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Any Gaussian cluster state can be generated by a multi-mode squeezing transformation

Stefano Zippilli, David Vitali

Published Jul 24, 2020• 0 citations
OpenAlex

Abstract

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 that any Gaussian cluster state can be approximated by a specific multi-mode squeezed state.

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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.
We consider the problems of constructing a cluster state from a set of orthogonal modes. It is shown that the commonly used unitary transformation is not reduced in this case to a set of standard operations of linear optics performed over fields in a squeezed state, but should be supplemented by a more complicated operation of a noise-free transformation of the quantum signal profile. At the same time, if it is possible to form a cluster whose node amplitudes have different time profiles, this property does not interfere with the performance of calculations on the cluster.
Gaussian continuous-variable cluster states are a unique quantum information resource as they currently scale up experimentally to much larger sizes than any qubit platform. We derive the first general criterion for a pure Gaussian state not to be expressible as a canonical cluster state, and show that such Gaussian states must then display hidden entanglement. This applies to experimentally relevant deviations from Gaussian cluster states, such as variations of the squeezing parameter from mode to mode, which cannot be captured by the infinite squeezing limit.
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.