764 research outputs found
Separability of a family of one parameter W and GHZ multiqubit states using Abe-Rajagopal q-conditional entropy approach
We employ conditional Tsallis q entropies to study the separability of
symmetric one parameter W and GHZ multiqubit mixed states. The strongest
limitation on separability is realized in the limit q-->infinity, and is found
to be much superior to the condition obtained using the von Neumann conditional
entropy (q=1 case). Except for the example of two qubit and three qubit
symmetric states of GHZ family, the -conditional entropy method leads to
sufficient - but not necessary - conditions on separability.Comment: 7 pages, 5 ps figures, RevteX, Accepted for publication in Physical
Review
General construction of noiseless networks detecting entanglement with help of linear maps
We present the general scheme for construction of noiseless networks
detecting entanglement with the help of linear, hermiticity-preserving maps. We
show how to apply the method to detect entanglement of unknown state without
its prior reconstruction. In particular, we prove there always exists noiseless
network detecting entanglement with the help of positive, but not completely
positive maps. Then the generalization of the method to the case of
entanglement detection with arbitrary, not necessarily hermiticity-preserving,
linear contractions on product states is presented.Comment: Revtex, 6 pages, 3 figures, published versio
Optimal strategy for a single-qubit gate and trade-off between opposite types of decoherence
We study reliable quantum information processing (QIP) under two different
types of environment. First type is Markovian exponential decay, and the
appropriate elementary strategy of protection of qubit is to apply fast gates.
The second one is strongly non-Markovian and occurs solely during operations on
the qubit. The best strategy is then to work with slow gates. If the two types
are both present, one has to optimize the speed of gate. We show that such a
trade-off is present for a single-qubit operation in a semiconductor quantum
dot implementation of QIP, where recombination of exciton (qubit) is Markovian,
while phonon dressing gives rise to the non-Markovian contribution.Comment: 4 pages, 1 figure; final versio
Bounds on the entanglement of two-qutrit systems from fixed marginals
We discuss the problem of characterizing upper bounds on entanglement in a bipartite quantum system when only the reduced density matrices (marginals) are known. In particular, starting from the known two-qubit case, we propose a family of candidates for maximally entangled mixed states with respect to fixed marginals for two qutrits. These states are extremal in the convex set of two-qutrit states with fixed marginals. Moreover, it is shown that they are always quasidistillable. As a by-product we prove that any maximally correlated state that is quasidistillable must be pure. Our observations for two qutrits are supported by numerical analysis
Limits for entanglement measures
We show that {\it any} entanglement measure suitable for the regime of
high number of entangled pairs satisfies where and
are entanglement of distillation and formation respectively. We also
exhibit a general theorem on bounds for distillable entanglement. The results
are obtained by use of a very transparent reasoning based on the fundamental
principle of entanglement theory saying that entanglement cannot increase under
local operations and classical communication.Comment: 4 pages, Revtex, typos correcte
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
On the geometric distance between quantum states with positive partial transposition and private states
We prove an analytic positive lower bound for the geometric distance between
entangled positive partial transpose (PPT) states of a broad class and any
private state that delivers one secure key bit. Our proof holds for any Hilbert
space of finite dimension. Although our result is proven for a specific class
of PPT states, we show that our bound nonetheless holds for all known entangled
PPT states with non-zero distillable key rates whether or not they are in our
special class.Comment: 16 page
Nonadditivity of Bipartite Distillable Entanglement follows from Conjecture on Bound Entangled Werner States
Assuming the validity of a conjecture in quant-ph/9910026 and
quant-ph/9910022 we show that the distillable entanglement for two bipartite
states, each of which individually has zero distillable entanglement, can be
nonzero. We show that this also implies that the distillable entanglement is
not a convex function. Our example consists of the tensor product of a bound
entangled state based on an unextendible product basis with a Werner state
which lies in the class of conjectured undistillable states.Comment: 4 pages RevTex, 1 figure, to appear in Phys. Rev. Lett. Title changed
and small paragraph adde
Dynamics of quantum entanglement
A model of discrete dynamics of entanglement of bipartite quantum state is
considered. It involves a global unitary dynamics of the system and periodic
actions of local bistochastic or decaying channel. For initially pure states
the decay of entanglement is accompanied with an increase of von Neumann
entropy of the system. We observe and discuss revivals of entanglement due to
unitary interaction of both subsystems. For some mixed states having different
marginal entropies of both subsystems (one of them larger than the global
entropy and the other one one smaller) we find an asymmetry in speed of
entanglement decay. The entanglement of these states decreases faster, if the
depolarizing channel acts on the "classical" subsystem, characterized by
smaller marginal entropy.Comment: 10 pages, Revtex, 10 figures, refined versio
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