Correspondence between continuous-variable and discrete quantum systems of arbitrary dimensions

We establish a mapping between a continuous-variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite-dimensional Hilbert space and thus can be considered as a universal resource of entanglement. An explicit example of the map and a proposal for its experimental realization are discussed.

Decoherence-based exploration of d-dimensional one-way quantum computation: Information transfer and basic gates

We study the effects of amplitude and phase damping decoherence in d-dimensional one-way quantum computation. We focus our attention on low dimensions and elementary unidimensional cluster state resources. Our investigation shows how information transfer and entangling gate simulations are affected for d >= 2. To understand motivations for extending the one-way model to higher dimensions, we describe how basic qudit cluster states deteriorate under environmental noise of experimental interest. In order to protect quantum information from the environment, we consider encoding logical qubits into qudits and compare entangled pairs of linear qubit-cluster states to single qudit clusters of equal length and total dimension. A significant reduction in the performance of cluster state resources for d > 2 is found when Markovian-type decoherence models are present.

Almost all quantum states have nonclassical correlations

Quantum discord quantifies nonclassical correlations in a quantum system including those not captured by entanglement. Thus, only states with zero discord exhibit strictly classical correlations. We prove that these states are negligible in the whole Hilbert space: typically a state picked out at random has positive discord and, given a state with zero discord, a generic arbitrarily small perturbation drives it to a positive-discord state. These results hold for any Hilbert-space dimension and have direct implications for quantum computation and for the foundations of the theory of open systems. In addition, we provide a simple necessary criterion for zero quantum discord. Finally, we show that, for almost all positive-discord states, an arbitrary Markovian evolution cannot lead to a sudden, permanent vanishing of discord.

Sequential measurement-based quantum computing with memories

We introduce a general scheme for sequential one-way quantum computation where static systems with long-living quantum coherence (memories) interact with moving systems that may possess very short coherence times. Both the generation of the cluster state needed for the computation and its consumption by measurements are carried out simultaneously. As a consequence, effective clusters of one spatial dimension fewer than in the standard approach are sufficient for computation. In particular, universal computation requires only a one-dimensional array of memories. The scheme applies to discrete-variable systems of any dimension as well as to continuous-variable ones, and both are treated equivalently under the light of local complementation of graphs. In this way our formalism introduces a general framework that encompasses and generalizes in a unified manner some previous system-dependent proposals. The procedure is intrinsically well suited for implementations with atom-photon interfaces.