Valence Bond Solids for Quantum Computation

Cluster states are entangled multipartite states which enable to do universal quantum computation with local measurements only. We show that these states have a very simple interpretation in terms of valence bond solids, which allows to understand their entanglement properties in a transparent way. This allows to bridge the gap between the differences of the measurement-based proposals for quantum computing, and we will discuss several features and possible extensions

A short impossibility proof of Quantum Bit Commitment

Bit commitment protocols, whose security is based on the laws of quantum mechanics alone, are generally held to be impossible on the basis of a concealment-bindingness tradeoff. A strengthened and explicit impossibility proof has been given in: G. M. D'Ariano, D. Kretschmann, D. Schlingemann, and R. F. Werner, Phys. Rev. A 76, 032328 (2007), in the Heisenberg picture and in a C*-algebraic framework, considering all conceivable protocols in which both classical and quantum information are exchanged. In the present paper we provide a new impossibility proof in the Schrodinger picture, greatly simplifying the classification of protocols and strategies using the mathematical formulation in terms of quantum combs, with each single-party strategy represented by a conditional comb. We prove that assuming a stronger notion of concealment--worst-case over the classical information histories--allows Alice's cheat to pass also the worst-case Bob's test. The present approach allows us to restate the concealment-bindingness tradeoff in terms of the continuity of dilations of probabilistic quantum combs with respect to the comb-discriminability distance.Comment: 15 pages, revtex

Quantum Error Correcting Codes Using Qudit Graph States

Graph states are generalized from qubits to collections of $n$ qudits of arbitrary dimension $D$, and simple graphical methods are used to construct both additive and nonadditive quantum error correcting codes. Codes of distance 2 saturating the quantum Singleton bound for arbitrarily large $n$ and $D$ are constructed using simple graphs, except when $n$ is odd and $D$ is even. Computer searches have produced a number of codes with distances 3 and 4, some previously known and some new. The concept of a stabilizer is extended to general $D$, and shown to provide a dual representation of an additive graph code.Comment: Version 4 is almost exactly the same as the published version in Phys. Rev.

On Haag Duality for Pure States of Quantum Spin Chain

We consider quantum spin chains and their translationally invariant pure states. We prove Haag duality for quasilocal observables localized in semi-infinite intervals when the von Neumann algebras generated by observables localized in these intervals are not type I

Quantum error-correcting codes associated with graphs

We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the 1-error correcting property of fivefold codes in any dimension. As new examples we construct a large class of codes saturating the singleton bound, as well as a tenfold code detecting 3 errors.Comment: 8 pages revtex, 5 figure

On the structure of Clifford quantum cellular automata

We study reversible quantum cellular automata with the restriction that these are also Clifford operations. This means that tensor products of Pauli operators (or discrete Weyl operators) are mapped to tensor products of Pauli operators. Therefore Clifford quantum cellular automata are induced by symplectic cellular automata in phase space. We characterize these symplectic cellular automata and find that all possible local rules must be, up to some global shift, reflection invariant with respect to the origin. In the one dimensional case we also find that every uniquely determined and translationally invariant stabilizer state can be prepared from a product state by a single Clifford cellular automaton timestep, thereby characterizing these class of stabilizer states, and we show that all 1D Clifford quantum cellular automata are generated by a few elementary operations. We also show that the correspondence between translationally invariant stabilizer states and translationally invariant Clifford operations holds for periodic boundary conditions.Comment: 28 pages, 2 figures, LaTe

Semicausal operations are semilocalizable

We prove a conjecture by DiVincenzo, which in the terminology of Preskill et al. [quant-ph/0102043] states that ``semicausal operations are semilocalizable''. That is, we show that any operation on the combined system of Alice and Bob, which does not allow Bob to send messages to Alice, can be represented as an operation by Alice, transmitting a quantum particle to Bob, and a local operation by Bob. The proof is based on the uniqueness of the Stinespring representation for a completely positive map. We sketch some of the problems in transferring these concepts to the context of relativistic quantum field theory.Comment: 4 pages, 1 figure, revte

Diabetes changes ionotropic glutamate receptor subunit expression level in the human retina

Early diabetic retinopathy is characterized by changes in subtle visual functions such as contrast sensitivity and dark adaptation. The outcome of several studies suggests that glutamate is involved in retinal neurodegeneration during diabetes. We hypothesized that the protein levels of ionotropic glutamate receptor subunits are altered in the retina during diabetes. Therefore, we investigated whether human diabetic patients have altered immunoreactivity of ionotropic glutamate receptor subunits in the retina.http://www.sciencedirect.com/science/article/B6SYR-4RS9SS1-1/1/232d6ae7147919a2286326863ee69f1

Entanglement, Haag-duality and type properties of infinite quantum spin chains

We consider an infinite spin chain as a bipartite system consisting of the left and right half-chain and analyze entanglement properties of pure states with respect to this splitting. In this context we show that the amount of entanglement contained in a given state is deeply related to the von Neumann type of the observable algebras associated to the half-chains. Only the type I case belongs to the usual entanglement theory which deals with density operators on tensor product Hilbert spaces, and only in this situation separable normal states exist. In all other cases the corresponding state is infinitely entangled in the sense that one copy of the system in such a state is sufficient to distill an infinite amount of maximally entangled qubit pairs. We apply this results to the critical XY model and show that its unique ground state provides a particular example for this type of entanglement.Comment: LaTeX2e, 34 pages, 1 figure (pstricks