EntanglementConsumer, SwapperProt, EntanglementTracker, EntanglerProt might fail to correctly track entangled states across a repeater chain

**Describe the bug 🐞**

Consider a repeater chain with two end nodes and more than one repeater. For example, consider repeater #2. Assume that the SwapperProt installed on that node just swapped slots 1 and 4 and saved two EntanglementHistory entries. Almost simultaneously, repeater #1 swapped slots 3 and 5.
Pre-swaps, slots 2.4 and 1.5 were entangled, so repeater #1 sends out an EntanglementUpdateX to repeater #2 regarding slot 2.4. Under normal circumstances, repeater #2 would map the EntanglementUpdateX message to the corresponding EntanglementHistory entry and correctly track the logical entangled state. However, the bug occurs if an EntanglerProt selects slot 2.2 and generates a new Bell pair in the time between the swap at repeater #2 and the delivery of EntanglementUpdate X to repeater #2. In this unfortunate case, the update will be mapped to the new EntanglementCounterpart entry available at repeater #2 regarding slot 2.2, and not to the EntanglementHistory entry, which would be the correct one. This creates a mismatch between the actual quantum state and the logical state of the simulation.

The runtime error manifests when the EntanglementConsumer tries to calculate the expectation value of observable X \otimes X on the end-to-end Bell pair. The expectation value returns `nothing` because the size of the quantum state of the two passed register slots is larger than a 2-qubit state (it's 4, because each of those slots is entangled to another slot somewhere in the network). Finally, when the EntanglementConsumer evaluates `real(nothing)`, the error occurs.

**Expected behavior**

I would expect this mismatch not to happen: the simulator should be able to map every update to the actual Bell pair they refer to, or at least be able to detect the mismatch (which is usually very unlikely to happen).

**Minimal Reproducible Example 👇**

```julia

using QuantumSavory.ProtocolZoo
using QuantumSavory
using Graphs
import ConcurrentSim
using ConcurrentSim: @process, now, Process

function repeater_chain(nrepeaters::Int, nslots::Int; linklength::AbstractFloat=0.0, coherencetime::Union{AbstractFloat, Nothing}=nothing)

    speedOfLightFiber = 2e8 # km/s
    delay = linklength / speedOfLightFiber
    delay_us = delay * 1e6 # in microseconds

    graph = grid([nrepeaters + 2])
    if coherencetime === nothing
        noisemodel = nothing
        registers = vcat([Register(nslots*5)], [Register(nslots) for _ in 1:nrepeaters], [Register(nslots*5)])
    else
        noisemodel = Depolarization(coherencetime)
        registers = vcat([Register(nslots*5)], [Register(nslots, noisemodel) for _ in 1:nrepeaters], [Register(nslots*5)])
    end
    return RegisterNet(graph, registers; classical_delay=delay_us)
end



function get_entangler(sim, net, nodeA, nodeB, rate)
    return EntanglerProt(sim, net, nodeA, nodeB; rate=rate, rounds=-1, margin=1, retry_lock_time=nothing)
end

function get_swapper(sim, net, node)
    return SwapperProt(sim, net, node; nodeL= <(node), nodeH= >(node), retry_lock_time=nothing)
end


function get_tracker(sim, net, node)
    return EntanglementTracker(sim, net, node)
end


function get_consumer(sim, net, nodeA, nodeB)
    return EntanglementConsumer(sim, net, nodeA, nodeB, period=nothing)
end


function setup(nrepeaters::Int, nslots::Int, linkcapacity::AbstractFloat; linklength::AbstractFloat=0.0, coherencetime::Union{AbstractFloat, Nothing}=nothing, outfolder::String="./out/", outfile::Union{String, Nothing}=nothing, usetempfile::Bool=false)
    net = repeater_chain(nrepeaters, nslots; linklength=linklength, coherencetime=coherencetime)
    sim = get_time_tracker(net)

    # Setup an entanglement tracker at each node
    for node in 1:(nrepeaters+2)
        tracker = get_tracker(sim, net, node)
        @process tracker()
    end

    # Setup the entanglement swapping protocols at each repeater
    for node in 2:(nrepeaters+1)
        swapper = get_swapper(sim, net, node)
        @process swapper()
    end

    # Setup the entangler protocol at each link
    for node in 1:(nrepeaters+1)
        entangler = get_entangler(sim, net, node, node+1, linkcapacity)
        @process entangler()
    end

    # Setup consumers at the end nodes
    consumer = get_consumer(sim, net, 1, nrepeaters+2)
    @process consumer()

    return (sim, net)
end


sim, net = setup(2, 100, 10.0; linklength=20.0, coherencetime=1e6)
run(sim, 500)


```

**Error & Stacktrace or other complete output produced by the MRE ⚠️**

```julia

ERROR: MethodError: no method matching real(::Nothing)
The function `real` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  real(::Type{Union{}}, Any...)
   @ Base complex.jl:123
  real(::ChainRulesCore.ZeroTangent)
   @ ChainRulesCore ~/.julia/packages/ChainRulesCore/Vsbj9/src/tangent_arithmetic.jl:111
  real(::Nemo.ZZiRingElem)
   @ Nemo ~/.julia/packages/Nemo/SKc7w/src/gaussiannumbers/ZZi.jl:157
  ...

Stacktrace:
 [1] macro expansion
   @ ~/.julia/dev/QuantumSavory/src/ProtocolZoo/ProtocolZoo.jl:495 [inlined]
 [2] (::QuantumSavory.ProtocolZoo.var"##prot::EntanglementConsumer_FSMI#487"{…})(_arg::Dict{…})
   @ QuantumSavory.ProtocolZoo ~/.julia/packages/ResumableFunctions/cprlE/src/macro.jl:461
 [3] execute(ev::ConcurrentSim.Operator, proc::Process)
   @ ConcurrentSim ~/.julia/packages/ConcurrentSim/V71SQ/src/processes.jl:32
 [4] (::ConcurrentSim.var"#append_callback##0#append_callback##1"{…})()
   @ ConcurrentSim ~/.julia/packages/ConcurrentSim/V71SQ/src/base.jl:51
 [5] step(sim::ConcurrentSim.Simulation)
   @ ConcurrentSim ~/.julia/packages/ConcurrentSim/V71SQ/src/simulations.jl:39
 [6] run(env::ConcurrentSim.Simulation, until::ConcurrentSim.Timeout)
   @ ConcurrentSim ~/.julia/packages/ConcurrentSim/V71SQ/src/base.jl:91
 [7] run(env::ConcurrentSim.Simulation, until::Int64)
   @ ConcurrentSim ~/.julia/packages/ConcurrentSim/V71SQ/src/events.jl:29
 [8] top-level scope
   @ ~/JuliaProjects/QSavoryBug/src/setup.jl:78
Some type information was truncated. Use `show(err)` to see complete types.

```

**Environment (please complete the following information):**

  - Output of `using Pkg; Pkg.status()`

```julia

Project QSavoryBug v1.0.0-DEV
Status `~/JuliaProjects/QSavoryBug/Project.toml`
  [6ed1e86c] ConcurrentSim v1.5.0
⌃ [86223c79] Graphs v1.13.1
⌃ [7ed4a6bd] LinearSolve v3.49.0
  [2de2e421] QuantumSavory v0.6.0 `~/.julia/dev/QuantumSavory`
Info Packages marked with ⌃ have new versions available and may be upgradable.

```

  - Output of `using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)`

```julia

Project QSavoryBug v1.0.0-DEV
Status `~/JuliaProjects/QSavoryBug/Manifest.toml`
  [47edcb42] ADTypes v1.20.0
⌅ [c3fe647b] AbstractAlgebra v0.44.13
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.43
  [79e6a3ab] Adapt v4.4.0
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
⌅ [7d9fca2a] Arpack v0.5.3
  [4fba245c] ArrayInterface v7.22.0
  [4c555306] ArrayLayouts v1.12.2
  [6e4b80f9] BenchmarkTools v1.6.3
  [e2ed5e7c] Bijections v0.2.2
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [70df07ce] BracketingNonlinearSolve v1.6.0
  [2a0fbf3d] CPUSummary v0.2.7
  [d360d2e6] ChainRulesCore v1.26.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [523fee87] CodecBzip2 v0.8.5
  [944b1d66] CodecZlib v0.7.8
⌅ [861a8166] Combinatorics v1.0.2
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.18.1
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [6ed1e86c] ConcurrentSim v1.5.0
  [992eb4ea] CondaPkg v0.2.33
  [187b0558] ConstructionBase v1.6.0
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [1f15a43c] CxxWrap v0.17.4
  [9a962f9c] DataAPI v1.16.0
⌅ [864edb3b] DataStructures v0.18.22
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.192.0
  [459566f4] DiffEqCallbacks v4.10.1
  [77a26b50] DiffEqNoiseProcess v5.24.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.7.12
  [31c24e10] Distributions v0.25.122
  [ffbed154] DocStringExtensions v0.9.5
  [5b8099bc] DomainSets v0.7.16
⌃ [7c1d4256] DynamicPolynomials v0.6.3
  [4e289a0a] EnumX v1.0.5
  [f151be2c] EnzymeCore v0.8.17
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [411431e0] Extents v0.1.6
  [7a1cc6ca] FFTW v1.10.0
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [7868e603] FastExpm v1.1.0
  [442a2c76] FastGaussQuadrature v1.1.0
  [a4df4552] FastPower v1.2.0
  [1a297f60] FillArrays v1.15.0
  [6a86dc24] FiniteDiff v2.29.0
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v1.3.0
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.2.0
  [5c1252a2] GeometryBasics v0.5.10
⌃ [86223c79] Graphs v1.13.1
  [c3af3a8c] GraphsMatching v0.2.1
  [f0d1745a] HalfIntegers v1.6.0
  [87dc4568] HiGHS v1.20.1
  [3e5b6fbb] HostCPUFeatures v0.1.18
  [e91730f6] Hungarian v0.7.0
  [34004b35] HypergeometricFunctions v0.3.28
  [2cd5bd5f] ILog2 v2.0.0
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [18e54dd8] IntegerMathUtils v0.1.3
  [8197267c] IntervalSets v0.7.13
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.6
  [c8e1da08] IterTools v1.10.0
  [42fd0dbc] IterativeSolvers v0.9.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.3.0
  [0f8b85d8] JSON3 v1.14.3
  [ae98c720] Jieko v0.2.1
  [4076af6c] JuMP v1.29.3
  [ccbc3e58] JumpProcesses v9.19.3
  [ba0b0d4f] Krylov v0.10.3
  [0b1a1467] KrylovKit v0.10.2
  [14b1564f] LEMONGraphs v0.1.1
  [8ac3fa9e] LRUCache v1.6.2
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.10
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.9.4
  [2d8b4e74] LevyArea v1.0.0
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.5.1
  [7a12625a] LinearMaps v3.11.4
⌃ [7ed4a6bd] LinearSolve v3.49.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [1914dd2f] MacroTools v0.5.16
  [d125e4d3] ManualMemory v0.1.8
  [8c4f8055] MathOptIIS v0.1.1
  [b8f27783] MathOptInterface v1.48.0
  [bb5d69b7] MaybeInplace v0.1.4
  [0b3b1443] MicroMamba v0.1.14
  [e1d29d7a] Missings v1.2.0
  [2e0e35c7] Moshi v0.3.7
  [46d2c3a1] MuladdMacro v0.2.4
⌃ [102ac46a] MultivariatePolynomials v0.5.9
  [d8a4904e] MutableArithmetics v1.6.7
  [d41bc354] NLSolversBase v7.10.0
  [77ba4419] NaNMath v1.1.3
⌅ [2edaba10] Nemo v0.49.5
  [46757867] NetworkLayout v0.4.10
  [8913a72c] NonlinearSolve v4.12.0
  [be0214bd] NonlinearSolveBase v2.5.0
  [5959db7a] NonlinearSolveFirstOrder v1.10.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.11.0
  [26075421] NonlinearSolveSpectralMethods v1.6.0
  [6fe1bfb0] OffsetArrays v1.17.0
  [429524aa] Optim v1.13.3
  [bac558e1] OrderedCollections v1.8.1
⌅ [bbf590c4] OrdinaryDiffEqCore v1.36.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.16.1
  [1344f307] OrdinaryDiffEqLowOrderRK v1.6.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.15.0
  [90014a1f] PDMats v0.11.36
  [65ce6f38] PackageExtensionCompat v1.0.2
  [69de0a69] Parsers v2.8.3
  [fa939f87] Pidfile v1.3.0
  [e409e4f3] PoissonRandom v0.4.7
  [f517fe37] Polyester v0.7.18
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.34
  [aea7be01] PrecompileTools v1.3.3
  [21216c6a] Preferences v1.5.0
  [08abe8d2] PrettyTables v3.1.2
  [27ebfcd6] Primes v0.5.7
  [43287f4e] PtrArrays v1.3.0
  [6099a3de] PythonCall v0.9.30
  [b50d4dc9] QECCore v0.1.1
  [1fd47b50] QuadGK v2.11.2
  [0525e862] QuantumClifford v0.10.0
  [5717a53b] QuantumInterface v0.4.2
  [6e0679c1] QuantumOptics v1.2.4
  [4f57444f] QuantumOpticsBase v0.5.9
  [2de2e421] QuantumSavory v0.6.0 `~/.julia/dev/QuantumSavory`
  [efa7fd63] QuantumSymbolics v0.4.11
  [74087812] Random123 v1.7.1
  [fb686558] RandomExtensions v0.4.4
  [e6cf234a] RandomNumbers v1.6.0
  [308eb6b3] RationalRoots v0.2.1
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.39.0
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.1.1
  [c5292f4c] ResumableFunctions v1.0.4
  [79098fc4] Rmath v0.9.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.16
  [fdea26ae] SIMD v3.7.2
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.128.0
  [19f34311] SciMLJacobianOperators v0.1.11
  [a6db7da4] SciMLLogging v1.7.1
  [c0aeaf25] SciMLOperators v1.14.0
  [431bcebd] SciMLPublic v1.0.0
  [53ae85a6] SciMLStructures v1.7.0
  [6c6a2e73] Scratch v1.3.0
  [efcf1570] Setfield v1.1.2
  [727e6d20] SimpleNonlinearSolve v2.9.0
  [699a6c99] SimpleTraits v0.9.5
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.2
  [0a514795] SparseMatrixColorings v0.4.23
  [276daf66] SpecialFunctions v2.6.1
  [aedffcd0] Static v1.3.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.15
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.8.0
  [2913bbd2] StatsBase v0.34.9
  [4c63d2b9] StatsFuns v1.5.2
  [789caeaf] StochasticDiffEq v6.86.0
  [7792a7ef] StrideArraysCore v0.5.8
  [5e0ebb24] Strided v2.3.2
  [4db3bf67] StridedViews v0.4.1
  [892a3eda] StringManipulation v0.4.2
  [856f2bd8] StructTypes v1.11.0
  [ec057cc2] StructUtils v2.6.0
  [8e1ec7a9] SumTypes v0.5.8
  [2efcf032] SymbolicIndexingInterface v0.3.46
⌃ [19f23fe9] SymbolicLimits v0.2.3
⌅ [d1185830] SymbolicUtils v3.32.0
⌅ [0c5d862f] Symbolics v6.58.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
  [ed4db957] TaskLocalValues v0.1.3
  [8ea1fca8] TermInterface v2.0.0
  [8290d209] ThreadingUtilities v0.5.5
  [a759f4b9] TimerOutputs v0.5.29
  [3bb67fe8] TranscodingStreams v0.11.3
  [781d530d] TruncatedStacktraces v1.4.0
  [9d95972d] TupleTools v1.6.0
  [a7c27f48] Unityper v0.1.6
  [c4a57d5a] UnsafeArrays v1.0.8
  [e17b2a0c] UnsafePointers v1.0.0
  [409d34a3] VectorInterface v0.5.0
  [9f57e263] WignerSymbols v2.0.0
⌅ [68821587] Arpack_jll v3.5.1+1
  [6e34b625] Bzip2_jll v1.0.9+0
  [5ae413db] EarCut_jll v2.2.4+0
  [f5851436] FFTW_jll v3.3.11+0
⌅ [e134572f] FLINT_jll v300.200.201+0
  [61579ee1] Ghostscript_jll v9.55.1+0
  [8fd58aa0] HiGHS_jll v1.12.0+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [aacddb02] JpegTurbo_jll v3.1.3+0
  [9f9b04fa] LEMON_jll v1.3.3+0
  [d00139f3] METIS_jll v5.1.3+0
  [856f044c] MKL_jll v2025.2.0+0
  [656ef2d0] OpenBLAS32_jll v0.3.29+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [f50d1b31] Rmath_jll v0.5.1+0
  [3eaa8342] libcxxwrap_julia_jll v0.14.7+0
⌅ [f8abcde7] micromamba_jll v1.5.12+0
  [1317d2d5] oneTBB_jll v2022.0.0+1
  [4d7b5844] pixi_jll v0.41.3+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.0
  [de0858da] Printf v1.11.0
  [9abbd945] Profile v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.3.0+1
  [781609d7] GMP_jll v6.3.0+2
  [deac9b47] LibCURL_jll v8.11.1+1
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [3a97d323] MPFR_jll v4.2.2+0
  [14a3606d] MozillaCACerts_jll v2025.5.20
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.1+0
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.5.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

```

  - Output of `versioninfo()`

```julia

Julia Version 1.12.1
Commit ba1e628ee49 (2025-10-17 13:02 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 10 × Apple M4
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, apple-m4)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_VSCODE_REPL = 1

```

**Additional context**

I would suggest two possible approaches to fix this:
1) Minimal Fix --> The entanglement consumer checks that the size of the quantum state is correct, and if not, discards the e2e Bell pair and maybe prints a warning
2) Full Fix (this could solve more bugs that could span from the same issue) --> Implementing a uuid identification system for Bell pairs in the network, so that every update message can be inequivocably mapped to its associated entry. This would require modifications to protocols as well as message formats, possibly complicating the logic.

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EntanglementConsumer, SwapperProt, EntanglementTracker, EntanglerProt might fail to correctly track entangled states across a repeater chain #303

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EntanglementConsumer, SwapperProt, EntanglementTracker, EntanglerProt might fail to correctly track entangled states across a repeater chain #303

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