{
  "raw_trace": 0.9999999999768219,
  "vector_gram_real": [
    [
      1.0000000000718763,
      -1.2932823113170624e-11
    ],
    [
      -1.2932823113170624e-11,
      0.9999999999730312
    ]
  ],
  "vector_gram_imag": [
    [
      -5.075329734885379e-18,
      2.7189187452266872e-11
    ],
    [
      -2.718918763295385e-11,
      -2.6108927688263322e-17
    ]
  ],
  "entropies": {
    "AC": 0.2517192097613849,
    "BC": 0.21646947916749007,
    "C": 0.16642597482316604,
    "ABC": 0.23466464764855216
  },
  "cmi": 0.06709806645715682,
  "fidelity_squared": 0.9517273509565525,
  "recovery_term": 0.07137976269920969,
  "gap": -0.004281696242052865,
  "spectrum_AC": [
    0.0002627484839727648,
    0.010620341293864797,
    0.02407113754351691,
    0.9650457726786458
  ],
  "spectrum_BC": [
    0.0002068337417658969,
    0.01395404057082988,
    0.0142734314675202,
    0.9715656942198849
  ],
  "spectrum_C": [
    0.02457814732374388,
    0.9754218526762564
  ],
  "spectrum_recovered": [
    2.2377019185851043e-06,
    6.315730224868376e-05,
    0.00021368062127842159,
    0.00035224842259533155,
    0.006029705041803892,
    0.009907864448201258,
    0.03376258149161335,
    0.949668524970341
  ],
  "recovered_trace": 1.0000000000000002,
  "trace_preservation_residual": 5.986480196785828e-16,
  "reference_recovery_residual": 1.3486778743806223e-16,
  "choi_min_eigenvalue": -2.7836465937698334e-16,
  "rotation_scan": [
    {
      "t": -4,
      "recovery_term": 0.056325494961613244
    },
    {
      "t": -2,
      "recovery_term": 0.06300669131688723
    },
    {
      "t": -1.6,
      "recovery_term": 0.0735576139344792
    },
    {
      "t": -0.8,
      "recovery_term": 0.027704971619698184
    },
    {
      "t": -0.4,
      "recovery_term": 0.048075193406396474
    },
    {
      "t": -0.02,
      "recovery_term": 0.07129234594152861
    },
    {
      "t": 0,
      "recovery_term": 0.07137976269920969
    },
    {
      "t": 0.02,
      "recovery_term": 0.0712988931688396
    },
    {
      "t": 0.4,
      "recovery_term": 0.04813866124759205
    },
    {
      "t": 0.8,
      "recovery_term": 0.027715328517006484
    },
    {
      "t": 1.6,
      "recovery_term": 0.07352781077471984
    },
    {
      "t": 2,
      "recovery_term": 0.06307043647878416
    },
    {
      "t": 4,
      "recovery_term": 0.0563708684116117
    }
  ],
  "averaged_rotations": {
    "quadrature_240": {
      "recovery_term": 0.05042295251935468,
      "trace": 1.0000000000000018
    },
    "quadrature_480": {
      "recovery_term": 0.050422952519348876,
      "trace": 1.000000000000006
    }
  },
  "white_noise_checks": [
    {
      "epsilon": 1e-06,
      "cmi": 0.0670885453097142,
      "recovery_term": 0.07107332157887253,
      "gap": -0.00398477626915833
    },
    {
      "epsilon": 0.0001,
      "cmi": 0.0666404822281185,
      "recovery_term": 0.06844288739555827,
      "gap": -0.0018024051674397773
    },
    {
      "epsilon": 0.001,
      "cmi": 0.0647522658664946,
      "recovery_term": 0.06283829184148998,
      "gap": 0.0019139740250046222
    },
    {
      "epsilon": 0.01,
      "cmi": 0.05893800603345406,
      "recovery_term": 0.049360525818319755,
      "gap": 0.009577480215134306
    }
  ]
}
Independent Choi cross-check: {
  "max_entry_discrepancy": 1.1282659987272323e-16,
  "choi_cmi": 0.06709806645715699,
  "choi_recovery_term": 0.07137975867170311,
  "gram_recovery_term": 0.07137976269920969
}
{
  "digits": 50,
  "raw_trace": "0.99999999997682180845905542546",
  "entropies": {
    "AC": "0.251719209761385263936158534288470331200974",
    "BC": "0.216469479167490084679899062079906306360794",
    "C": "0.166425974823166391859510996490263688757863",
    "ABC": "0.234664647648552225734394258471573703057727"
  },
  "cmi": "0.067098066457156731022152341406539245746179",
  "fidelity_squared": "0.951727350956551818421971227591955546447117",
  "recovery_term": "0.0713797626992106875750337196347365161893581",
  "gap": "-0.00428169624205395655288137822819727044317909",
  "recovered_trace_error": "1.069105886e-50"
}
{
  "digits": 80,
  "raw_trace": "0.99999999997682180845905542546",
  "entropies": {
    "AC": "0.251719209761385263936158534288470331200974400905959009378701715677180025",
    "BC": "0.216469479167490084679899062079906306360793811031839800237761490840285843",
    "C": "0.166425974823166391859510996490263688757862618796640849455461875050485716",
    "ABC": "0.234664647648552225734394258471573703057726617168263469503816543457018999"
  },
  "cmi": "0.0670980664571567310221523414065392457461789759728944906571847880099611532",
  "fidelity_squared": "0.951727350956551818421971227591955546447116768470637657721364991739946431",
  "recovery_term": "0.071379762699210687575033719634736516189358070288618495644958932502537955",
  "gap": "-0.00428169624205395655288137822819727044317909431572400498777414449257680178",
  "recovered_trace_error": "4.216879196e-81"
}
Exact state and marginal positivity checks passed.
Certified entropy AC ['0.25171920976095', '0.25171920976185']
Certified entropy BC ['0.21646947916702', '0.21646947916794']
Certified entropy C ['0.16642597482304', '0.16642597482330']
{
  "method": "Exact rational a posteriori certificate; explicit logarithm series remainder",
  "entropies_bits": {
    "AC": [
      "0.25171920976095",
      "0.25171920976185"
    ],
    "BC": [
      "0.21646947916702",
      "0.21646947916794"
    ],
    "C": [
      "0.16642597482304",
      "0.16642597482330"
    ],
    "ABC": [
      "0.23466464764843",
      "0.23466464764867"
    ]
  },
  "spectra": {
    "AC": [
      [
        "0.00026274848396",
        "0.00026274848399"
      ],
      [
        "0.01062034129385",
        "0.01062034129388"
      ],
      [
        "0.02407113754350",
        "0.02407113754353"
      ],
      [
        "0.96504577267863",
        "0.96504577267866"
      ]
    ],
    "BC": [
      [
        "0.00020683374175",
        "0.00020683374178"
      ],
      [
        "0.01395404057081",
        "0.01395404057084"
      ],
      [
        "0.01427343146751",
        "0.01427343146754"
      ],
      [
        "0.97156569421987",
        "0.97156569421990"
      ]
    ],
    "C": [
      [
        "0.02457814732373",
        "0.02457814732376"
      ],
      [
        "0.97542185267624",
        "0.97542185267627"
      ]
    ],
    "ABC_nonzero": [
      [
        "0.03834773620363",
        "0.03834773620366"
      ],
      [
        "0.96165226379634",
        "0.96165226379637"
      ]
    ]
  },
  "cmi_bits": [
    "0.06709806645602",
    "0.06709806645830"
  ],
  "squared_fidelity": [
    "0.95172735095655",
    "0.95172735095656"
  ],
  "recovery_term_bits": [
    "0.07137976269921",
    "0.07137976269922"
  ],
  "gap_bits": [
    "-0.00428169624320",
    "-0.00428169624091"
  ],
  "sqrt_residual_squared_less_than": "1e-60",
  "invsqrt_residual_squared_less_than": "1e-60",
  "recovered_state_operator_error_less_than": "1e-24",
  "certified_coarse_gap_interval": [
    "-0.00428170",
    "-0.00428169"
  ],
  "gap_is_strictly_negative": true
}
All checks passed. The certified gap is strictly negative.
