Success rates for linear optical generation of cluster states in coincidence basis

TL;DR

This paper analyzes the success probabilities of linear optical methods for generating photonic cluster states, revealing that current approaches are suboptimal and proposing optimized schemes with higher success rates.

Contribution

The study provides a numerical optimization of fusion schemes, demonstrating that maximal success probabilities are higher than previously assumed for linear optical cluster state generation.

Findings

Optimal success probability for fusing n unentangled qubits is 1/2^(n-1)

Fusing m Bell pairs into a cluster has a success probability of 1/4^(m-1)

Current methods are significantly below the theoretical maximum success rates

Abstract

We report on theoretical research in photonic cluster-state computing. Finding optimal schemes of generating non-classical photonic states is of critical importance for this field as physically implementable photon-photon entangling operations are currently limited to measurement-assisted stochastic transformations. A critical parameter for assessing the efficiency of such transformations is the success probability of a desired measurement outcome. At present there are several experimental groups which are capable of generating multi-photon cluster states carrying more than eight qubits. Separate photonic qubits or small clusters can be fused into a single cluster state by a probabilistic optical CZ gate conditioned on simultaneous detection of all photons with 1/9 success probability of each gate. This design mechanically follows the original theoretical scheme of cluster state generation proposed more than a decade ago by Raussendorf, Browne and Briegel. The optimality of the destructive CZ gate in application to linear optical cluster state generation has not been analyzed previously. Our results reveal that this method is far from the optimal one. Employing numerical optimization we have identified that maximal success probability of fusing n unentangled dual-rail optical qubits into a linear cluster state is equal to 1/2^(n-1); m-tuple of photonic Bell pair states, commonly generated via spontaneous parametric down-conversion, can be fused into a single cluster with the maximal success probability of 1/4^(m-1).