Relationships between Models for Concurrency

Models for concurrency can be classified with respect to three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. The classifications are formalized through the medium of category theory

Deterministic Behavioural Models for Concurrency

This paper offers three candidates for a deterministic, noninterleaving, behaviour model which generalizes Hoare traces to the noninterleaving situation. The three models are all proved equivalent in the rather strong sense of being equivalent as categories. The models are: deterministic labelled event structures, generalized trace languages in which the independence relation is context-dependent, and deterministic languages of pomsets

A Classification of Models for Concurrency

Models for concurrency can be classified with respect to the three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. The classifications are formalised through the medium of category theory

Energy Spectrum and Exact Cover in an Extended Quantum Ising Model

We investigate an extended version of the quantum Ising model which includes beyond-nearest neighbour interactions and an additional site-dependent longitudinal magnetic field. Treating the interaction exactly and using perturbation theory in the longitudinal field, we calculate the energy spectrum and find that the presence of beyond-nearest-neighbour interactions enhances the minimal gap between the ground state and the first excited state, irrespective of the nature of decay of these interactions along the chain. The longitudinal field adds a correction to this gap that is independent of the number of qubits. We discuss the application of our model to implementing specific instances of 3-satisfiability problems (Exact Cover) and make a connection to a chain of flux qubits.Comment: 9 pages, 3 figures, published versio

Entanglement Detection Using Majorization Uncertainty Bounds

Entanglement detection criteria are developed within the framework of the majorization formulation of uncertainty. The primary results are two theorems asserting linear and nonlinear separability criteria based on majorization relations, the violation of which would imply entanglement. Corollaries to these theorems yield infinite sets of scalar entanglement detection criteria based on quasi-entropic measures of disorder. Examples are analyzed to probe the efficacy of the derived criteria in detecting the entanglement of bipartite Werner states. Characteristics of the majorization relation as a comparator of disorder uniquely suited to information-theoretical applications are emphasized throughout.Comment: 10 pages, 1 figur

Fast and robust two-qubit gates for scalable ion trap quantum computing

We propose a new concept for a two-qubit gate operating on a pair of trapped ions based on laser coherent control techniques. The gate is insensitive to the temperature of the ions, works also outside the Lamb-Dicke regime, requires no individual addressing by lasers, and can be orders of magnitude faster than the trap period

Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries

The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C^n tensor C^n whose operator-Schmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C^3 tensor C^3 with operator-Schmidt number S for every S in {1,...,9}. This corollary was unexpected, since it contradicted reasonable conjectures of Nielsen et al [Phys. Rev. A 67 (2003) 052301] based on intuition from a striking result in the two-qubit case. By the results of Dur, Vidal, and Cirac [Phys. Rev. Lett. 89 (2002) 057901 quant-ph/0112124], who also considered the two-qubit case, our result implies that there are nine equivalence classes of unitaries on C^3 tensor C^3 which are probabilistically interconvertible by (stochastic) local operations and classical communication. As another corollary, a prescription is produced for constructing maximally-entangled operators from biunimodular functions. Reversing tact, we state a generalized operator-Schmidt decomposition of the quantum Fourier transform considered as an operator C^M_1 tensor C^M_2 --> C^N_1 tensor C^N_2, with M_1 x M_2 = N_1 x N_2. This decomposition shows (by Nielsen's bound) that the communication cost of the QFT remains maximal when a net transfer of qudits is permitted. In an appendix, a canonical procedure is given for removing basis-dependence for results and proofs depending on the "magic basis" introduced in [S. Hill and W. Wootters, "Entanglement of a pair of quantum bits," Phys Rev. Lett 78 (1997) 5022-5025, quant-ph/9703041 (and quant-ph/9709029)].Comment: More formal version of my talk at the Simons Conference on Quantum and Reversible Computation at Stony Brook May 31, 2003. The talk slides and audio are available at http://www.physics.sunysb.edu/itp/conf/simons-qcomputation.html. Fixed typos and minor cosmetic

Enhancement of Entanglement Percolation in Quantum Networks via Lattice Transformations

We study strategies for establishing long-distance entanglement in quantum networks. Specifically, we consider networks consisting of regular lattices of nodes, in which the nearest neighbors share a pure, but non-maximally entangled pair of qubits. We look for strategies that use local operations and classical communication. We compare the classical entanglement percolation protocol, in which every network connection is converted with a certain probability to a singlet, with protocols in which classical entanglement percolation is preceded by measurements designed to transform the lattice structure in a way that enhances entanglement percolation. We analyze five examples of such comparisons between protocols and point out certain rules and regularities in their performance as a function of degree of entanglement and choice of operations.Comment: 12 pages, 17 figures, revtex4. changes from v3: minor stylistic changes for journal reviewer, minor changes to figures for journal edito

Structural change in multipartite entanglement sharing: a random matrix approach

We study the typical entanglement properties of a system comprising two independent qubit environments interacting via a shuttling ancilla. The initial preparation of the environments is modeled using random-matrix techniques. The entanglement measure used in our study is then averaged over many histories of randomly prepared environmental states. Under a Heisenberg interaction model, the average entanglement between the ancilla and one of the environments remains constant, regardless of the preparation of the latter and the details of the interaction. We also show that, upon suitable kinematic and dynamical changes in the ancilla-environment subsystems, the entanglement-sharing structure undergoes abrupt modifications associated with a change in the multipartite entanglement class of the overall system's state. These results are invariant with respect to the randomized initial state of the environments.Comment: 10 pages, RevTeX4 (Minor typo's corrected. Closer to published version