
the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261
(1998)]. Such approximations allow to represent in an optimal way any density
operator as a sum of a separable state and an entangled state of a certain
form. For two qubit systems (M=N=2) the best separable approximation has a form
of a mixture of a separable state and a projector onto a pure entangled state.
We formulate a necessary condition that the pure state in the best separable
approximation is not maximally entangled. We demonstrate that the weight of the
entangled state in the best separable approximation in arbitrary dimensions
provides a good entanglement measure. We prove in general for arbitrary M and N
that the best separable approximation corresponds to a mixture of a separable
and an entangled state which are both unique. We develop also a theory of
optimal separable approximations for states with positive partial transpose
(PPT states). Such approximations allow to decompose any density operator with
positive partial transpose as a sum of a separable state and an entangled PPT
state. We discuss procedures of constructing such decompositions.Comment: 12 pages, 2 figure
Separability and entanglement in 2x3xN composite quantum systems
The separability and entanglement of quantum mixed states in \Cb^2 \otimes
\Cb^3 \otimes \Cb^N composite quantum systems are investigated. It is shown
that all quantum states with positive partial transposes and rank
are separable.Comment: Latex, 15 page
- âŠ