Gaussian cluster states are ideal infinitely squeezed states. In practice it is possible to construct only approximated version of them with finite squeezing. Here we show how to determine the specific multimode squeezing transformation, which generates a faithful approximation of any given Gaussian cluster state.
The linear optical creation of Gaussian cluster states, a potential resource for universal quantum computation, is investigated. First, using Bloch-Messiah reduction, we show how to achieve canonical cluster-state generation, otherwise based on pairwise acting quantum nondemolition gates, by off-line squeezers and beam splitters. Moreover, we find that, in terms of squeezing resources, the canonical states are rather wasteful. Hence we propose a systematic way to create a whole family of cluster-type states, including potentially cheaper states. Any given cluster (or graph) state can be realized this way. As an example, we consider a protocol in which a single-mode quantum state propagates through a multiple-rail cluster. Such a redundant encoding may reduce errors due to finite squeezing.
Continuous-variable (CV) cluster states are a universal quantum computing platform that has experimentally out-scaled qubit platforms by orders of magnitude. The implementation of CV cluster states uses multimode squeezed Gaussian states and fault tolerance thresholds for CV quantum computing have been predicted for realistic squeezing. An outstanding question has been whether any Gaussian state can be expressed as a cluster state. We show here that Gaussian states can present hidden entanglement, which is not captured by the corresponding cluster state graph and therefore invalidates this graph. Hidden entanglement vanishes in the infinite squeezing limit, which should therefore be used with extreme caution. We derive a general procedure to detect hidden entanglement in an arbitrary Gaussian state and validate it as a CV cluster state. These results are relevant to all experimental implementations of CV cluster states to date.
Continuous-variable Gaussian cluster states are a potential resource for universal quantum computation. They can be efficiently and unconditionally built from sources of squeezed light using beam splitters. Here we report on the generation of three different kinds of continuous-variable four-mode cluster states. In our realization, the resulting cluster-type correlations are such that no corrections other than simple phase-space displacements would be needed when quantum information propagates through these states. At the same time, the inevitable imperfections from the finitely squeezed resource states and from additional thermal noise are minimized, as no antisqueezing components are left in the cluster states.