P. van Loock

Experimental generation of four-mode continuous-variable cluster states

Continuous-variable Gaussian cluster states are a potential resource for universal quantum computation. Here we report on the optical generation and theoretical verification of three different kinds of four-mode continuous variable cluster states.

Continuous-variable sampling from photon-added or photon-subtracted squeezed states

We introduce a new family of quantum circuits in Continuous Variables and we show that, relying on the widely accepted conjecture that the polynomial hierarchy of complexity classes does not collapse, their output probability distribution cannot be efficiently simulated by a classical computer. These circuits are composed of input photon-subtracted (or photon-added) squeezed states, passive linear optics evolution, and eight-port homodyne detection. We address the proof of hardness for the exact probability distribution of these quantum circuits by exploiting mappings onto different architectures of sub-universal quantum computers. We obtain both a worst-case and an average-case hardness result. Hardness of Boson Sampling with eight-port homodyne detection is obtained as the zero squeezing limit of our model. We conclude with a discussion on the relevance and interest of the present model in connection to experimental applications and classical simulations.

Generalized conditions for genuine multipartite continuous-variable entanglement

We derive a hierarchy of continuous-variable multipartite entanglement conditions in terms of second-order moments of position and momentum operators that generalizes existing criteria. Each condition corresponds to a convex optimization problem which, given the covariance matrix of the state, can be numerically solved in a straightforward way. The conditions are independent of partial transposition and thus are also able to detect bound entangled states. Our approach can be used to obtain an analytical condition for genuine multipartite entanglement. We demonstrate that even a special case of our conditions can detect entanglement very efficiently. Using multi-objective optimization it is also possible to numerically verify genuine entanglement of some experimentally realizable states.

Higher-order Einstein-Podolsky-Rosen correlations and inseparability conditions for continuous variables

We derive two types of sets of higher-order conditions for bipartite entanglement in terms of continuous variables. One corresponds to an extension of the well-known Duan inequalities from second to higher moments describing a kind of higher-order Einstein-Podolsky-Rosen (EPR) correlations. Only the second type, however, expressed by powers of the mode operators leads to tight conditions with a hierarchical structure. We start with a minimization problem for the single-partite case and, using the results obtained, establish relevant inequalities for higher-order moments satisfied by all bipartite separable states. A certain fourth-order condition cannot be violated by any Gaussian state and we present non-Gaussian states whose entanglement is detected by that condition. Violations of all our conditions are provided, so they can all be used as entanglement tests.

Tripartite separability conditions exponentially violated by Gaussian states

Starting with a set of conditions for bipartite separability of arbitrary quantum states in any dimension and expressed in terms of arbitrary operators whose commutator is a

Generation of Four‐Mode Continuous‐Variable Cluster States

c

Demonstration of a measurement-based quantum nondemolition interaction

-number, we derive a hierarchy of conditions for tripartite separability of continuous-variable three-mode quantum states. These conditions have the form of inequalities for higher-order moments of linear combinations of the mode operators. They enable one to distinguish between all possible kinds of tripartite separability, while the strongest violation of these inequalities is a sufficient condition for genuine tripartite entanglement. We construct Gaussian states for which the violation of our conditions grows exponentially with the order of the moments of the mode operators. By going beyond second moments, our conditions are expected to be useful as well for the detection of tripartite entanglement of non-Gaussian states.

Optical Quantum Computation with Continuous-Variable Cluster States

Cluster states are sufficient resources for realizing quantum computation. Their implementations can be achieved via either discrete‐variable systems (especially qubit systems) or continuous‐variable systems. Here we report on the experimental generation of an important example of a continuous‐variable cluster state, a four‐mode linear cluster state.

Experimental verification of continuous-variable tripartite entanglement

We experimentally demonstrate a quantum nondemolition (QND) interaction, based upon offline-prepared, squeezed ancilla states and homodyne measurements with feedforward. The resulting QND gate is verified via the criteria for QND measurements of each conjugate quadrature.

Optical hybrid approaches to quantum information

We describe an extension of the cluster-state model for universal quantum computation from qubits to qumodes (quantized harmonic oscillators), i.e., a translation from discrete to continuous quantum variables, and discuss potential optical realizations via approximate cluster states in form of multi-mode squeezed Gaussian states.