Updated the CHSH model to use the app's log

README.md

@@ -382,7 +382,7 @@ respond with a bit, $R_A,R_B\in \lbrace 0,1\rbrace$.
 If the logical AND of questions equals the logical XOR of responses,
 they win. It can be shown that in the repeated game Alice and Bob can win
 at most 75% of the time. This classical limit,
-$P(Q_A\wedge Q_B = R_A\oplus R_B)\leq 75\\%$, is called the CHSH inequality.
+$Pr[Q_A\wedge Q_B = R_A\oplus R_B]\leq 75\\%$, is called the CHSH inequality.
 
 Suppose we now change the game so that the referee sends Alice and Bob not
 only two random bits but also two entangled particles. From actual physical
@@ -392,7 +392,7 @@ This is called the violation of CHSH inequality.
 
 In the following CliqueVM model, we show the violation of CHSH inequality
 using multithreaded evolution and bit rotations (circular shift).
-The final results that the model prints to the console log are the following:
+The final results that the model prints to the log are the following:
 
 ```
 --- SIMULATION STARTS ---
@@ -407,8 +407,8 @@ The final results that the model prints to the console log are the following:
 Copy the JSON string below and import it to the app:
 ```json
 {
-  "init":"// Create a matrix for the results\nthis.qs = [[0,0],[0,1],[1,0],[1,1]]; // Possible questions\nthis.rs = [[0,0],[0,1],[1,0],[1,1]]; // Possible responses\nthis.results = {};\nfor( const q of this.qs ) {\n  const qkey = q.join('*');\n  this.results[qkey] = {};\n  for( const r of this.rs ) {\n    const rkey = r.join('^');\n    this.results[qkey][rkey] = {\n      status: ( (q[0] * q[1]) === (r[0] ^ r[1]) ) ? 'WIN' : 'Lost',\n      weight: BigInt(0)\n    };\n  }\n}\n\n// Spin in computational basis\nthis.spinup = '00001111';\nthis.spindown = '11110000';\n\n\n// Helper functions for binary vector rotation and Hamming distance metric\nthis.rot = (s,n) => { return s.slice(-n % s.length) + s.slice(0,-n % s.length); }\nthis.dhamm = (s,t) => { return [...s].reduce( (a,b,i) => a + (b === t.charAt(i) ? 0 : 1),0 ) }\n\n// Start the first round\nconsole.log('--- SIMULATION STARTS ---');\n\nreturn [ \"Questions\"];",
-  "oper":"// Location is the first part of the state and the same within the clique\n// Subsequent parts of the state contain the messages and memories\nconst location = c[0].split(\"-\")[0];\nconst messages = {};\nc.forEach( x => {\n  const m = x.split('-')[1];\n  if ( m ) {\n    const p = m.split('+');\n    messages[p[0]] = (p.length > 2 ? p.slice(1) : p[1]);\n  }\n});\n\n// Classical state machine\nconst ops = [];\nif ( location === 'Questions' ) {\n  \n  // Send classical messages, one for Alice, one for Bob\n  const [ QA, QB ] = this.qs.shift();\n  ops.push( [ \"AliceQ-Question+\" + QA, \"BobQ-Question+\" + QB, \"Particle\" ] );\n\n  // Next question, if no more questions then report\n  if ( this.qs.length ) {\n    ops.push( [ \"Questions\" ] );\n  } else {\n    ops.push( [ \"ZZZReport\" ] );\n  }\n  \n} else if ( location === 'Particle' ) {\n\n  // Send entangled spin particles to Alice and Bob\n  // Here particle is a superposition of all binary rotations\n  for( let i=0; i<this.spinup.length; i++ ) {\n    ops.push( [\n      'AliceSG-Particle+' + this.rot(this.spinup,i),\n      'BobSG-Particle+' + this.rot(this.spindown,i)\n    ]);\n  }\n  \n} else if ( location === 'AliceQ' ) {\n\n  // Parse message and set measurement angle:\n  // - If question is 0, do not rotate\n  // - If question is 1, rotate -45° (-2*pi/8)\n  const question = messages[\"Question\"];\n  const rotate = ( question === '0' ? 0 : Math.round( (-2/8) * this.spinup.length) );\n  const setting = this.rot(this.spinup, rotate);\n  ops.push( [ 'AliceSG-Measure+' + question + '+' + setting ] );\n  \n} else if ( location === 'AliceSG' ) {\n\n  // Parse message\n  const [question,setting] = messages[\"Measure\"];\n  const particle = messages[\"Particle\"];\n\n  // Simulate Stern–Gerlach\n  // You as an observer can only detect up/down, which\n  // respond to responses 0/1\n  const d = this.dhamm(particle,setting);\n  const limit = Math.round(this.spinup.length / 2);\n  const R0 = 'Responses-Alice+' + question + '+' + '0';\n  const R1 = 'Responses-Alice+' + question + '+' + '1';\n  if ( d > limit ) ops.push( [ R1, R1 ] );\n  if ( d == limit ) ops.push( [ R0 ], [ R1 ] );\n  if ( d < limit ) ops.push( [ R0, R0 ] );\n  \n} else if ( location === 'BobQ' ) {\n\n  // Parse message and set measurement angle:\n  // - If question is 0, rotate 135° (3*pi/8)\n  // - If question is 1, rotate -135° (-3*pi/8)\n  const question = messages[\"Question\"];\n  const rotate = ( question === '0' ? Math.round( (3/8) * this.spinup.length) : Math.round( (-3/8) * this.spinup.length) );\n  const setting = this.rot(this.spinup, rotate);\n  ops.push( [ 'BobSG-Measure+' + question + '+' + setting ] );\n  \n} else if ( location === 'BobSG' ) {\n\n  // Parse message\n  const [question,setting] = messages[\"Measure\"];\n  const particle = messages[\"Particle\"];\n\n  // Simulate Stern–Gerlach\n  // You as an observer can only detect up/down, which\n  // respond to responses 0/1\n  const d = this.dhamm(particle,setting);\n  const limit = Math.round(this.spinup.length / 2);\n  const R0 = 'Responses-Bob+' + question + '+' + '0';\n  const R1 = 'Responses-Bob+' + question + '+' + '1';\n  if ( d > limit ) ops.push( [ R1, R1] );\n  if ( d == limit ) ops.push( [ R0 ], [ R1 ] );\n  if ( d < limit ) ops.push( [ R0, R0 ] );\n  \n} else if ( location === 'Responses' ) {\n\n  // Parse the original questions and the responses\n  const [QA,RA] = messages[\"Alice\"];\n  const [QB,RB] = messages[\"Bob\"];\n  \n  // Add the weight to the report\n  // For an observer, Charlie, the weight is the number of permutations with\n  // the clique, which is the factorial of the clique size.\n  this.results[QA+'*'+QB][RA+'^'+RB].weight += this.factorial(c.length);\n  \n} else if ( location === 'Report' ) {\n  \n  // Print report for all questions\n  for( let [q,rs] of Object.entries(this.results) ) {\n\n    // Sum of the factorials in order to calculate the probabilities\n    const tot = Object.values(rs).reduce( (a,b) => a + (b.weight || BigInt(0)), BigInt(0) );\n\n    // Print summary for question q\n    let s = [];\n    for( let [r,vs] of Object.entries(rs) ) {\n      const p = Number( (vs.weight || BigInt(0) ) * 10000n / tot ) / 10000;\n      s.push( r + ' ' + vs.status.padStart(4) + ' ' + (100*p).toFixed(1).padStart(4) + '%' );\n    }\n    console.log( q + ' == ' + s.join(' | ') );                \n  }\n\n  console.log('--- SIMULATION ENDS ---');\n  \n} else if ( location.startsWith('Z') ) {\n  // Delayed state\n  ops.push( c.map( x => x.substring(1) ) );\n}\n\nreturn ops;",
+  "init":"// Create a matrix for the results\nthis.qs = [[0,0],[0,1],[1,0],[1,1]]; // Possible questions\nthis.rs = [[0,0],[0,1],[1,0],[1,1]]; // Possible responses\nthis.results = {};\nfor( const q of this.qs ) {\n  const qkey = q.join('∧');\n  this.results[qkey] = {};\n  for( const r of this.rs ) {\n    const rkey = r.join('⊕');\n    this.results[qkey][rkey] = {\n      status: ( (q[0] * q[1]) === (r[0] ^ r[1]) ) ? 'W' : 'L',\n      weight: BigInt(0)\n    };\n  }\n}\n\n// Spin in computational basis\nthis.spinup = '00001111';\nthis.spindown = '11110000';\n\n\n// Helper functions for binary vector rotation and Hamming distance metric\nthis.rot = (s,n) => { return s.slice(-n % s.length) + s.slice(0,-n % s.length); }\nthis.dhamm = (s,t) => { return [...s].reduce( (a,b,i) => a + (b === t.charAt(i) ? 0 : 1),0 ) }\n\n// Start the first round\nthis.log('--- SIMULATION STARTS ---');\n\nreturn [ \"Questions\"];",
+  "oper":"// Location is the first part of the state and the same within the clique\n// Subsequent parts of the state contain the messages and memories\nconst location = c[0].split(\"-\")[0];\nconst messages = {};\nc.forEach( x => {\n  const m = x.split('-')[1];\n  if ( m ) {\n    const p = m.split('+');\n    messages[p[0]] = (p.length > 2 ? p.slice(1) : p[1]);\n  }\n});\n\n// Classical state machine\nconst ops = [];\nif ( location === 'Questions' ) {\n  \n  // Send classical messages, one for Alice, one for Bob\n  const [ QA, QB ] = this.qs.shift();\n  ops.push( [ \"AliceQ-Question+\" + QA, \"BobQ-Question+\" + QB, \"Particle\" ] );\n\n  // Next question, if no more questions then report\n  if ( this.qs.length ) {\n    ops.push( [ \"Questions\" ] );\n  } else {\n    ops.push( [ \"ZZZReport\" ] );\n  }\n  \n} else if ( location === 'Particle' ) {\n\n  // Send entangled spin particles to Alice and Bob\n  // Here particle is a superposition of all binary rotations\n  for( let i=0; i<this.spinup.length; i++ ) {\n    ops.push( [\n      'AliceSG-Particle+' + this.rot(this.spinup,i),\n      'BobSG-Particle+' + this.rot(this.spindown,i)\n    ]);\n  }\n  \n} else if ( location === 'AliceQ' ) {\n\n  // Parse message and set measurement angle:\n  // - If question is 0, do not rotate\n  // - If question is 1, rotate -45° (-2*pi/8)\n  const question = messages[\"Question\"];\n  const rotate = ( question === '0' ? 0 : Math.round( (-2/8) * this.spinup.length) );\n  const setting = this.rot(this.spinup, rotate);\n  ops.push( [ 'AliceSG-Measure+' + question + '+' + setting ] );\n  \n} else if ( location === 'AliceSG' ) {\n\n  // Parse message\n  const [question,setting] = messages[\"Measure\"];\n  const particle = messages[\"Particle\"];\n\n  // Simulate Stern–Gerlach\n  // You as an observer can only detect up/down, which\n  // respond to responses 0/1\n  const d = this.dhamm(particle,setting);\n  const limit = Math.round(this.spinup.length / 2);\n  const R0 = 'Responses-Alice+' + question + '+' + '0';\n  const R1 = 'Responses-Alice+' + question + '+' + '1';\n  if ( d > limit ) ops.push( [ R1, R1 ] );\n  if ( d == limit ) ops.push( [ R0 ], [ R1 ] );\n  if ( d < limit ) ops.push( [ R0, R0 ] );\n  \n} else if ( location === 'BobQ' ) {\n\n  // Parse message and set measurement angle:\n  // - If question is 0, rotate 135° (3*pi/8)\n  // - If question is 1, rotate -135° (-3*pi/8)\n  const question = messages[\"Question\"];\n  const rotate = ( question === '0' ? Math.round( (3/8) * this.spinup.length) : Math.round( (-3/8) * this.spinup.length) );\n  const setting = this.rot(this.spinup, rotate);\n  ops.push( [ 'BobSG-Measure+' + question + '+' + setting ] );\n  \n} else if ( location === 'BobSG' ) {\n\n  // Parse message\n  const [question,setting] = messages[\"Measure\"];\n  const particle = messages[\"Particle\"];\n\n  // Simulate Stern–Gerlach\n  // You as an observer can only detect up/down, which\n  // respond to responses 0/1\n  const d = this.dhamm(particle,setting);\n  const limit = Math.round(this.spinup.length / 2);\n  const R0 = 'Responses-Bob+' + question + '+' + '0';\n  const R1 = 'Responses-Bob+' + question + '+' + '1';\n  if ( d > limit ) ops.push( [ R1, R1] );\n  if ( d == limit ) ops.push( [ R0 ], [ R1 ] );\n  if ( d < limit ) ops.push( [ R0, R0 ] );\n  \n} else if ( location === 'Responses' ) {\n\n  // Parse the original questions and the responses\n  const [QA,RA] = messages[\"Alice\"];\n  const [QB,RB] = messages[\"Bob\"];\n  \n  // Add the weight to the report\n  // For an observer, Charlie, the weight is the number of permutations with\n  // the clique, which is the factorial of the clique size.\n  this.results[QA+'∧'+QB][RA+'⊕'+RB].weight += this.factorial(c.length);\n  \n} else if ( location === 'Report' ) {\n  \n  // Print report for all questions\n  for( let [q,rs] of Object.entries(this.results) ) {\n\n    // Sum of the factorials in order to calculate the probabilities\n    const tot = Object.values(rs).reduce( (a,b) => a + (b.weight || BigInt(0)), BigInt(0) );\n\n    // Print summary for question q\n    let s = [];\n    for( let [r,vs] of Object.entries(rs) ) {\n      const p = Number( (vs.weight || BigInt(0) ) * 10000n / tot ) / 10000;\n      s.push( r + ' ' + vs.status + ' ' + (100*p).toFixed(1).padStart(4) + '%' );\n    }\n    this.log( q + ' == ' + s.join(' | ') );                \n  }\n\n  this.log('--- SIMULATION ENDS ---');\n  \n} else if ( location.startsWith('Z') ) {\n  // Delayed state\n  ops.push( c.map( x => x.substring(1) ) );\n}\n\nreturn ops;",
   "coord":"// Coordinate is the first part of the state\nreturn s.split('-')[0];",
   "show":"return true;",
   "detectors":"return [];"