Abstract
Photonic cluster states are a crucial resource for optical quantum computing. Recently a quantum dot single photon source has been demonstrated to produce strings of single photons in a small linear cluster state. Sources of this kind could produce much larger cluster states, but high photon loss rates make it impossible to characterize the entanglement generated by quantum state tomography. We present a benchmarking method for such sources that can be used to demonstrate useful long-range entanglement with currently available collection/detection efficiencies below 1%. The measurement of the polarization state of single photons in different bases can provide an estimate for the three-qubit correlation function ⟨ZXZ⟩. This value constrains correlations spanning more than three qubits, which in turn provide a lower bound for the localizable entanglement between any two qubits in the large state produced by the source. Finite localizable entanglement can be established by demonstrating ⟨ZXZ⟩>23. This result enables photonic experiments demonstrating computationally useful entanglement with currently available technology.
Highlights
Measurement-based quantum computation (MBQC)[1] has become a promising candidate for the most resource-efficient way to build a universal quantum computer
We find that a linear state ρ with expectation values Zi−1XiZi+1 ≥ ZXZ enables a quantum teleportation channel across k qubits of fidelity k+1
The experiment reported in Ref. 10 is claimed to demonstrate localizable entanglement (LE) across five photons, the states produced contained three photons at most
Summary
Measurement-based quantum computation (MBQC)[1] has become a promising candidate for the most resource-efficient way to build a universal quantum computer. The greatest challenge of MBQC is the generation of a sufficiently large entangled resource state This step is critical because only certain types of multi-qubit entanglements are known to enable universal quantum computation,[2] most prominently cluster state entanglement.[3,4]. Photonic systems have been proposed to generate cluster states.[5,6] Recently a complete architecture for a linear optical quantum computer has been developed that relies on the probabilistic fusion of many small entangled states into one large cluster state.[7] In this proposal, the generation of the entangled resource state requires only the generation of many maximally entangled three-photon states, at the cost of a significant overhead of single-photon detection measurements and classical information processing. Cluster state entanglement across many qubits can be demonstrated by measuring ZXZ in future experiments
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