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

Combined Theoretical and Experimental Study of the Moiré Dislocation Network at the SrTiO3-(La,Sr)(Al,Ta)O3 Interface.

Recently, a highly ordered Moiré dislocation lattice was identified at the interface between a SrTiO3 (STO) thin film and the (LaAlO3)0.3(Sr2TaAlO6)0.7 (LSAT) substrate. A fundamental understanding of the local ionic and electronic structures around the dislocation cores is crucial to further engineer the properties of these complex multifunctional heterostructures. Here, we combine experimental characterization via analytical scanning transmission electron microscopy with results of molecular dynamics and density functional theory calculations to gain insights into the structure and defect chemistry of these dislocation arrays. Our results show that these dislocations lead to undercoordinated Ta/Al cations at the dislocation core, where oxygen vacancies can easily be formed, further facilitated by the presence of cation vacancies. The reduced Ti3+ observed experimentally at the dislocations by electron energy-loss spectroscopy is a consequence of both the structure of the dislocation itself and of the electron doping due to oxygen vacancy formation. Finally, the experimentally observed Ti diffusion into the LSAT around the dislocation core occurs only together with cation vacancy formation in the LSAT or Ta diffusion into STO

Combined theoretical and experimental study of the Moir\'e dislocation network at the SrTiO3_3-(La,Sr)(Al,Ta)O3_3 interface

Recently a highly ordered Moir\'e dislocation lattice was identified at the interface between a \ce{SrTiO3} (STO) thin film and the (LaAlO$_3$)$_{0.3}$(Sr$_2$TaAlO$_6$)$_{0.7}$ (LSAT) substrate. A fundamental understanding of the local ionic and electronic structure around the dislocation cores is crucial to further engineer the properties of these complex multifunctional heterostructures. Here we combine experimental characterization via analytical scanning transmission electron microscopy with results of molecular dynamics and density functional theory calculations to gain insights into the structure and defect chemistry of these dislocation arrays. Our results show that these dislocations lead to undercoordinated Ta/Al cations at the dislocation core, where oxygen vacancies can easily be formed, further facilitated by the presence of cation vacancies. The reduced Ti$^{3+}$ observed experimentally at the dislocations by electron energy-loss spectroscopy are a consequence of both the structure of the dislocation itself, as well as of the electron-doping due to oxygen vacancy formation. Finally, the experimentally observed Ti diffusion into LSAT around the dislocation core occurs only together with cation-vacancy formation in LSAT or Ta diffusion into STO

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 $H = \sum_j (S_j^x S_{j+1}^x + S_j^y S_{j+1}^y + \Delta S_j^z S_{j+1}^z) + D \sum_j (S_j^z)^2$, where $\Delta$ denotes the $XXZ$ anisotropy parameter of the nearest-neighbor interactions and $D$ the on-site anisotropy parameter. We restrict ourselves to the case with $\Delta \ge 0$ and $D \ge 0$ 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 $\Delta$-$D$ plane consists of four phases; the XY 1 phase, the Haldane/large-$D$ phase, the intermediate-$D$ phase and the N\'eel phase. The remarkable natures of the phase diagram are: (1) the Haldane state and the large-$D$ state belong to the same phase; (2) there exists the intermediate-$D$ phase which was predicted by Oshikawa in 1992; (3) the shape of the phase diagram on the $\Delta$-$D$ plane is different from that believed so far. We note that this is the first report of the observation of the intermediate-$D$ phase

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

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

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