Add DepolarizedBellPair

examples/GHZsetup/GHZsetup.jl

@@ -2,19 +2,20 @@ using ResumableFunctions
 using ConcurrentSim
 using Revise
 using QuantumSavory
+using QuantumSavory.StatesZoo
 using QuantumSavory.ProtocolZoo
 using QuantumClifford: ghz
 const bell = StabilizerState("XX ZZ")
 const perfect_pair = (Z1⊗Z1 + Z2⊗Z2) / sqrt(2)
 const perfect_pair_dm = SProjector(perfect_pair)
 const mixed_dm = MixedState(perfect_pair_dm)
 
-noisy_pair_func_depol(p) = p*perfect_pair_dm + (1-p)*mixed_dm
-
-function noisy_pair_func(F)
-    p = (4*F-1)/3
-    return noisy_pair_func_depol(p)
-end
+# noisy_pair_func_depol(p) = p*perfect_pair_dm + (1-p)*mixed_dm
+# function noisy_pair_func(F)
+#     p = (4*F-1)/3
+#     return noisy_pair_func_depol(p)
+# end
+noisy_pair_func(F) = DepolarizedBellPair(F=F)
 
 S = 5 # number of sensors
 F = 0.99 # fidelity

examples/congestionchain/setup.jl

@@ -14,6 +14,7 @@ using Revise
 
 # The workhorse for the simulation
 using QuantumSavory
+using QuantumSavory.StatesZoo
 
 # Predefined useful circuits
 using QuantumSavory.CircuitZoo: EntanglementSwap
@@ -66,7 +67,8 @@ end
 const perfect_pair = (Z1⊗Z1 + Z2⊗Z2) / sqrt(2)
 const perfect_pair_dm = SProjector(perfect_pair)
 const mixed_dm = MixedState(perfect_pair_dm)
-noisy_pair_func(F) = F*perfect_pair_dm + (1-F)*mixed_dm # TODO make a depolarization helper
+# noisy_pair_func(F) = F*perfect_pair_dm + (1-F)*mixed_dm # TODO make a depolarization helper
+noisy_pair_func(F) = DepolarizedBellPair(F=F)
 const XX = X⊗X
 const ZZ = Z⊗Z
 const YY = Y⊗Y

examples/firstgenrepeater/setup.jl

@@ -11,6 +11,7 @@ using Revise
 
 # The workhorse for the simulation
 using QuantumSavory
+using QuantumSavory.StatesZoo
 
 # Predefined useful circuits
 using QuantumSavory.CircuitZoo: EntanglementSwap, Purify2to1
@@ -63,7 +64,8 @@ end
 const perfect_pair = (Z1⊗Z1 + Z2⊗Z2) / sqrt(2)
 const perfect_pair_dm = SProjector(perfect_pair)
 const mixed_dm = MixedState(perfect_pair_dm)
-noisy_pair_func(F) = F*perfect_pair_dm + (1-F)*mixed_dm # TODO make a depolarization helper
+# noisy_pair_func(F) = F*perfect_pair_dm + (1-F)*mixed_dm # TODO make a depolarization helper
+noisy_pair_func(F) = DepolarizedBellPair(F=F)
 const XX = X⊗X
 const ZZ = Z⊗Z
 const YY = Y⊗Y

examples/firstgenrepeater_v2/setup.jl

@@ -11,6 +11,7 @@ using Revise
 
 # The workhorse for the simulation
 using QuantumSavory
+using QuantumSavory.StatesZoo
 
 # Predefined useful circuits
 using QuantumSavory.CircuitZoo: EntanglementSwap, Purify2to1
@@ -58,7 +59,8 @@ end
 const perfect_pair = (Z1⊗Z1 + Z2⊗Z2) / sqrt(2)
 const perfect_pair_dm = SProjector(perfect_pair)
 const mixed_dm = MixedState(perfect_pair_dm)
-noisy_pair_func(F) = F*perfect_pair_dm + (1-F)*mixed_dm # TODO make a depolarization helper
+# noisy_pair_func(F) = F*perfect_pair_dm + (1-F)*mixed_dm # TODO make a depolarization helper
+noisy_pair_func(F) = DepolarizedBellPair(F=F)
 const XX = X⊗X
 const ZZ = Z⊗Z
 const YY = Y⊗Y

examples/purificationMBQC/MBQC.jl

@@ -3,6 +3,7 @@ using ConcurrentSim
 using Revise
 
 using QuantumSavory
+using QuantumSavory.StatesZoo
 using QuantumSavory.ProtocolZoo
 import QuantumSavory: Tag
 
@@ -12,12 +13,12 @@ global_logger(ConsoleLogger(stderr, Logging.Debug))
 const perfect_pair = (Z1⊗Z1 + Z2⊗Z2) / sqrt(2)
 const perfect_pair_dm = SProjector(perfect_pair)
 const mixed_dm = MixedState(perfect_pair_dm)
-noisy_pair_func_depol(p) = p*perfect_pair_dm + (1-p)*mixed_dm
-
-function noisy_pair_func(F)
-    p = (4*F-1)/3
-    return noisy_pair_func_depol(p)
-end
+# noisy_pair_func_depol(p) = p*perfect_pair_dm + (1-p)*mixed_dm
+# function noisy_pair_func(F)
+#     p = (4*F-1)/3
+#     return noisy_pair_func_depol(p)
+# end
+noisy_pair_func(F) = DepolarizedBellPair(F=F)
 
 @kwdef struct MBQCSetUp
     node::Int

src/StatesZoo/StatesZoo.jl

@@ -9,6 +9,7 @@ import LinearAlgebra
 import LinearAlgebra: tr
 
 export BarrettKokBellPair, BarrettKokBellPairW,
+    DepolarizedBellPair,
     stateexplorer, stateexplorer!, stateparameters, stateparametersrange
 
 
@@ -30,6 +31,8 @@ stateparametersrange(::Any) = ()
 
 include("barrett_kok.jl")
 
+include("depolarized.jl")
+
 include("genqo.jl")
 
 include("state_explorer.jl")

src/StatesZoo/depolarized.jl

@@ -0,0 +1,46 @@
+"""
+$TYPEDEF
+
+Fields:
+
+$FIELDS
+
+A symbolic representation of a depolarized pure state:
+`p |ψ⟩⟨ψ| + (1-p) I/d`
+
+where `|ψ⟩` is an arbitrary pure two-qubit state (default: |Φ⁺⟩ = (|00⟩+|11⟩)/√2),
+and `I/d` is the maximally mixed state in the same Hilbert space.
+
+The fidelity `F = ⟨ψ|ρ|ψ⟩` with respect to `|ψ⟩` relates to the depolarization parameter by:
+- `F = (3p + 1) / 4`
+- `p = (4F - 1) / 3`
+
+Can be constructed from either parameter:
+- `DepolarizedBellPair(p)` — depolarization parameter `p ∈ [0, 1]`, defaults to |Φ⁺⟩
+- `DepolarizedBellPair(p, pure_state)` — with a custom pure state
+- `DepolarizedBellPair(F=F)` — from fidelity `F ∈ [1/4, 1]`, defaults to |Φ⁺⟩
+- `DepolarizedBellPair(F=F, pure_state=s)` — from fidelity with a custom pure state
+"""
+@withmetadata struct DepolarizedBellPair <: AbstractTwoQubitState
+    """Depolarization parameter `p ∈ [0, 1]`, related to fidelity by `F = (3p+1)/4`"""
+    p
+    """The ideal pure state being depolarized (default: |Φ⁺⟩)"""
+    pure_state
+end
+
+const _depolarized_default_bell = (Z1⊗Z1 + Z2⊗Z2) / sqrt(2)
+
+DepolarizedBellPair(p) = DepolarizedBellPair(p, _depolarized_default_bell)
+DepolarizedBellPair(; F, pure_state=_depolarized_default_bell) = DepolarizedBellPair((4 * F - 1) / 3, pure_state)
+
+stateparameters(::Type{DepolarizedBellPair}) = (:p,)
+stateparametersrange(::Type{DepolarizedBellPair}) = (p=(;min=0,max=1,good=1),)
+
+symbollabel(x::DepolarizedBellPair) = "ρᵖ"
+
+function express_nolookup(x::DepolarizedBellPair, r::QuantumOpticsRepr)
+    (; p, pure_state) = x
+    pure_dm = SProjector(pure_state)
+    mixed_dm = MixedState(pure_dm)
+    return express(p*pure_dm + (1-p)*mixed_dm, r)
+end

test/setup_circuitzoo_purification.jl

@@ -1,5 +1,6 @@
 using QuantumSavory.CircuitZoo
 using QuantumSavory.CircuitZoo: EntanglementSwap, Purify2to1, Purify3to1, Purify3to1Node, Purify2to1Node, PurifyStringent, StringentHead, StringentBody, PurifyExpedient, PurifyStringentNode, PurifyExpedient
+using QuantumSavory.StatesZoo
 
 const bell = StabilizerState("XX ZZ")
 export bell;
@@ -12,7 +13,8 @@ export bell;
 const perfect_pair = (Z1⊗Z1 + Z2⊗Z2) / sqrt(2)
 const perfect_pair_dm = SProjector(perfect_pair)
 const mixed_dm = MixedState(perfect_pair_dm)
-noisy_pair_func(F) = F*perfect_pair_dm + (1-F)*mixed_dm # TODO make a depolarization helper
+# noisy_pair_func(F) = F*perfect_pair_dm + (1-F)*mixed_dm # TODO make a depolarization helper
+noisy_pair_func(F) = DepolarizedBellPair(F=F)
 
 
 # Qclifford repr

test/test_stateszoo_api.jl

@@ -11,6 +11,7 @@ _evalf(x) = express(x)
 
 for S in [BarrettKokBellPair, BarrettKokBellPairW,
     GenqoUnheraldedSPDCBellPairW, GenqoMultiplexedCascadedBellPairW,
+    DepolarizedBellPair
     ] # TODO use some abstract supertype to automatically get all of these
     params = QuantumSavory.StatesZoo.stateparameters(S)
     paramdict = QuantumSavory.StatesZoo.stateparametersrange(S)

test/test_stateszoo_depolarized.jl

@@ -0,0 +1,38 @@
+@testitem "StatesZoo DepolarizedBellPair" begin
+using Test
+using QuantumSavory
+using QuantumSavory.StatesZoo
+using QuantumOpticsBase
+using LinearAlgebra
+
+# p-constructor and fidelity-constructor consistency
+p = 0.7
+F = (3p + 1) / 4
+s_from_p = DepolarizedBellPair(p)
+s_from_F = DepolarizedBellPair(F=F)
+@test express(s_from_p) ≈ express(s_from_F)
+
+# trace is 1 for any p
+for p in [0.0, 0.5, 1.0]
+    dm = express(DepolarizedBellPair(p))
+    @test tr(dm) ≈ 1
+end
+
+# at p=1, pure Bell state: ⟨ZZ⟩ = 1
+reg = Register(2)
+initialize!(reg[1:2], DepolarizedBellPair(1.0))
+@test observable(reg[1:2], Z⊗Z) ≈ 1
+
+# at p=0, maximally mixed: density matrix = I/4
+dm_mixed = express(DepolarizedBellPair(0.0))
+@test dm_mixed.data ≈ LinearAlgebra.I / 4
+
+# fidelity-to-p and p-to-fidelity roundtrip
+for F in [0.25, 0.5, 0.75, 1.0]
+    p_rt = (4F - 1) / 3
+    @test (3p_rt + 1) / 4 ≈ F
+    dm = express(DepolarizedBellPair(F=F))
+    @test tr(dm) ≈ 1
+end
+
+end