A post-selected linear-optical controlled- gate (success probability
PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Physical realizations and quantum technologies · Physical realizations and quantum technologies
Quantum Information and Technology, Ch Trapped ions, neutral atoms, photons, NMR and spins in solids
Problem
A post-selected linear-optical controlled-Z gate (success probability 1/9, quoted) is used, followed by local operations, to herald a photonic Bell pair. State tomography gives a measured squared fidelity (the squared-type quantity hardware papers quote, as defined for average and process fidelities) against ∣Φ+⟩ of F2=0.95.
((a)) Find the root fidelity F=∣⟨Φ+∣ψ⟩∣ used for pure-state overlaps.
((b)) Model the heralded state as a Werner-type mixture ρ=w∣Φ+⟩⟨Φ+∣+(1−w)I/4, for which F2=w+(1−w)/4. Find the weight w, and use the Werner-state entanglement condition (w>1/3 for entanglement) to state whether the heralded pair is entangled.
((c)) The combined success probability of the gate together with 90% photon-detection efficiency per photon is p=(1/9)×0.92. If attempts are made at 108 per second, estimate the mean time to obtain one successful heralded pair, and compare it with a superconducting two-qubit gate (Chapter 17's datasheet figures) that succeeds essentially deterministically in 60ns.