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Now at #IWQNS @SumeetKatri6
from @LSU on Robust NEtwork Architectures and topologies for entanglement distibution #LTQI #IWQNS

@LSU Sorry, wrong twitter handle: it’s @SumeetKhatri6
#LTQI #IWQNS

@LSU @SumeetKhatri6 .@SumeetKhatri6 : looks at 2D networks without quantum repeaters, using the multiplicity of paths to add robustness to losses and node failure.
#IWQNS #LTQI

@LSU @SumeetKhatri6 .@SumeetKhatri6: Architecture described by a graph, each each being a photonic Bell pair, each vertex being a quantum memory, where arbitrary multi qubit operation can be performes #LTQI #IWQNS

@LSU @SumeetKhatri6 .@SumeetKhatri6 :
Each link has a failure probability p_i
Each memory has a cutoff time t* translating to cutof fnumber of trials n*
#LTQI #IWQNS

@LSU @SumeetKhatri6 .@SumeetKathri6’s figures of merits:
1. Full connectivity time N_full, expected nr of trials to connect all links
2. Time to obtain chain of links between A and B N_AB
3. How big is the biggest cluster after time t
S
#LTQI #IWQNS

@LSU @SumeetKhatri6 .@SumeetKathri6. N_full(G,n*). Only depends of nr of links M.
Assumes p_i=p ∀i
If n*=0, E(N_full(M,0))=1/p^M
If n*=∞, E(N_full(M,0))=∑_n (1 — (1 — (1 — p)ⁿ⁻¹)^M) when sum goes from 1 to ∞
Finite n*: in between
#LTQI #IWQNS

.@SumeetKhatri6 : For N_AB , point to point connectivity time, similar formulae, with Nr of paths n_p as exponenent:
1/(1—(1—p^M)^{n_p} ) and ∑_n (1 — (1 — (1 — p)ⁿ⁻¹)^M) ^{n_p}

@SumeetKhatri6 .@SumeetKathri6; Average largest cluster size.
S_n^max upper bounded by L_n, nuber of established links
E(L_n(M,∞))=M(1–(1–p)ⁿ)
E(L_n(M,∞))=Mp
For Smax, on square and triangular lattices, one sees a percolation threshold, (lower on Δ) which decreases with n*
#LTQI #IWQNS

@SumeetKhatri6 @threadreaderapp Please kindly unroll