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a6a5d8e | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | # SPDX-License-Identifier: Apache-2.0
"""Tests for a11oy.formulas.holevo_bound (Holevo 1973). thesis_v22.pdf §2."""
import math
import pytest
from a11oy.formulas import holevo_bound as hb
def test_capacity_binding_bound():
out = hb.holevo_capacity(dim=4, snr=1.0) # log2(4)=2 vs log2(2)=1 -> binding=1
assert abs(out["value"] - 1.0) < 1e-9
assert out["binding_bound_bits"] == out["value"]
def test_capacity_dim_binds_when_low_dim():
out = hb.holevo_capacity(dim=2, snr=100.0) # log2(2)=1 vs log2(101)~6.66 -> binding=1
assert abs(out["value"] - 1.0) < 1e-9
def test_chi_zero_for_identical_states():
# identical pure states -> chi = 0
spec = [1.0, 0.0]
chi = hb.holevo_chi([0.5, 0.5], [spec, spec])
assert abs(chi) < 1e-9
def test_chi_orthogonal_pure_states():
# two orthogonal pure states, equal prob -> chi = 1 bit
chi = hb.holevo_chi([0.5, 0.5], [[1.0, 0.0], [0.0, 1.0]])
assert abs(chi - 1.0) < 1e-9
def test_schema():
out = hb.holevo_capacity(8, 3.0)
assert out["citation"] == "thesis_v22.pdf §2"
assert "Holevo" in out["lean_theorem"]
@pytest.mark.parametrize("dim,snr", [(0, 1.0), (2, -1.0)])
def test_invalid(dim, snr):
with pytest.raises(ValueError):
hb.holevo_capacity(dim, snr)
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