Public release

Q3/Documentation/English/SearchIndex/5/indexMetadata.wl

@@ -1,6 +1,6 @@
 <|"IndexedPaths" -> None, "Driver" -> "Lucene", 
- "CreationDate" -> DateObject[{2024, 6, 18, 20, 3, 
-    24.119154`8.134937053097945}, "Instant", "Gregorian", 9.], 
+ "CreationDate" -> DateObject[{2024, 6, 19, 19, 43, 
+    34.452477`8.289795431347985}, "Instant", "Gregorian", 9.], 
  "Version" -> 5, "Synonyms" -> None, "Method" -> "BM25", 
  "Language" -> "English", "ContentFieldOptions" -> 
   <|"Title" -> <|"Stored" -> True, "Weight" -> 2|>, 

Q3/Kernel/Pauli.wl

@@ -4746,11 +4746,11 @@ TraceDistance[a_, b_, ss:{___?SpeciesQ}] :=
 Fidelity::usage = "Fidelity[\[Rho],\[Sigma]] returns the fidelity of the states \[Rho] and \[Sigma]. \[Rho] and \[Sigma] can take a vector (pure state), matrix (mixed state), ket expression (pure state), or opertor expression (mixed state).\nSee also ClassicalFidelity."
 
 Fidelity[a_?MatrixQ, b_?MatrixQ] := With[
-  {c = MatrixPower[a, 1/2]},
+  { c = MatrixPower[a, 1/2] },
   Tr @ MatrixPower[c . b . c, 1/2]
- ]
+]
 
-Fidelity[v_?VectorQ, m_?MatrixQ] := Chop @ Sqrt[Conjugate[v] . m . v]
+Fidelity[v_?VectorQ, m_?MatrixQ] := Sqrt[Conjugate[v] . m . v]
 
 Fidelity[m_?MatrixQ, v_?VectorQ] := Fidelity[v, m]
 
@@ -4796,9 +4796,7 @@ probabilityQ[_] = False
 (**** </Fidelity> *****)
 
 
-(* ***************************************************************** *)
-(*     <GraphForm>                                                   *)
-(* ***************************************************************** *)
+(**** <GraphForm> ****)
 
 Vertex::usage = "Vertex[a, b, ...] represents an interaction vertex.\nNot to be confused with Vertices in Graph or related functions."
 
@@ -5089,9 +5087,7 @@ chiralVertexRulesShort[ii_List, jj_List, spec:{__Rule}] := spec
 chiralVertexRulesShort[ii_List, jj_List, spec:{row_, col_}] :=
   Join[ vertexRulesShort[ii, row], vertexRulesShort[jj, col] ]
 
-(* ***************************************************************** *)
-(*     </GraphForm>                                                  *)
-(* ***************************************************************** *)
+(**** </GraphForm> ****)
 
 
 (***** <TridiagonalToeplitzMatrix> ****)

Q3/Kernel/VonNeumann.wl

@@ -7,57 +7,42 @@ BeginPackage["Q3`"]
 { VonNeumannEntropy, QuantumLog };
 { RenyiEntropy };
 
-{ EntanglementEntropy };
+{ EntanglementEntropy, CrossEntropy };
 
 { MutualInformation };
 
 
 Begin["`Private`"]
 
+(**** <WeightedLog> ****)
+
 WeightedLog::usage = "WeightedLog[z] returns -z*Log[2, z], the weighted logarithm to base 2.\nWeightedLog[0] = 0.\nWeightedLog[p, q] returns -p*Log[2, q].\nWeightedLog[0, q] = 0.\nWeightedLog[p>0, 0] = \[Infinity]."
 
 SetAttributes[WeightedLog, Listable]
 
 WeightedLog[0] = 0
 
-WeightedLog[z_] := 0 /; Chop[z] == 0
-
-WeightedLog[z_?Positive] := -z * Log2[z]
-
-
-WeightedLog[0, _] = 0
-
-WeightedLog[_?Positive, 0] = Infinity
-
-WeightedLog[p_?Positive, q_?Positive] := -p * Log2[q]
-
+WeightedLog[_?ZeroQ] = 0
 
 WeightedLog[z_] := -z * Log2[z]
 
 
-ShannonEntropy::usage = "ShannonEntropy[{p1, p2, \[Ellipsis]}] returns the base 2 Shannon entropy of the probability distribution {p1, p2, \[Ellipsis]}.\nShannonEntropy[{p1, p2, \[Ellipsis]}, {q1, q2, \[Ellipsis]}] returns the relative entropy between the two probability distributions {p1, p2, \[Ellipsis]} and {q1, q2, \[Ellipsis]}."
+WeightedLog[0, _] = 0
 
-ShannonEntropy::noprb = "`` does not seem to be a probability distribution."
+WeightedLog[_?ZeroQ, _] = 0
 
-ShannonEntropy[pp_?VectorQ] :=
-  (Message[ShannonEntropy::noprb, pp]; 0) /;
-  Not @ AllTrue[Chop @ pp, NonNegative]
+WeightedLog[_?Positive, _?ZeroQ] = Infinity
 
-ShannonEntropy[pp_?VectorQ, qq_?VectorQ] :=
-  (Message[ShannonEntropy::noprb, pp]; 0) /;
-  Not @ AllTrue[Chop @ pp, NonNegative]
+WeightedLog[_, _?ZeroQ] = ComplexInfinity
 
-ShannonEntropy[pp_?VectorQ, qq_?VectorQ] :=
-  (Message[ShannonEntropy::noprb, qq]; 0) /;
-  Not @ AllTrue[Chop @ qq, NonNegative]
+WeightedLog[p_, q_] := -p * Log2[q]
 
-ShannonEntropy[pp_?VectorQ] := Total[WeightedLog @ pp]
+(**** </WeightedLog> ****)
 
-ShannonEntropy[pp_?VectorQ, qq_?VectorQ] :=
-  Total[WeightedLog[pp, qq]] - Total[WeightedLog[pp]]
 
+(**** <QuantumLog> ****)
 
-QuantumLog::usage = "QuantumLog[p, q] returns -Tr[p ** Log[2, q]] for the observables p and q.\nQuantumLog[p, q, {s1, s2, \[Ellipsis]}] assumes that states p and q, either density operators or ket vectors, are defined for the systems {s1, s2, \[Ellipsis]}.\nQuantumLog is a low-level mathematical function intended for the use in VonNeumannEntropy or related functions."
+QuantumLog::usage = "QuantumLog[p, q] returns -Tr[p ** Log[2, q]] for the density operators p and q.\nQuantumLog[p, q, {s1, s2, \[Ellipsis]}] assumes that states p and q, either density operators or ket vectors, are defined for the systems {s1, s2, \[Ellipsis]}.\nQuantumLog is a low-level mathematical function intended for the use in VonNeumannEntropy or related functions."
 
 QuantumLog[a_?VectorQ, b_?VectorQ] :=
   If[Fidelity[a, b] == 1, 0, Infinity]
@@ -70,7 +55,7 @@ QuantumLog[a_?MatrixQ, b_?VectorQ] := Module[
   vec = Flatten[vec];
   If[ AllTrue[vec, NumericQ], vec = Normalize[vec] ];
   If[ Fidelity[vec, b] == 1, 0, Infinity ]
- ]
+]
 
 QuantumLog[a_?VectorQ, b_?MatrixQ] := Module[
   {val, vec},
@@ -79,28 +64,58 @@ QuantumLog[a_?VectorQ, b_?MatrixQ] := Module[
     vec = Orthogonalize[vec]
    ];
   Total @ WeightedLog[Abs[Conjugate[a] . Transpose[vec]]^2, val]
- ]
+]
 
 QuantumLog[a_?MatrixQ, b_?MatrixQ] := Module[
   { aval, avec,
     bval, bvec },
   {aval, avec} = Eigensystem[a];  
   If[ AllTrue[Flatten @ avec, NumericQ] && Not[UnitaryMatrixQ @ avec],
     avec = Orthogonalize[avec]
-   ];
+  ];
   {bval, bvec} = Eigensystem[b];
   If[ AllTrue[Flatten @ bvec, NumericQ] && Not[UnitaryMatrixQ @ bvec],
     bvec = Orthogonalize[bvec]
-   ];
+  ];
   Total @ WeightedLog[aval . Abs[Conjugate[avec] . Transpose[bvec]]^2, bval]
- ]
+]
 
 
 QuantumLog[a_, b_, ss:{___?SpeciesQ}] :=
   QuantumLog[Matrix[a, ss], Matrix[b, ss]]
 
 QuantumLog[a_, b_] := QuantumLog[a, b, Agents @ {a, b}]
 
+(**** </QuantumLog> ****)
+
+
+(**** <ShannonEntropy> ****)
+
+ShannonEntropy::usage = "ShannonEntropy[{p1, p2, \[Ellipsis]}] returns the base 2 Shannon entropy of the probability distribution {p1, p2, \[Ellipsis]}.\nShannonEntropy[{p1, p2, \[Ellipsis]}, {q1, q2, \[Ellipsis]}] returns the relative entropy between the two probability distributions {p1, p2, \[Ellipsis]} and {q1, q2, \[Ellipsis]}."
+
+ShannonEntropy::noprb = "`` does not seem to be a probability distribution."
+
+ShannonEntropy[pp_?VectorQ] :=
+  (Message[ShannonEntropy::noprb, pp]; 0) /;
+  Not @ AllTrue[Chop @ pp, NonNegative]
+
+ShannonEntropy[pp_?VectorQ, qq_?VectorQ] :=
+  (Message[ShannonEntropy::noprb, pp]; 0) /;
+  Not @ AllTrue[Chop @ pp, NonNegative]
+
+ShannonEntropy[pp_?VectorQ, qq_?VectorQ] :=
+  (Message[ShannonEntropy::noprb, qq]; 0) /;
+  Not @ AllTrue[Chop @ qq, NonNegative]
+
+ShannonEntropy[pp_?VectorQ] := Total[WeightedLog @ pp]
+
+ShannonEntropy[pp_?VectorQ, qq_?VectorQ] :=
+  Total[WeightedLog[pp, qq]] - Total[WeightedLog[pp]]
+
+(**** </ShannonEntropy> ****)
+
+
+(**** <VonNeumannEntropy> ****)
 
 VonNeumannEntropy::usage = "VonNeumannEntropy[mat|vec] returns the base 2 VonNeumann entropy of the quantum state described by the density matrix 'mat' or vector 'vec'.\nVonNeumannEntropy[mat1, mat2] returns the quantum relative entropy of the mixed state mat1 with respect to mat2."
 
@@ -127,6 +142,8 @@ VonNeumannEntropy[rho_, sgm_, ss:{___?SpeciesQ}] :=
 VonNeumannEntropy[rho_, sgm_] :=
   VonNeumannEntropy[rho, sgm, Agents @ {rho, sgm}]
 
+(**** </VonNeumannEntropy> ****)
+
 
 (**** <MutualInformation> ****)
 
@@ -192,7 +209,8 @@ RenyiEntropy[a_?Positive, rho_?MatrixQ, sgm_?MatrixQ] :=
       Dot[
         MatrixPower[sgm, (1-a)/(2*a)], rho,
         MatrixPower[sgm, (1-a)/(2*a)]
-       ], a ] ] / (a - 1)
+       ], a ] 
+  ] / (a - 1)
 
 
 RenyiEntropy[a_, rho_] := RenyiEntropy[a, rho, Agents @ rho]
@@ -224,7 +242,7 @@ EntanglementEntropy::qubit = "`` does not seem to be a vector or matrix for qubi
 EntanglementEntropy[rho:(_?VectorQ|_?MatrixQ), jj:{__Integer}] := (
   Message[EntanglementEntropy::qubit, rho];
   rho
- ) /; Not @ IntegerQ @ Log[2, Length @ rho]
+) /; Not @ IntegerQ @ Log[2, Length @ rho]
 
 EntanglementEntropy[rho:(_?VectorQ|_?MatrixQ), jj:{__Integer}] :=
   EntanglementEntropy[rho, ConstantArray[2, Log[2, Length @ rho]], jj]
@@ -243,21 +261,37 @@ EntanglementEntropy[expr_, ss:{__?SpeciesQ}] := Module[
   qq = Union[qq, rr];
   jj = Flatten @ Map[FirstPosition[qq, #]&, Complement[qq, rr]];
   VonNeumannEntropy @ PartialTrace[Matrix[expr, qq], Dimension[qq], jj]
- ]
+]
 
 
 EntanglementEntropy[expr_, jj:{__Integer}] := Module[
   { nn = Length @ FirstCase[expr, _Ket, Infinity] },
   VonNeumannEntropy @ PartialTrace[Matrix[expr], Complement[Range @ nn, jj]]
- ] /; fPauliKetQ[expr]
+] /; fPauliKetQ[expr]
 
 EntanglementEntropy[expr_, jj:{__Integer}] := Module[
   { nn = Length @ FirstCase[expr, _Pauli, Infinity] },
   VonNeumannEntropy @ PartialTrace[Matrix[expr], Complement[Range @ nn, jj]]
- ] /; Not @ FreeQ[expr, _Pauli]
+] /; Not @ FreeQ[expr, _Pauli]
 
 (**** </EntanglementEntropy> ****)
 
+
+(**** <CrossEntropy> ****)
+
+CrossEntropy::usage = "CrossEntropy[{p1, p2, \[Ellipsis]}, {q1, q2, \[Ellipsis]}] returns the classical cross-entropy between two probability distributions {p1, p2, \[Ellipsis]} and {q1, q2, \[Ellipsis]}.\nCrossEntropy[rho, sgm] returns the quantum cross-entropy between two density matrices rho and sgm."
+
+CrossEntropy[pp_?VectorQ, qq_?VectorQ] := Total @ WeightedLog[pp, pp]
+
+CrossEntropy[rho_?MatrixQ, sgm_?MatrixQ] := QuantumLog[rho, sgm]
+
+CrossEntropy[rho_, sgm_] := With[
+  { ss = Agents @ {rho, sgm} },
+  QuantumLog[Matrix[rho, ss], Matrix[sgm, ss]]
+]
+
+(**** </CrossEntropy> ****)
+
 End[]
 
 EndPackage[]