639 research outputs found
Multiparticle entanglement purification for graph states
We introduce a class of multiparticle entanglement purification protocols
that allow us to distill a large class of entangled states. These include
cluster states, GHZ states and various error correction codes all of which
belong to the class of two-colorable graph states. We analyze these schemes
under realistic conditions and observe that they are scalable, i.e. the
threshold value for imperfect local operations does not depend on the number of
parties for many of these states. When compared to schemes based on bipartite
entanglement purification, the protocol is more efficient and the achievable
quality of the purified states is larger. As an application we discuss an
experimental realization of the protocol in optical lattices which allows one
to purify cluster states.Comment: 4 pages, 2 figures; V2: some typos corrected; V3: published versio
Entanglement purification with noisy apparatus can be used to factor out an eavesdropper
We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. Our proof applies to all possible attacks (individual and coherent). Due to the quantum nature of the entanglement purification protocol, it is also possible to use the obtained quantum channel for secure transmission of quantum information
Multiparticle entanglement purification for two-colorable graph states
We investigate multiparticle entanglement purification schemes which allow
one to purify all two colorable graph states, a class of states which includes
e.g. cluster states, GHZ states and codewords of various error correction
codes. The schemes include both recurrence protocols and hashing protocols. We
analyze these schemes under realistic conditions and observe for a generic
error model that the threshold value for imperfect local operations depends on
the structure of the corresponding interaction graph, but is otherwise
independent of the number of parties. The qualitative behavior can be
understood from an analytically solvable model which deals only with a
restricted class of errors. We compare direct multiparticle entanglement
purification protocols with schemes based on bipartite entanglement
purification and show that the direct multiparticle entanglement purification
is more efficient and the achievable fidelity of the purified states is larger.
We also show that the purification protocol allows one to produce private
entanglement, an important aspect when using the produced entangled states for
secure applications. Finally we discuss an experimental realization of a
multiparty purification protocol in optical lattices which is issued to improve
the fidelity of cluster states created in such systems.Comment: 22 pages, 8 figures; replaced with published versio
On the Minimum Degree up to Local Complementation: Bounds and Complexity
The local minimum degree of a graph is the minimum degree reached by means of
a series of local complementations. In this paper, we investigate on this
quantity which plays an important role in quantum computation and quantum error
correcting codes. First, we show that the local minimum degree of the Paley
graph of order p is greater than sqrt{p} - 3/2, which is, up to our knowledge,
the highest known bound on an explicit family of graphs. Probabilistic methods
allows us to derive the existence of an infinite number of graphs whose local
minimum degree is linear in their order with constant 0.189 for graphs in
general and 0.110 for bipartite graphs. As regards the computational complexity
of the decision problem associated with the local minimum degree, we show that
it is NP-complete and that there exists no k-approximation algorithm for this
problem for any constant k unless P = NP.Comment: 11 page
Haldane, Large-D and Intermediate-D States in an S=2 Quantum Spin Chain with On-Site and XXZ Anisotropies
Using mainly numerical methods, we investigate the ground-state phase diagram
of the S=2 quantum spin chain described by , where
denotes the anisotropy parameter of the nearest-neighbor interactions and
the on-site anisotropy parameter. We restrict ourselves to the case with
and for simplicity. Each of the phase boundary lines
is determined by the level spectroscopy or the phenomenological renormalization
analysis of numerical results of exact-diagonalization calculations. The
resulting phase diagram on the - plane consists of four phases; the
XY 1 phase, the Haldane/large- phase, the intermediate- phase and the
N\'eel phase. The remarkable natures of the phase diagram are: (1) the Haldane
state and the large- state belong to the same phase; (2) there exists the
intermediate- phase which was predicted by Oshikawa in 1992; (3) the shape
of the phase diagram on the - plane is different from that believed
so far. We note that this is the first report of the observation of the
intermediate- phase
Renal Function but Not Asymmetric Dimethylarginine Is Independently Associated with Retinopathy in Type 2 Diabetes
Background. Asymmetric dimethylarginine (ADMA) is associated with macrovascular disease and possibly with microangiopathy in type 2 diabetes (T2DM). We tested the hypothesis that ADMA is related to diabetic retinopathy (DR) independently of macrovascular disease. Methods. This cross-sectional study included 127 T2DM patients selected to achieve equal distributions of patients with and without macrovascular disease in the groups with and without DR. Results. Patients with DR had increased ADMA, longer diabetes duration, and reduced glomerular filtration rate (GFR). ADMA correlated with GFR (Ï = -0.35; P < .001), diabetes duration (Ï = 0.19; P = .048), and age (Ï = 0.19; P = .033). Logistic regression analysis revealed an association of ADMA with DR. After adjustment for macrovascular disease, this association remained significant (OR 1.48; 95% CI:â1.02â2.15; P = .039). Inclusion of GFR and T2DM duration into the model abolished this significant relationship. GFR remained the only independent predictor for DR. A 10âmL/min/1.73âm2 GFR decrease was associated with DR in a multivariate model (OR 1.30; 95% CI:â1.08â1.56; P = .006). Conclusions. These findings indicate an association between ADMA and DR in T2DM independent of macrovascular disease. This relationship is modified by GFR, the only parameter significantly related to DR in multivariate analysis
Quantum Communication and Decoherence
In this contribution we will give a brief overview on the methods used to
overcome decoherence in quantum communication protocols. We give an
introduction to quantum error correction, entanglement purification and quantum
cryptography. It is shown that entanglement purification can be used to create
``private entanglement'', which makes it a useful tool for cryptographic
protocols.Comment: 31 pages, 10 figures, LaTeX, book chapter to appear in ``Coherent
Evolution in Noisy Environments'', Lecture Notes in Physics, (Springer
Verlag, Berlin-Heidelberg-New York). Minor typos correcte
A security proof of quantum cryptography based entirely on entanglement purification
We give a proof that entanglement purification, even with noisy apparatus, is
sufficient to disentangle an eavesdropper (Eve) from the communication channel.
In the security regime, the purification process factorises the overall initial
state into a tensor-product state of Alice and Bob, on one side, and Eve on the
other side, thus establishing a completely private, albeit noisy, quantum
communication channel between Alice and Bob. The security regime is found to
coincide for all practical purposes with the purification regime of a two-way
recurrence protocol. This makes two-way entanglement purification protocols,
which constitute an important element in the quantum repeater, an efficient
tool for secure long-distance quantum cryptography.Comment: Follow-up paper to quant-ph/0108060, submitted to PRA; 24 pages,
revex
Entanglement purification of multi-mode quantum states
An iterative random procedure is considered allowing an entanglement
purification of a class of multi-mode quantum states. In certain cases, a
complete purification may be achieved using only a single signal state
preparation. A physical implementation based on beam splitter arrays and
non-linear elements is suggested. The influence of loss is analyzed in the
example of a purification of entangled N-mode coherent states.Comment: 6 pages, 3 eps-figures, using revtex
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